CN104200439B - Image super-resolution method based on adaptive filtering and regularization constraint - Google Patents
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Abstract
The invention discloses an image super-resolution method based on adaptive filtering and regularization constraint and mainly aims at solving the problems of blocking and virtual edges which are produced in an image super-resolution method based on constraint reconstruction in the prior art. The image super-resolution method based on adaptive filtering and regularization constraint comprises the implementation steps of firstly, inputting a high-resolution image, fuzzifying the high-resolution image, performing downsampling on the fuzzy image and performing interpolation on the low-resolution image, secondly, calculating an adaptive filter coefficient matrix to obtain a high-frequency image, thirdly optimizing the high-frequency image to obtain the optimal high-frequency image, and finally, optimizing the high-resolution image to obtain the optimal high-resolution image. The image super-resolution method based on the adaptive filtering and the regularization constraint is capable of performing super-resolution enlargement on the image by use of only one observation image and well keeping the edge and texture details of the image, and can be applied to image super-resolution reconstruction of a medical image, a video monitoring image and a remote sensing image.
Description
Technical Field
The invention belongs to the technical field of image processing, and further relates to an image super-resolution method based on adaptive filtering and regular constraint in the fields of remote sensing images, video monitoring and medical images.
Background
In the imaging fields of remote sensing images, video monitoring, medical images and the like, a single image super-resolution reconstruction method for reconstructing a high-resolution image from a low-resolution image is adopted for improving the image resolution. At present, a single image is mainly based on sparse representation and a regular constraint method to realize super-resolution reconstruction.
Four people, Yang, J, Wright, J, Huang, T, Ma, y, disclose a method for implementing Super-Resolution reconstruction of a single Image based on sparse Representation in the document "Image Super-Resolution viascan reconstruction" (IEEE trans. on Image Processing vol.19 No.11 pp.2861-2873 nov.2010). The method includes the steps of giving a low-resolution image, dividing the image into a plurality of blocks, conducting sparse coding on each low-resolution image block, enabling the low-resolution image block to adaptively find K low-resolution blocks in low-resolution data to enable a representation error to be minimum and representation coefficients to be sparse enough, then linearly combining the K high-resolution image blocks corresponding to the low-resolution image blocks, and fusing all the high-resolution image blocks to obtain a final high-resolution image. The method has the defects that the sparse coding process is complex in calculation, and the method does not process the edges and the textures of the image.
Zuo, W, Lin, Z discloses a method for solving a super-resolution problem using gradient smoothness constraints in the document "A Generalized accessed calculated maximum gradient Image application for Total-Variation-Based Image retrieval" (IEEE trans. on Image Processing vol.20 No.10 pp.2748-2759 Oct.2011.). The method converts the super-resolution problem into an optimization problem by adding a penalty function, and obtains a final high-resolution image by solving the optimization problem. The method has the defects that the method model needs to be established under the assumption that the image is smooth in slices, the precondition that all images can not be met is not met, and in addition, the method can also introduce the blocking effect of the image to cause the blurring of the super-resolution image.
A patent applied to Suzhou New line of sight cultural science and technology development Limited company, namely an image super-resolution reconstruction method based on sparse representation (application date: 2013.07.16 application number: 201310296581.3 publication number: CN 103366347A), discloses an image super-resolution reconstruction method based on sparse representation. The method comprises the steps of firstly calculating gradient information of a low-resolution image and residual error information of a high-resolution image and the low-resolution image, then obtaining a low-resolution feature set and a high-resolution feature set through a sparse expression method, finally finding corresponding residual error information in the high-resolution feature set, and fusing the residual error information to the low-resolution image to obtain a high-resolution image. The method has the defects that the sparse expression method for calculating the low-resolution feature set and the high-resolution feature set is high in calculation complexity, poor in real-time performance and limited in practical application range.
Disclosure of Invention
The invention aims to provide an image super-resolution method based on adaptive filtering and regular constraint aiming at the defects of the prior art, and the obtained high-resolution image has sharp edges and abundant texture details by optimizing the high-frequency part of the constrained image.
The method comprises the following specific steps:
(1) obtaining an initial high-resolution remote sensing image:
(1a) inputting a high-resolution remote sensing image;
(1b) generating a Gaussian blur matrix with the mean value of 0, the variance of 1.6 and the size of 7 multiplied by 7;
(1c) convolving the high-resolution remote sensing image by using a Gaussian fuzzy matrix to obtain a high-resolution fuzzy remote sensing image;
(1d) respectively sampling the high-resolution fuzzy remote sensing image by 3 times in the horizontal direction and the vertical direction to obtain a low-resolution remote sensing image;
(1e) amplifying the low-resolution remote sensing image by 3 times by adopting an interpolation amplification method to obtain an initial high-resolution image;
(2) calculating an adaptive filter coefficient matrix:
(2a) generating a self-adaptive filter of the initial high-resolution remote sensing image by adopting a self-adaptive filter generation method to obtain a coefficient matrix of the self-adaptive filter;
(2b) calculating an initial high frequency remote sensing image by using the following formula:
u0＝k0-Fk0
wherein u is0Representing the initial high-frequency remote sensing image, k0Representing an initial high-resolution remote sensing image, and F representing a coefficient matrix of an adaptive filter;
(3) obtaining an optimal high-frequency remote sensing image:
(3a) two adjacent columns of pixels in the initial high-resolution remote sensing image are subjected to pairwise difference to obtain a horizontal gradient operator of the remote sensing image; carrying out pairwise difference on two adjacent lines of pixels in the initial high-resolution remote sensing image to obtain a vertical gradient operator of the image;
(3b) calculating the total variation of the high-frequency remote sensing image by using the following formula:
wherein Q represents the total variation of the high-frequency remote sensing image, D1And D2Respectively representing horizontal and vertical gradient operators of the remote sensing image, and u represents a high-frequency remote sensing image;
(3c) performing wavelet domain transformation on the high-frequency remote sensing image to obtain a wavelet transformation matrix of the high-frequency remote sensing image;
(3d) calculating a projection matrix of the high-frequency remote sensing image in a wavelet domain by using the following formula:
B＝ΨTu
wherein, B represents a projection matrix of the high-frequency remote sensing image in a wavelet domain, psiTA transposed matrix representing a wavelet transformation matrix of the high-frequency remote sensing image, and u represents the high-frequency remote sensing image;
(3e) solving the following formula by adopting an optimization equation solving method to obtain an optimal high-frequency remote sensing image:
wherein U represents the optimal high-frequency remote sensing image α1Regularization parameters representing total variation of high frequency remote sensing images, α1＝4.0e-5；α2Regularization parameters representