CN108810534B - Image compression method based on direction boosting wavelet and improved SPIHT under the Internet of Things - Google Patents

Abstract

An image compression method based on direction-lifting wavelet and improved SPIHT under the Internet of Things relates to an image compression method. The purpose of the present invention is to solve the problem that the existing SPIHT method rarely considers the edge blur or ringing effect caused by the lack of high-frequency information, and cannot preserve more details in the image, resulting in low coding efficiency. The process is as follows: 1. Obtain the segmented image block; 2. Obtain the best prediction direction of the segmented image block; 4. Using the best prediction direction, perform wavelet transform based on direction boosting on the interpolated image blocks, respectively, to obtain each transformed image block; 5. Constitute the entire transformed image from all the transformed image blocks; 6. Use the improved SPIHT The method encodes the obtained transformed image to obtain an encoded image. The present invention is used in the field of image compression.

Description

Image compression method based on direction boosting wavelet and improved SPIHT under the Internet of Things

technical field

The present invention relates to an image compression method.

Background technique

Due to the great progress of computing technology and sensor technology in recent years, the Internet of things (IoT) has also entered a period of rapid development [1] (Sezer OB, DogduE, Ozbayoglu AM (2018) Context-Aware Computing, Learning, and Big Data in Internet of Things: A Survey. IEEE Internet of Things Journal 5(1): 1-27. http://dx.doi.org/10.1109/JIOT.2017.2773600). In the sense of IoT, “things” refer to a wide range of devices, such as heart monitoring devices, temperature measurement devices, and autonomous vehicles, etc. [2-3] ([2] XuL D., HeW, Li S (2014) Internet of things in industries: a survey. IEEE Transactions on Industrial Informatics 10(4): 2233-2243 . http://dx.doi.org/10.1109/TII.2014.2300753 [3] Iqbal MM, Farhan M, Jabbar S, et al (2018) Multimediabased IoT-centric smart framework for eLearning paradigm. Multimed Tools Appl1-20. https://doi.org/10.1007/s11042-018-5636-y). IoT allows these devices to be remotely sensed or controlled through network facilities, and the node energy, storage space, and network bandwidth of this kind of network are far smaller than those of traditional networks. Moreover, with the development of multimedia technology, the amount of data to be transmitted also increases rapidly, and users often put forward higher requirements on the quality of multimedia signals (such as images or videos). Therefore, how to efficiently transmit multimedia signals in the IoT environment is an urgent problem that needs to be solved. The basic results of the IoT system are shown in Figure 1. In IoT, different devices are often used for different applications, which makes these devices have different data processing capabilities and transmission requirements [4] (Khan R, Khan SU, Zaheer R, et al (2013) Future Internet: The Internet of Things Architecture, Possible Applications and Key Challenges [C]. International Conference on Frontiers of Information Technology. IEEE, 257-260. http://dx.doi.org/10.1109/FIT.2012.53). In this case, a compression method with low complexity and capable of supporting multi-bit rate transmission is more suitable. As a key technology in multimedia communication, image compression is indispensable in our life. An effective image compression method should be able to make full use of the statistical correlation of the signal, first fully represent the signal, and then effectively encode the represented signal. In order to improve the image compression performance, scholars at home and abroad have done a lot of work on image representation and coding performance improvement methods. In image representation, transformation-based methods are most commonly used. The discrete cosine transform (Discrete cosine transform, DCT) is the basis of the JPEG standard. JPEG performs better at low compression ratios, but when compression ratios are high, blocking artifacts can appear in the reconstructed image. Discrete wavelet transform (DWT) solves this problem and has been the most important tool in the field of image analysis and coding for the past two decades [5] (Liu S, Fu W, He L, et al. (2017) Distribution of primaryadditional errors in fractal encoding method. Multimed Tools Appl76(4):5787-5802. http://dx.doi.org/10.1007/s11042-014-2408-1). Many well-known image compression methods or standards, such as EZW[6](JMShapiro(1993)Embedded image coding using zerotrees of waveletcoefficients.IEEE Trans Signal Process41(12):3445–3462.http://dx.doi.org/10.1109 /78.258085), SPIHT[7](Said A,Pearlman WA(1996)A new,fast,and efficientimage codec based on set partitioning in hierarchical trees.IEEE TransCircuits SystVideo Technol6(3):243–250.http://dx .doi.org/10.1109/76.499834), SPECK[8] (Pearlman WA, Islam A, NagarajN, Said A (2004) Efficient low complexity image coding with a set-partitioning embedded block coder. IEEE Trans Circuits Syst Video Technol, 14(3 ):1219–1235.http://dx.doi.org/10.1109/TCSVT.2004.835150), and JEPG2000[9](JPEG2000 Image Coding System,ISO/IECStd.15444-1,(2000)), both based on DWT's. Although DWT can effectively represent the horizontal and vertical directional information of the image, its isotropic property makes it unable to represent the directional features of the image well, such as edges and textures [10] (Shi C, Zhang J, Chen H, Zhang Y(2015) A Novel Hybrid Method for RemoteSensing Image Approximation Using the Tetrolet Transform. IEEE JSel TopicsAppl Earth Observ 7(12):4949-4959. http://dx.doi.org/10.1109/JSTARS.2014.2319304 ). Therefore, some directional wavelet bases are proposed, such as curvelet [11] (Candès EJ, Donoho DL (2004) New tight frames of curvelets and optimal representations of objects with piecewise C2 singularities. Commun Pure Appl Math57(2):219–266.http ://dx.doi.org/10.1002/cpa.10116), contourlet[12](Do MN, Martin V(2005) The contourlet transform: an efficient directional multiresolution imagerepresentation, IEEE Trans Image Process 14(2):2091-2106 .http://dx.doi.org/10.1109/TIP.2005.859376), directionlet[13](V.Velisavljevic,B.Beferull-Lozano,M.Vetterli,PLDragotti(2006)Directionlets:Anisotropic multidirectionalrepresentation with separable filtering.IEEE Trans Image Process15(7):1916–1933.http://dx.doi.org/10.1109/TIP.2006.877076), and shearlets[14](Kutyniok G,Lim WQ(2011)Full length article:Compactly supported shearlets are optimallysparse. Journal of Approximation Theory 163:1564-1589. http://dx.doi.org/10.1016/j.jat.2011.06.005) et al. These wavelet bases are more sensitive to some specific directions, so they can retain more specific direction features of the image. Some adaptive directional wavelet bases, such as bandelet [15] (Erwan LP, Stéphane M (2005) Sparse geometric image representations with bandelets. IEEE TransSignal Process 14(4): 423-438. http://dx.doi.org/10.1109 /TIP.2005.843753), wedgelet[16](Donoho DL(1999) Wedgelets:nearly minimax estimation ofedges.Annals of Statistics27(3):859-897.http://dx.doi.org/10.1214/aos/1018031261) , grouplet[17] (Mallat S (2009) Geometrical grouplets.Appl.ComputHarmon Anal26(2):161-180.http://dx.doi.org/10.1016/j.acha.2008.03.004), and EPWT ( Easy path wavelet transform), which enables a more flexible representation of images. However, these wavelet bases usually have complex designs, and some are even redundant, which makes them not widely used in image compression.

The method based on wavelet lifting can perform adaptive lifting locally in the image. Much work is to integrate specific lifting methods into the wavelet transform framework to improve compression performance, such as [19-23] ([19] Ding W, Wu F, Wu X, Li S, Li H (2007) Adaptive directional lifting -based wavelet transform for imagecoding.IEEE Trans Image Process 16(2):416-427.http://dx.doi.org/10.1109/TIP.2005.843753[20]C.Chang and B.Girod(2007)Direction adaptive discrete wavelet transform for image compression. IEEE Trans Image Process 16(5): 1289–1302. http://dx.doi.org/10.1109/TIP.2007.894242 [21] Zhang L, Qiu B (2013) Fastorientation prediction-based discrete wavelet transform for remote sensingimage compression. Remote Sensing Letters 4(12): 1156-1165. https://doi.org/10.1080/2150704X.2013.858838 [22] Chen D, Li Y, Zhang H, Gao W (2017) Invertibleupdate-then -predict integer lifting wavelet for lossless imagecompression.EURASIP JAdvSignal Process 1:1-9.http://dx.doi.org/10.1186/s13634-016-0443-y[23]Hasan M M,Wahid K A(2017)Low- Cost Architecture of Modified Daubechies Lifting Wavelets Using Integer Polynomial Mapping. IEEE Trans Circuits Syst 64(5): 585-589. http://doi.org/10.1109/tcsii.2016.258409 1). These boosting-based compression methods are usually associated with adaptive segmentation, statistical models, direction prediction, or modified wavelet bases, and the improvement in compression performance is mainly obtained from rate-distortion-optimized segmentation or encoding side information. Of these methods, protection of important image details is rarely considered during the compression process. This problem will affect the further improvement of coding efficiency, especially for textured regions. In addition, the inability to adequately represent image details will also affect the subjective quality of reconstructed images. Therefore, how to design an effective image representation method is an important issue in image compression.

Encoding is another key link in image compression. For wavelet transformed images, the coefficients at the same spatial position in different high-frequency subbands have strong correlation. Furthermore, after an efficient image representation, a large number of unimportant "blocks" usually appear in the high frequency region of the wavelet. If these unimportant "blocks" can be encoded in a suitable way, the encoding performance will be further improved. For image compression based on wavelet transform, embedded block coding with optimized truncation (EBCOT) is a well-known coding method and is adopted by the JPEG2000 standard [9] (JPEG2000 Image Coding System, ISO/IEC). Std. 15444-1, (2000)). The basic idea of EBCOT is to divide each subband into several blocks, such as 32×32 or 64×64, and then encode these blocks separately, and at different bit rates, according to the post compression rate distortion technology (post compression rate distortion, PCRD), truncate these code streams. Despite the good coding performance, a disadvantage of JPEG2000 is that it does not exploit the correlation between co-located coefficients between subbands [24] (Christophe E, Mailhes C, Duhamel P (2008) Hyperspectral imagecompression: adapting SPIHT and EZW to anisotropic 3-D wavelet coding. IEEE Trans Image Process 17(12): 2334-2346. http://dx.doi.org/10.1109/TIP.2008.2005824). According to the analysis of [25] (D.S.Taubman and M.W.Marcellin (2002) JPEG2000 ImageCompression Fundamentals, Standards and Practice. Boston, MA: Kluwer), the selection of truncation points in JPEG2000 compensates for the lack of the parent-child relationship between sub-bands. However, this comes at the cost of higher computational complexity. [26] (Lewis A S, Knowles G (1992) Image Compression Using the 2-DWavelet Transform. IEEE Trans Image Process 1(2): 244-250. http://dx.doi.org/10.1109/83.136601) states that, Tree-like structure is an effective method to represent the relationship of subband coefficients in wavelet images. For tree-like data structures, SPIHT is the most commonly used encoding method, which can utilize the parent-child relationship between subbands, thereby providing better encoding performance. In recent years, image compression methods based on improved SPIHT have been proposed, such as [27-29]([27]Hamdi M, Rhouma R, Belghith S(2017) A selective compression-encryption of images based on SPIHT coding and Chirikov Standard Map 131 :514-526.SignalProcessing.http://dx.doi.org/10.1016/j.sigpro.2016.09.011[28]Song X,Huang Q,Chang S,He J,Wang H(2016)Three-dimensional separate descendant-based SPIHTalgorithm for fast compression of high-resolution medical images sequences.IETImage Processing11(1):80-87.http://dx.doi.org/10.1049/iet-ipr.2016.0564[29]Zhang M,Tong X(2017 )Joint image encryption and compressionscheme based on IWT and SPIHT.Optics&Lasers in Engineering90:254-274.http://dx.doi.org/10.1016/j.optlaseng.2016.10.025), and others will improve the SPIHT method for Video Image Compression [30-32] ([30] Kim S, Jang JH, Lee HJ, Rhee CE (2017) Fine-scalable SPIHTHardware Design for Frame Memory Compression in Video Codec. Journal of Semiconductor Technology Andence17(3):446-457 .http://dx.doi.org/10.5573/JSTS.2017.17.3.446 [31] El-Bakery EM, El-Rabaie S, Zahran O, El-Samie FEA (2017) Chaotic Interleaving for the Transmissio n of Compressed Video Frames with Self-Embedded Digital Signatures. Wireless Personal Communications 96(2): 1635-1651. http://dx.doi.org/10.1007/s11277-017-4218-z [32] Sowmyayani S, Rani P A J ( 2016) An Efficient Temporal Redundancy Transformation for Wavelet Based VideoCompression. International Journal of Image & Graphics 16(3): 1650015. http://dx.doi.org/10.1142/S0219467816500157). This shows that the SPIHT method has become a popular technique in multimedia communication due to its low complexity and flexibility. Although there have been many studies on the SPIHT method, most of these studies focus on how to further reduce bit redundancy or scan redundancy, and rarely consider edge blurring or ringing effects caused by the absence of high-frequency information.

SUMMARY OF THE INVENTION

The purpose of the present invention is to solve the problem that the existing SPIHT method seldom considers the edge blur or ringing effect caused by the lack of high-frequency information, and cannot retain more details in the image, resulting in low coding efficiency. Image compression method based on directional lifting wavelet and improved SPIHT.

The specific process of the image compression method based on the direction boosting wavelet and the improved SPIHT under the Internet of Things is as follows:

Step 1: Perform image block segmentation on the remote sensing image to obtain segmented image blocks;

Step 2: Calculate the best prediction direction for the segmented image blocks respectively, and obtain the best prediction direction of the segmented image blocks;

Step 3: Perform weighted directional interpolation on the fractional sample values by calculating the weighted directional interpolation filter coefficients to obtain an interpolated image block;

Step 4: Using the best prediction direction obtained in Step 2, perform wavelet transform based on direction boosting on the interpolated image blocks, respectively, to obtain each transformed image block, that is, each transformed code block;

Step 5, forming the entire transformed image from all the transformed image blocks;

Step 6: Encode the transformed image obtained in step 5 by using the improved SPIHT method to obtain an encoded image.

The beneficial effects of the present invention are:

The present invention proposes a new image compression method, which combines a directional interpolation-based adaptive lifting wavelet transform (DIAL-DWT) with an improved SPIHT method. The main innovation points include two parts: one is the proposed adaptive lifting wavelet transform, which can fully represent the image by using the directional interpolation filter and the best adaptive lifting direction; the second is the improved SPIHT coding, which can try to It preserves important details in the image while providing better overall coding performance. The proposed compression method is asymmetric and has low complexity at the decoding end, which makes the method very suitable for various IoT terminals with different requirements for data transmission and real-time performance. Experimental results show that the proposed method not only has higher compression performance than traditional compression methods, but also can largely improve the subjective quality of reconstructed images.

The present invention designs a DIAL model, which can calculate the best lifting direction of all image blocks separately, and perform weighted direction interpolation on the fractional samples during the lifting process. Therefore, the wavelet transform based on the DIAL model combines the best direction prediction and weighted direction interpolation in the process of direction lifting, which can provide a more effective image representation, which helps to preserve more direction features of the image. Due to the high concentration of image energy, the image representation method can provide more "longer" zero trees, thereby improving coding efficiency. It solves the problem that the existing SPIHT methods rarely consider the edge blur or ringing effect caused by the lack of high-frequency information, and cannot retain more details in the image, resulting in low coding efficiency.

The present invention designs an improved SPIHT method, which only changes the scanning order of the insignificant list (List of insignificant sets, LIS) in the existing SPIHT method, does not require additional calculation, and can encode more many important coefficients. The improved SPIHT method can retain more important details in the image, which can improve the overall coding performance, and does not require additional computation and additional bits as header files.

The images in different image libraries are tested at different bit rates, and the experimental results show that the PSNR is improved by up to 1.3dB.

Description of drawings

Figure 1 is a basic IoT system framework diagram;

Figure 2a is the basic process diagram of forward decomposition of one-dimensional directional lifting wavelet transform, x is the original image, X _e is the even-numbered sample set in the image, X _o is the odd-numbered sample set in the image, and DA_P _o is used in the first-level transformation. to the direction adaptive prediction operator, DA_U _o is the direction adaptive update operator used in the first-level transformation, DA_P _k is the direction adaptive prediction operator used in the k-1 transformation, and DA_U _k is The direction adaptive update operator used in the k-1 transformation, _{Ke is the weight of the low-frequency components of the transformed image, K o is} the weight of the high-frequency components of the transformed image, a is the low-frequency component of the finally obtained transformed image, and b is the high-frequency component of the finally obtained transformed image;

Figure 2b is a basic process diagram of the reverse synthesis of one-dimensional directional lifting wavelet transform, x _e is the even-numbered sample set in the reconstructed image, x _o is the odd-numbered sample set in the reconstructed image;

FIG. 3 a is a schematic diagram of a reference direction set of horizontal wavelet transform based on direction boosting, where m is the abscissa of the position of the image block, and n is the ordinate of the position of the image block;

3b is a schematic diagram of a reference direction set of vertical wavelet transform based on direction lifting;

4 is a process diagram for calculating the optimal prediction direction of a given image block, and k is the sequence number of the reference direction;

Fig. 5 is a process diagram of direction interpolation in horizontal change;

Fig. 6 is a process diagram of generating a directional interpolation filter, a _-3 , a _{- 2} , a _{- 1} , _a0 , a1, a2 are the parameters of the interpolation filter;

Fig. 7a is a first-order wavelet decomposition result diagram of a 9/7 wavelet filter;

Fig. 7b is the first-order wavelet decomposition result diagram of the wavelet filter based on ADL;

Fig. 7c is the first-order wavelet decomposition result diagram of the wavelet filter based on DIAL model;

Figure 8 shows the NLA results obtained by different sparse representation methods. NLA is nonlinear estimation, The DIAL model is DIAL (directional interpolation-based adaptive lifting wavelet transform, DIAL-DWT) model, and ADL is Adaptive direction lifting (Adaptive direction lifting). ), PSNR is the peak signal-to-noise ratio;

Figure 9a is a schematic diagram of the Europa3 test remote sensing image set;

Figure 9b is a schematic diagram of the bank test remote sensing image set;

Figure 9c is a schematic diagram of aerial test remote sensing image set;

Figure 9d is a schematic diagram of the Lena test remote sensing image set;

Figure 9e is a schematic diagram of the Baboon test remote sensing image set;

Figure 9f is a schematic diagram of the pleiades_portdebouc_pan test remote sensing image set;

10 is a comparison diagram of the Kappa coefficient results of the method proposed by the present invention and the SPIHT method under different bit rates; the abscissa is the bit rate, and the unit is bpp; the ordinate is the Kappa coefficient;

Lenaproposed is that the method of the present invention compresses the test image Lena, and Lena SPIHT is the SPIHT method that compresses the test image Lena;

Baboonproposed is the Baboon compression of the test image by the method of the present invention, and Baboon SPIHT is the Baboon compression of the test image by the SPIHT method;

The bank proposed is the method of the present invention to compress the test image bank, and the bank SPIHT is the SPIHT method to compress the test image bank;

aerial proposed is the aerial compression of the test image by the method of the present invention, and aerial SPIHT is the aerial compression of the test image by the SPIHT method;

europa3 proposed is the method of the present invention to compress the test image europa3, and europa3 SPIHT is the SPIHT method to compress the test image europa3;

WoodlandHills proposed is the method of the present invention to compress the test image WoodlandHills, and WoodlandHills SPIHT is the SPIHT method to compress the test image WoodlandHills;

Fig. 11a is a reconstruction diagram obtained by the compression method proposed by the present invention at a bit rate of 0.0625bpp;

Figure 11b shows the reconstruction image obtained by the traditional SPIHT method at a bit rate of 0.0625bpp

Fig. 11c is a reconstruction diagram obtained by the compression method proposed by the present invention at a bit rate of 0.125bpp;

Figure 11d is the reconstruction image obtained by the traditional SPIHT method at a bit rate of 0.125bpp;

Fig. 11e is a reconstruction diagram obtained by the compression method proposed by the present invention at a bit rate of 0.25bpp;

Figure 11f is the reconstruction image obtained by the traditional SPIHT method at a bit rate of 0.25bpp;

Fig. 11g is a reconstruction diagram obtained by the compression method proposed by the present invention at a bit rate of 0.5bpp;

Figure 11h is the reconstruction image obtained by the traditional SPIHT method at a bit rate of 0.5bpp;

Fig. 11i is a reconstruction diagram obtained by the compression method proposed by the present invention at a bit rate of 1bpp;

Figure 11j shows the reconstruction image obtained by the traditional SPIHT method at a bit rate of 1 bpp.

Detailed ways

Specific embodiment 1: The specific process of the image compression method based on the direction-lifting wavelet and the improved SPIHT under the Internet of Things of this embodiment is:

Step 1: Perform image block segmentation on the remote sensing image to obtain segmented image blocks;

Step 2: Calculate the best prediction direction for the segmented image blocks respectively, and obtain the best prediction direction of the segmented image blocks;

Step 3: Perform weighted direction interpolation on the fractional sample values that need to be used in the direction boosting process by calculating the weighted direction interpolation filter coefficient to obtain an interpolated image block;

Step 4: Using the best prediction direction obtained in Step 2, perform wavelet transform based on direction boosting on the interpolated image blocks, respectively, to obtain each transformed image block, that is, each transformed code block;

Step 5, forming the entire transformed image from all the transformed image blocks;

Step 6: Encode the transformed image obtained in step 5 by using the improved SPIHT method to obtain an encoded image.

Embodiment 2: The difference between this embodiment and Embodiment 1 is that: in the step 1, the remote sensing image is divided into image blocks to obtain the divided image blocks; the specific process is:

In order to make the lifting direction consistent with the local texture direction of the image, image segmentation is performed first. In [19], a rate-distortion-optimized segmentation method based on a quadtree is adopted. However, the efficiency of this segmentation method is closely related to the image content. For some image types, such as remote sensing images, they usually reflect complex landforms, so the detailed information is usually rich, and there are few large flat areas. At this time, the adaptive segmentation method is difficult to show its advantages. The reason is that, for images with complex content, it is very likely that almost all blocks are the smallest blocks allowed to be segmented as a result of the adaptive segmentation method, which is almost the same as directly segmenting blocks of the same size, but But at the cost of higher computational complexity. Besides, another overhead of adopting adaptive segmentation method is the large amount of side information. For rate-distortion-based methods, the corresponding "split trees" are different for different bit rates. In order to decode correctly, these "split trees" are also sent to the decoder as side information. The more complex the image content, the more branches the "segmentation tree" has, and the more side information is generated from it. Therefore, rate-distortion-optimized segmentation methods based on quadtrees are not suitable for all images.

Based on the above analysis, in order to make the segmentation method general, a block segmentation method of the same size is adopted here. For an image I of size M×N, let the block size be 16×16. Therefore, the initial image block can be represented as B _i,j , i=1,2,K,M/16,j=1 _, 2,...,N/16. Any two image blocks are not repeated, and all image blocks constitute the whole image I. After transformation, the block size depends on the number of decomposition layers. Assuming that the total number of decomposition layers of the directional wavelet transform is J, for the decomposition layer k, the corresponding block size is L _k ×L _k . That is to say

L _k = 16/2 ^k-1 , k = 1, 2, K, J

Compared with the rate-distortion-optimized adaptive quad-tree segmentation method, this same-sized segmentation method greatly reduces the complexity and does not require the transmission of side information.

为Next, calculate the best prediction direction for each block. Assuming that the reference direction set is θ _ref = [-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7], for each Block B _l , l=0,1, K MN/256-1, the corresponding best prediction direction

for

D(·) represents a measure of image distortion. In this paper, D(·) is defined as |·|. That is, for each block _B1 , its best prediction direction is the direction corresponding to the smallest prediction error. The process of finding the best block prediction direction is shown in Figure 4.

图像块中每个样本的预测和更新过程见图2a。It can be produced from Figure 4 that, for a given image, firstly along all reference directions θ _{ref, i} (i=1, 2, K, 15), directional wavelet transform is performed respectively. Then, in these transformed images, the prediction errors are calculated respectively for the blocks B _l (l=0, 1, K, MN/256-1) at the same position, and the direction corresponding to the minimum prediction error is the best prediction direction

The prediction and update process of each sample in the image block is shown in Figure 2a.

Compared with the adaptive segmentation method, the proposed direction-lifting wavelet transform does not need to transmit the "split tree" at each bit rate, but only the best prediction direction for each block. Therefore, the side information required for the proposed method is small.

The remote sensing image is divided into blocks of the same size, and the divided image blocks are obtained. The block size here should be consistent with the block size in the subsequent coding stage.

Adaptive Lifting Wavelet Transform Based on Direction Interpolation (DIAL-DWT)

The traditional two-dimensional lifting wavelet transform only utilizes adjacent samples in the horizontal or vertical direction. However, most natural images contain many different directional information, such as edges, contours, and textures, which make the traditional two-dimensional lifting wavelet transform not well represented for these directional information. How to provide an effective image representation method is the key to improve image compression performance. Here, a new DIAL-DWT method is proposed. The method now divides the image into several blocks and then calculates the best lifting direction for each block. Next, the fractional samples are interpolated with an directional interpolation filter, thereby preserving more directional properties in the interpolated image. The detailed design process of the DIAL-DWT method method is as follows.

The structure of the direction-lifting wavelet transform

A typical lifting wavelet transform consists of four steps: splitting, predicting, updating, and normalizing [33] (SweldensW (1995) The lifting scheme: a construction of second generation wavelets. SIAM JMath Anal29(2):511-546.http: https://dx.doi.org/10.1137/S0036141095289051). Without loss of generality, the basic direction-lifting wavelet transform is also based on these four steps. The frameworks of one-dimensional direction-lifting wavelet transform and inverse transform are shown in Fig. 2a and Fig. 2b, respectively.

For a two-dimensional image x(m,n) _m,n∈Z , first, all samples are divided into two parts: the set of even samples x _e and the set of odd samples x _o .

In the prediction stage, odd-numbered samples are predicted by adjacent even-numbered samples, and the prediction direction is obtained by a certain criterion. Assuming that the direction adaptive prediction operator is DA_P, the prediction process can be expressed as

d[m,n]=x _o [m,n]+DA_P _e [m,n] (2)

In the update stage, even samples are updated by the prediction errors of adjacent samples, and the update direction is the same as the prediction direction. Assuming that the direction adaptive update operator is DA_U, the update process can be expressed as

c[m,n]=x _e [m,n]+DA_U _d [m,n] (3)

Here, the direction prediction operator DA_P is

The direction update operator DA_U is

Here, p _i and u _j denote the coefficients of the high-pass filter and the low-pass filter, respectively. θ _v represents the direction of prediction and update.

Finally, the boosted outputs are weighted with coefficients _{Ke and K o ,} respectively.

After the above process is completed, a low-pass subband L and a high-pass subband H in the horizontal direction can be obtained. Next, in the same way, a one-dimensional column direction transformation is performed.

The choice of the lifting direction θ is very important. For better image representation, the image is first divided into several image blocks, and the lifting direction is calculated separately for each block. For a given block, all samples within the block are boosted in the same direction. In theory, the more reference lift directions, the better the representation of the image patch, but the more side information needs to be transmitted. Conversely, if there are only a few reference lift directions, the image is not well represented. Here, 15 reference lift directions are selected for both the one-dimensional horizontal transform and the vertical transform, as shown in Fig. 3a and Fig. 3b, respectively. The directional filter can be represented along the direction d ₌ (d _x , dy ) ^T , d∈i ² . Here, the 15 reference directions utilize some adjacent integer and fractional samples. These reference directions are as follows: d _-7 =(3,-1) ^T ,d- ₆ =(2,-1) ^T ,d- ₅ =(1,-1) ^T ,d _-4 =(3/4, -1) ^T ,d _-3 =(1/2,-1) ^T ,d _-2 =(1,-3) ^T ,d _-1 =(1/4,-1) ^T ,d ₀ =(0 ,-1) ^T , d ₁ =(-1/4,-1) ^T , d ₂ =(-1,-3) ^T , d ₃ =(-1/2,-1) ^T , d ₄ =( -3/4,-1) ^T , d ₅ =(-1,-1) ^T , d ₆ =(-2,-1) ^T ,d ₇ =(-3,-1) ^T . The reference orientation set is shown in Figure 3.

Other steps and parameters are the same as in the first embodiment.

Embodiment 3: This embodiment differs from Embodiment 1 or 2 in that: in the second step, the best prediction direction is calculated for the divided image blocks respectively, and the optimal prediction direction of the divided image blocks is obtained; the specific process for:

For the wavelet transform based on directional boosting, the prediction error and the high frequency subband are closely related. The larger the prediction error, the more information in the high frequency subband, and the lower the coding performance. For an image block, the best prediction direction should be the direction that minimizes the residual information of high-frequency subbands.

The process of calculating the best prediction direction of an image block is as follows: as shown in Figure 4,

Suppose the reference direction set is θ _ref , the reference direction set θ _ref contains 15 reference directions, and these directions are marked as {-7,-6,-5,-4,-3,-2,-1,0,1, 2, 3, 4, 5, 6, 7}; set the total number of image blocks after segmentation to be Na, and each image block to be B _l , l=0,1,K,N _{a -1} ;

_The segmented image blocks B1 are respectively subjected to direction prediction along all reference directions θ _ref,i (i=1, 2, K, 15) to obtain predicted image blocks in all reference directions;

Under the mean square error criterion, the pixels of the predicted image block in all reference directions are compared with the pixels of the remote sensing image in step 1, and the reference direction corresponding to the smallest error is the best prediction direction of the predicted image block.

计算如下Predict the best prediction direction for an image block

Calculated as follows

In the formula, D( ) is the image distortion function, x(m, n) is the sample value corresponding to the position (m, n) in the image block B _l , DA_P ⁱ is the prediction operator of the ith reference direction, m is The abscissa of the corresponding position, n is the ordinate of the corresponding position; let D(·)=|·|;

Samples: called pixels in the original image, and coefficients in the transformed image. That is to say, before the first-level wavelet transform, it is called pixel here. But wavelet transform is usually multi-level, starting from the second level, here are all coefficients. For convenience of presentation, they are collectively referred to as samples here.

Repeat the above process until the best prediction direction of all the segmented image blocks is determined;

Compared with the adaptive segmentation method, the proposed wavelet transform method based on direction boosting does not need to additionally transmit all the "segmentation trees" at a given bit rate, but only needs to transmit the best prediction direction corresponding to the block. Therefore, the proposed method needs to transmit very little auxiliary information.

Other steps and parameters are the same as in the first or second embodiment.

Embodiment 4: This embodiment differs from one of Embodiments 1 to 3 in that: in step 3, by calculating the weighted directional interpolation filter coefficients, weighted directional interpolation is performed on the fractional sample values that need to be used in the direction boosting process. , to obtain the interpolated image block; the specific process is:

Orientation interpolation

For the wavelet transform based on direction lifting, some lifting directions need to use the sample value of the fractional position. That is, the tangent tanθ of the lift direction is not always an integer. Therefore, it is necessary to interpolate samples at fractional positions. The interpolation process can be expressed as

Here, k represents the integer position used in the interpolation process; a _k represents the parameters of the interpolation filter. In essence, the process of sub-pixel interpolation is the design process of the optimal interpolation filter. Most wavelet transforms based on directional boosting use the Sinc interpolation method. However, similar to some other interpolation methods, Sinc interpolation only interpolates fractional samples with samples along the horizontal or vertical direction, which blurs the orientation information in the image. For images with more texture or details, if the Sinc interpolation method is used, the direction prediction error will increase. In this paper, a directional interpolation method is employed that utilizes adjacent integer samples to interpolate fractional positions along the local texture direction. Taking horizontal transformation as an example, the process of directional interpolation is shown in Figure 5.

For different fractional sample positions, the integer samples used for interpolation are also different, which is adapted to the characteristics of the local signal. Since different integer samples contribute differently to fractional sample positions, the interpolation filters should also be different [34] (Liu Y, Ngan K N (2008) Weighted adaptive lifting-based wavelet transform for imagecoding. IEEE Trans. Image Process 17(4): 500 -511. http://dx.doi.org/10.1109/TIP.2008.917104). The interpolation filter used is shown in Figure 6. It can be seen from Figure 6 that the final coefficients of the directional interpolation filter are determined by three filters, namely, a bilinear filter, a Telenor 4-tap filter, and a 2-tap filter. The coefficients of these filters are shown in Table 1.

The interpolation filter coefficients used in Table 1

In Figure 6, a number of different integer samples are used for the interpolation of fractional samples, the interpolation direction being adapted to the local characteristics of the signal used for interpolation. For example, to interpolate samples at quarter positions, not only samples at integer positions {a _-2 ,a _-1 ,a ₀ ,a ₁ } but also samples along the prediction direction {a _-3 ,a ₂ }. These samples {a _-3 ,a _-2 ,a _-1 ,a ₀ ,a ₁ ,a ₂ } can be used to build a directional interpolation filter and then make predictions on the samples at fractional positions. It can be seen from Figure 6 that {a _-3 ,a ₂ } is the input of the bilinear filter, {a _-2 ,a _-1 ,a ₀ ,a ₁ } is the input of the Telenor 4-tap filter, the bilinear The output of the filter and the Telenor 4-tap filter together form the input of the 2-tap filter. Therefore, the output of the 2-tap filter is the coefficient of the directional interpolation filter. The correspondence between the directional interpolation filter coefficients and the samples at different fractional positions is shown in Table 2.

Table 2 Directional interpolation filter coefficients

The final output of the directional interpolation filter is determined by three filters: bilinear filter, Telenor 4-tap filter and 2-tap filter;

In the following two rows of the row where the current sample is located, take two samples in the column two columns apart from the column where the sample is located, as the input of the bilinear filter; in the row where the current sample is located, the upper row, and the lower row In the two rows, the four samples in the next column of the sample are respectively taken as the input of the Telenor 4-tap filter. The output of the bilinear filter and the Telenor4-tap filter constitute the input of the 2-tap filter. , the output of the 2-tap filter is the weighting coefficient of the directional interpolation filter;

As can be seen from Figure 6, the {c _-3 ,c ₂ } integer samples are the input of the bilinear filter, and the {c _-2 ,c _-1 ,c ₀ ,c ₁ } integer samples are the Telenor4-tap filter. The input, the output of the bilinear filter and the Telenor4-tap filter constitute the input of the 2-tap filter, and the output of the 2-tap filter is the weighting coefficient of the directional interpolation filter;

A directional interpolation filter is constructed by integer position samples {c _-3 ,c _-2 ,c _-1 ,c ₀ ,c ₁ ,c ₂ } and weighting coefficients, and the directional interpolation filter performs weighted directional interpolation on the sample values of fractional positions, Get the interpolated image patch.

Other steps and parameters are the same as one of the first to third embodiments.

Embodiment 5: This embodiment differs from one of Embodiments 1 to 4 in that: in the step 4, the optimal prediction direction obtained in step 2 is used to perform wavelet transform based on direction boosting on the interpolated image blocks, respectively. The transformed image blocks, that is, the transformed code blocks; the specific process is as follows:

分别利用公式(2)和(3)对步骤三得到的插值图像块进行基于方向提升的小波变换：According to the best prediction direction obtained in step 2

Use formulas (2) and (3) to perform wavelet transform based on direction boosting on the interpolated image block obtained in step 3:

The direction prediction operator DA_P is

In the formula, x _e [m,n] is the even-numbered sample set of the interpolated image block obtained in step 3, DA_P _e [m,n] is the direction prediction operator corresponding to the even-numbered sample set; i represents the serial number of the high-pass filter coefficient, p _i represents the high-pass filter coefficient;

The interpolated image block is divided into two parts: the set of even samples x _e [m,n] and the set of odd samples x _o [m,n];

The direction update operator DA_U is

In the formula, j represents the serial number of the low-pass filter coefficient, u _j represents the low-pass filter coefficient, DA_U _d [m,n] is the direction update operator corresponding to the odd sample set; Odd samples after prediction of even samples, denoted as

d[m,n]=x _o [m,n]+DA_P _e [m,n]

x _o [m,n] is the odd sample set of the interpolated image block obtained in step 3;

Each transformed code block is obtained by using the direction prediction operator and the direction update operator.

Other steps and parameters are the same as one of the first to fourth embodiments.

Embodiment 6: This embodiment is different from one of Embodiments 1 to 5 in that: in the step 6, an improved SPIHT method is used to encode the transformed image obtained in the step 5 to obtain an encoded image; the specific process is:

The SPIHT encoding method is to encode the transformed image. The coefficients mentioned in the coding method all refer to the wavelet coefficients in the transformed image.

Tree-based coding methods have received increasing attention recently. Among these tree-based coding methods, the SPIHT method is the most widely used due to its good rate-distortion performance and moderate complexity. However, the scanning manner of the SPIHT method limits its coding performance. In the scanning process of SPIHT, the importance of coefficients is only judged by the absolute value of their assignment. In fact, the human eye is more sensitive to the contour distortion of the image. In the high frequency subbands, the wavelet coefficients at the image contour tend to have larger amplitudes. The gray level change of an image is usually slow, so in the high frequency subband, the wavelet coefficients surrounding the important coefficients usually also have larger amplitudes. From another point of view, if the coefficients surrounding a coefficient are all important, there is a high probability that this coefficient is also important, even if the coefficient magnitude does not reach the specified threshold. The more important coefficients that surround a coefficient, the more important that coefficient is usually. Therefore, if those coefficients with many important "neighbors" are also encoded preferentially, at a given bit rate, more important coefficients will be encoded, thereby improving the quality of the reconstructed image.

A good image coding algorithm should not only provide good coding performance, but also have faster operation speed. However, the two are often contradictory. The reason is that the improvement of coding performance often comes at the cost of increased computational complexity. Therefore, how to reduce the algorithm complexity while providing good coding performance is another problem that needs to be studied.

This paper proposes an improved SPIHT method that preferentially scans coefficients with important "neighbors" to improve coding performance. In order to reduce the complexity of the algorithm, the proposed method only changes part of the scanning order of SPIHT and does not require additional computation. Another advantage of the proposed method is that the scanning order is adaptively determined by the previously obtained important coefficients, so there is no need to store any information as a header file.

For the SPIHT algorithm, the D and L sets are represented by a list of insignificant sets (LIS). Firstly, LSP is initialized as an empty table, LIP is initialized as the lowest frequency subband coefficient position set, and LIS is initialized as the root node coordinate set of each spatial direction tree. Image compression is achieved by encoding records in LIP, LIS, and LSP in turn for each bit plane.

Step 61: Initialize the threshold value T=2 ^n￠ , initialize the tables LSP, LIS and LIP; n￠ is the maximum value of the number of bit planes;

The table LSP is initialized as an empty table, LIP is initialized as the lowest frequency subband coefficient position set, and LIS is initialized as the root node coordinate set of each spatial direction tree;

Step 62: Encode LIP according to the table LSP, LIS and LIP, the process is:

Step 621. Determine whether the LIP set contains important coefficients according to the threshold (the coefficient corresponding to the position of the important coefficient is the important coefficient), if yes, output 1 and the sign bit, the coefficient is positive, the sign bit is 0, the coefficient is negative, and the sign bit is is 1, the important coefficient position (i, j) is removed from the LIP and added to the end of the LSP;

If not, output 0;

Judging whether the LIP set contains important coefficients according to the threshold, the process is as follows:

If the coefficient is greater than the threshold, it is an important coefficient; if the coefficient is less than or equal to the threshold, it is not an important coefficient;

Step 622, judge whether all the coefficient positions contained in the LIP set have been processed, if not, re-execute step 621; if execute step 63;

Step 63: Encode LIS, the process is:

Step 631. Determine whether the current record of the LIS is D(i,j) or L(i,j). If the current record of the LIS is D(i,j), go to step 632. If the current record of the LIS is D(i,j) L(i,j), execute step 635;

D(i,j) is the coordinate set of all descendants of the coefficient position (i,j);

L(i,j) is the coordinate set of all non-direct descendants of the coefficient position (i,j);

Step 632: Determine whether D(i,j) contains important coefficients according to the threshold, if the output is 1, otherwise the output is 0;

If D(i,j) contains important coefficients, decompose D(i,j) into L(i,j) and O(i,j); mark L(i,j) into the tail of LIS;

O(i,j) is the coordinate set of all children of the coefficient position (i,j);

Determine whether D(i,j) contains important coefficients according to the threshold. The process is as follows:

If the coefficient is greater than the threshold, it is an important coefficient; if the coefficient is less than or equal to the threshold, it is not an important coefficient;

Use 4 coefficients of O(i, j) to build a quadtree and encode (encoded as output 0 or 1), if the root of the quadtree (the largest of the 4 coefficients) is greater than or equal to the threshold, it means that these four coefficients If there are important coefficients, output 1; otherwise, if the root of the quadtree (the largest of the four coefficients) is less than the threshold, it means that there are no important coefficients in the four coefficients, and output 0; go to step 633;

Step 633: Put the important coefficients (important coefficients among the 4 coefficients) into the LIP or LSP, and output the sign of the important coefficients (the important coefficients among the 4 coefficients), the important coefficients are positive, the sign is 0, and the important coefficients are negative , the symbol is 1; execute step 634;

Step 634: Determine whether L(i,j) is empty,

If so, delete D(i,j) from LIS; execute step 638;

If not, move the L(i,j) coefficient position (i,j) to the end of LIS; go to step 638;

Step 635: Determine whether L(i,j) is marked (in step 632, mark L(i,j) obtained by decomposing D(i,j) (the mark will be set in the program) ), if yes, go to step 636, if not, go to step 637;

Step 636: Determine whether L(i,j) contains important coefficients according to the threshold. Yes, L(i,j) is important, delete L(i,j) from LIS, and replace D(2i,2j), D (2i+1,2j), D(2i,2j+1) and D(2i+1,2j+1) are added to the end of LIS without outputting any information; go to step 638;

No, L(i,j) is not important, go to step 638;

Judging whether L(i,j) contains important coefficients according to the threshold, the process is as follows:

If the coefficient is greater than the threshold, it is an important coefficient; if the coefficient is less than or equal to the threshold, it is not an important coefficient;

Step 637: Determine whether L(i,j) contains important coefficients according to the threshold. If yes, L(i,j) is important, then delete L(i,j) from LIS, and D(2i,2j) , D(2i+1,2j), D(2i,2j+1), and D(2i+1,2j+1) are added to the end of the LIS, and the code is output; execute step 638;

No, L(i,j) is not important, no information is output;

Judging whether L(i,j) contains important coefficients according to the threshold, the process is as follows:

If the coefficient is greater than the threshold, it is an important coefficient; if the coefficient is less than or equal to the threshold, it is not an important coefficient;

Step 638; determine whether the root node coordinates of all spatial direction trees in the LIS have been processed, if not, re-execute step 631; if so, execute step 64;

Step 64: Clear all the labels of L(i,j), check each (i,j) in the LSP, if it is not newly added in the sorting scan (in this iteration), output the first number of the coefficient corresponding to the position. There are n bits (the third bit of 101 is 1), and step 65 is performed; if it is newly added in the sorting scan, no information is output;

Step 65: Determine whether the length of the compressed code stream has reached the specified length, and if so, output the compressed code stream; if not, T=T/2, execute step 62.

It can be seen from the LIS encoding process that if the importance of L(i,j) is judged first, and then the four coefficients of O(i,j) are encoded, one bit can be saved. Since L(i,j) is unimportant with high probability, this saves a lot of bits. It is worth noting that this process does not add extra bits or computation, but only changes the order of judgment. Moreover, when L(i,j) obtained by splitting from D(i,j) is important, then O(i,j) has a high probability to contain important coefficients. Therefore, O(i,j) can be encoded in an efficient way.

For the SPIHT algorithm, the D and L sets are represented by a list of insignificant sets (LIS). First, the LSP performs image compression by encoding the records in LIP, LIS, and LSP in turn for each bit plane.

The detailed LIS scanning process in the improved SPIHT algorithm is shown in Algorithm 1.

Other steps and parameters are the same as one of the specific embodiments one to five.

Adopt the following examples to verify the beneficial effects of the present invention:

Example 1:

The image compression method based on the direction-lifting wavelet and the improved SPIHT under the Internet of Things of the present embodiment is specifically prepared according to the following steps:

First, experiments are designed to verify the effectiveness of the proposed DIAL model. Then, the improved SPIHT algorithm is tested. Finally, the proposed method is compared with commonly used compression methods under different bit rates and using different quality evaluation criteria.

The proposed DIAL model

To demonstrate the effectiveness of the proposed DIAL model, the commonly used "Barbara" is adopted as the test image. The image size is 512×512. The test image was decomposed by 9/7 biorthogonal wavelet filter, wavelet filter based on ADL, and wavelet filter based on DIAL model, respectively, and the decomposition results obtained are shown in Figures 7a, 7b, and 7c. It can be seen from Figure 8 that, compared with the decomposition result obtained by using the 9/7 wavelet filter, the high-frequency subband of the transformed image obtained by the ADL-based wavelet filter has smaller coefficient amplitudes. For the wavelet filter based on the DIAL model, the high frequency sub-bands in the transformed image look almost black, indicating that the sparse results obtained by this method are optimal. The reason is that during the boosting process, the DIAL model considers more directional information, which helps to concentrate more energy in the low frequency subbands in the image. Moreover, compared with the commonly used Sinc interpolation method, the DIAL model adopts directional interpolation, which is able to interpolate fractional pixel positions along the local texture direction. Therefore, more directional information in the image can be preserved. All of these help the DIAL model achieve better sparsity performance.

Table 3 shows the average amplitude of the high-frequency coefficients obtained by using these three transform methods, and the percentage reduction in the amplitude of the high-frequency subband coefficients relative to the traditional 9/7 wavelet transform (represented by numbers in parentheses) . It can be seen from Table 3 that for each high frequency subband, the average magnitude of the coefficients of the DIAL model is the smallest.

Table 3 Average coefficient amplitudes and reduction percentages of LH, HL, and HH under three transformation methods

The DIAL model does not require adaptive decomposition based on rate-distortion optimization. Moreover, the entropy coding method can be used to further reduce the side information. Therefore, the side information that needs to be transmitted is greatly reduced. The comparison results of the side information are shown in Figure 4. As can be seen from Figure 4, compared with the ADL method, the proposed DIAL method requires less side information, which is very beneficial to improve the compression efficiency.

Table 4. Bit rate (bpp) of side information for a given bit rate

Non-linear estimation (NLA) is an efficient method to measure the sparse representation ability of a given transform [35] (Eslami R, Radha H (2007) A new family of nonredundant transforms using hybridwavelets and directional filter banks. IEEE Trans Image Process 16 (4): 1152-1167. http://dx.doi.org/10.1109/TIP.2007.891791). If it has good NLA performance, the transformation method has potential in some signal processing applications, such as coding, denoising, and feature extraction. Therefore, several sets of experiments are designed to test the NLA performance of the proposed DIAL model-based wavelet transform. For the test image "Barbara", the NLA performances of different methods are shown in Figure 8 under the condition of retaining different numbers of coefficients. It can be seen from Figure 8 that the wavelet transform based on the DIAL model has always been superior to the ordinary 9/7 wavelet transform and the wavelet transform based on ADL. Especially when the number of retention coefficients M is small, the NLA performance of the proposed method is more obvious. For other test images, such as "Boats", "Fingerprint", "GoldHill", and some texture images, testing NAL performance with the same method, the same conclusion can be obtained.

The performance of the proposed compression method

The proposed compression method combines the wavelet transform based on the DIAL model with the improved SPIHT method. To demonstrate the effectiveness of the proposed method, some experimental comparisons are performed. Here, six test images are selected, from different sensors and reflecting different scenarios. Among them, "bank", "aerial", "Lena", "Baboon", and "WoodlandHills" are selected from the USC-SIPI database [36] (USC-SIPI database. [Online]: http://sipi.usc.edu /database/), "Europa3" is selected from the CCSDS test image set [37] (Consultative committee for spacedata systems, CCSDS test images. [Online]. Available: http://cwe.ccsds.org/sls/docs/sls- dc/). These test images are 512×512 in size, as shown in Figures 9a, 9b, 9c, 9d, 9e, 9f.

In the experiment, the number of wavelet decomposition layers is set to five. The above test images are compressed by the proposed compression method and the traditional SPIHT method, respectively. The PSNR results obtained at different bit rates are shown in Table 5.

Table 5 presents the PSNR results (dB) obtained by the compression method and the traditional SPIHT method

As can be seen from Table 5, the coding performance of the proposed compression method is better than that of SPIHT at all given bit rates. This is because the DIAL model can provide good sparse representation results, concentrating more energy of the image into low-frequency subbands. For zerotree-based coding methods, this means that more "longer" zerotrees can be generated in the same bit plane. Moreover, the improved SPIHT method enables more efficient scans of these zero trees. All these contribute to the proposed compression method for better coding performance.

To comprehensively evaluate the proposed compression method, the Kappa coefficient is also adopted as a quality evaluation metric. The Kappa coefficient is often used to evaluate classification accuracy [38] (Gaucherel C, Alleaume S, Hely C (2008) The ComparisonMap Profile Method: A Strategy for Multiscale Comparison of Quantitative and Qualitative Images. IEEE TransGeosciRemote Sens, 46(9):2708-2719. http://dx.doi.org/10.1109/TIP.2007.891791). Reference [39] (Cohen J(1960) A coefficient of agreement for nominal scales. Educational and PsychologicalMeasurement 20(1): 37-46.) pointed out that the Kappa coefficient can also be used as a measure of the consistency of the original and reconstructed images. For these test images, the Kappa coefficients obtained by the proposed method and the general SPIHT compression method at different bit rates are shown in Fig. 10. From Figure 10, it can be seen that at all given bit rates, the Kappa coefficient of the proposed compression method is still better than the results obtained with the SPIHT method.

Besides PSNR and Kappa coefficient, the subjective quality of the image is also an important indicator to evaluate the performance of the compression algorithm. Taking the test image "bank" as an example, the reconstructed images obtained by different compression methods under different bit rates are shown in Figures 11a to 11j. From Figures 11a, 11b, 11c, 11d, 11e, 11f, 11g, 11h, 11i, and 11j, it can be seen that the proposed compression method can provide better visual quality of reconstructed images, especially in boxes with more texture information Area. This proves that the proposed compression method helps to preserve more main details of the image. The present invention can also have other various embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art can make various corresponding changes and deformations according to the present invention, but these corresponding changes and deformations are all It should belong to the protection scope of the appended claims of the present invention.

Claims (5)

1. the image compression method based on direction promotion wavelet and improved SPIHT under the Internet of Things, is characterized in that: the concrete process of described method is: Step 1: Perform image block segmentation on the remote sensing image to obtain segmented image blocks; Step 2: Calculate the best prediction direction for the segmented image blocks respectively, and obtain the best prediction direction of the segmented image blocks; Step 3: Perform weighted directional interpolation on the fractional sample values by calculating the weighted directional interpolation filter coefficients to obtain an interpolated image block; Step 4: Using the best prediction direction obtained in Step 2, perform wavelet transform based on direction boosting on the interpolated image blocks, respectively, to obtain each transformed image block, that is, each transformed code block; Step 5, forming the entire transformed image from all the transformed image blocks; Step 6, utilize the improved SPIHT method to encode the transformed image obtained in step 5 to obtain the encoded image; In the described step 6, the improved SPIHT method is utilized to encode the transformed image obtained in the step 5 to obtain the encoded image; the specific process is: Step 61. Initialize the threshold

Initialize tables LSP, LIS and LIP;

is the maximum number of bit planes; The table LSP is initialized as an empty table, LIP is initialized as the lowest frequency subband coefficient position set, and LIS is initialized as the root node coordinate set of each spatial direction tree; Step 62: Encode LIP according to the table LSP, LIS and LIP, the process is: Step 621. Determine whether the LIP set contains important coefficients according to the threshold. If yes, output 1 and the sign bit. The coefficient is positive, the sign bit is 0, the coefficient is negative, and the sign bit is 1. ) is removed from the LIP and added to the end of the LSP; If not, output 0; Judging whether the LIP set contains important coefficients according to the threshold, the process is as follows: If the coefficient is greater than the threshold, it is an important coefficient; if the coefficient is less than or equal to the threshold, it is not an important coefficient; Step 622, judge whether all the coefficient positions contained in the LIP set have been processed, if not, re-execute step 621; if execute step 63; Step 63: Encode LIS, the process is: Step 631. Determine whether the current record of the LIS is D(i,j) or L(i,j). If the current record of the LIS is D(i,j), go to step 632. If the current record of the LIS is D(i,j) L(i,j), execute step 635; D(i,j) is the coordinate set of all descendants of the coefficient position (i,j); L(i,j) is the coordinate set of all non-direct descendants of the coefficient position (i,j); Step 632: Determine whether D(i,j) contains important coefficients according to the threshold, if the output is 1, otherwise the output is 0; If D(i,j) contains important coefficients, decompose D(i,j) into L(i,j) and O(i,j); put L(i,j) at the end of LIS; O(i,j) is the coordinate set of all children of the coefficient position (i,j); Determine whether D(i,j) contains important coefficients according to the threshold. The process is as follows: If the coefficient is greater than the threshold, it is an important coefficient; if the coefficient is less than or equal to the threshold, it is not an important coefficient; Use the four coefficients of O(i, j) to build a quadtree and encode it. If the root of the quadtree is greater than or equal to the threshold, it means that there are important coefficients in these four coefficients, and output 1; otherwise, if the tree of the quadtree is greater than or equal to the threshold If the root is less than the threshold, and there are no important coefficients among the four coefficients, output 0; go to step 633; Step 633: Put the important coefficient into the LIP or LSP, and output the sign of the important coefficient, the important coefficient is positive, the sign is 0, the important coefficient is negative, and the sign is 1; execute step 634; Step 634: Judge whether L(i,j) is empty, If so, delete D(i,j) from LIS; execute step 638; If not, move the L(i,j) coefficient position (i,j) to the end of LIS; go to step 638; Step 635, judge whether L(i, j) is marked, if yes, execute step 636, if not, execute step 637; Step 636: Determine whether L(i,j) contains important coefficients according to the threshold. Yes, L(i,j) is important, delete L(i,j) from LIS, and replace D(2i,2j), D (2i+1,2j), D(2i,2j+1) and D(2i+1,2j+1) are added to the end of LIS without outputting any information; go to step 638; No, L(i,j) is not important, go to step 638; Judging whether L(i,j) contains important coefficients according to the threshold, the process is as follows: If the coefficient is greater than the threshold, it is an important coefficient; if the coefficient is less than or equal to the threshold, it is not an important coefficient; Step 637: Determine whether L(i,j) contains important coefficients according to the threshold. If yes, L(i,j) is important, then delete L(i,j) from LIS, and D(2i,2j) , D(2i+1,2j), D(2i,2j+1), and D(2i+1,2j+1) are added to the end of the LIS, and the code is output; execute step 638; No, L(i,j) is not important, no information is output; Judging whether L(i,j) contains important coefficients according to the threshold, the process is as follows: If the coefficient is greater than the threshold, it is an important coefficient; if the coefficient is less than or equal to the threshold, it is not an important coefficient; Step 638; determine whether the root node coordinates of all spatial direction trees in the LIS have been processed, if not, re-execute step 631; if so, execute step 64; Step 64: Clear all L(i,j) marks, check each (i,j) in the LSP, if it is not newly added in the sorting scan, output the nth bit of the coefficient corresponding to this position, and execute the step Sixty-five; if it is newly added in the sorting scan, no information is output; Step 65: Determine whether the length of the compressed code stream has reached the specified length, and if so, output the compressed code stream; if not, T=T/2, execute step 62. 2. the image compression method based on direction boosting wavelet and improving SPIHT under the Internet of Things according to claim 1, is characterized in that: in described step 1, remote sensing image is carried out image block segmentation, obtains the image block after segmentation; Concrete process is : The remote sensing image is divided into blocks of the same size, and the divided image blocks are obtained. The block size here should be consistent with the block size in the subsequent coding stage. 3. the image compression method based on direction boosting wavelet and improved SPIHT under the described Internet of Things according to claim 2, it is characterized in that: in described step 2, the best prediction direction is calculated respectively to the image block after segmentation, obtains the image block after segmentation The best prediction direction of ; the specific process is: Assuming that the reference direction set is θ _ref , the reference direction set θ _ref contains 15 reference directions, denoted as {-7,-6,-5,-4,-3,-2,-1,0,1,2,3 , 4, 5, 6, 7}; let the total number of image blocks after segmentation be Na , and each image block be B _l , l=0,1,K,N _{a -1} ; _The segmented image blocks B1 are respectively subjected to direction prediction along all reference directions θ _ref,i (i=1, 2, K, 15) to obtain predicted image blocks in all reference directions; Under the mean square error criterion, the pixels of the predicted image block in all reference directions are compared with the pixels of the remote sensing image in step 1, and the reference direction corresponding to the smallest error is the best prediction direction of the predicted image block.

Predict the best prediction direction for an image block

Calculated as follows

In the formula, D( ) is the image distortion function, x(m, n) is the sample value corresponding to the position (m, n) in the image block B _l , DA_P ⁱ is the prediction operator of the ith reference direction, m is The abscissa of the corresponding position, n is the ordinate of the corresponding position; let D(·)=|·|; The above process is repeated until the best prediction directions for all the segmented image blocks are determined. 4. according to the image compression method of improving wavelet in direction and improving SPIHT under the described Internet of Things of claim 3, it is characterized in that: in described step 3, by calculating weighted direction interpolation filter coefficient, the fractional sample value is carried out weighted direction interpolation, Obtain the interpolated image block; the specific process is: The final output of the directional interpolation filter is determined by three filters: bilinear filter, Telenor4-tap filter and 2-tap filter; In the following two rows of the row where the current sample is located, take two samples in the column two columns apart from the column where the sample is located, as the input of the bilinear filter; in the row where the current sample is located, the upper row, and the lower row In the two rows, the four samples in the next column of the sample are respectively taken as the input of the Telenor 4-tap filter. The output of the bilinear filter and the Telenor4-tap filter constitute the input of the 2-tap filter. , the output of the 2-tap filter is the weighting coefficient of the directional interpolation filter; The directional interpolation filter is constructed by the input samples of the bilinear filter, the input samples of the Telenor4-tap filter and the weighting coefficients. The directional interpolation filter performs weighted directional interpolation on the sample values of the fractional positions to obtain the interpolated image block. 5. the image compression method based on direction boosting wavelet and improving SPIHT under the described Internet of Things according to claim 4, is characterized in that: in described step 4, utilize the best prediction direction that step 2 obtains, carry out direction-based direction to interpolation image block respectively. The improved wavelet transform is used to obtain each transformed image block, that is, each transformed code block; the specific process is as follows: According to the best prediction direction obtained in step 2

Use formulas (2) and (3) to perform wavelet transform based on direction boosting on the interpolated image block obtained in step 3: The direction prediction operator DA_P is

In the formula, x _e [m,n] is the even-numbered sample set of the interpolated image block obtained in step 3, DA_P _e [m,n] is the direction prediction operator corresponding to the even-numbered sample set; i represents the serial number of the high-pass filter coefficient, p _i represents the high-pass filter coefficient; The interpolated image block is divided into two parts: the set of even samples x _e [m,n] and the set of odd samples x _o [m,n];

The direction update operator DA_U is

In the formula, j represents the serial number of the low-pass filter coefficient, u _j represents the low-pass filter coefficient, DA_U _d [m,n] is the direction update operator corresponding to the odd sample set; Odd samples after prediction of even samples, denoted as d[m,n]=x _o [m,n]+DA_P _e [m,n] x _o [m,n] is the odd sample set of the interpolated image block obtained in step 3; Each transformed code block is obtained by using the direction prediction operator and the direction update operator.

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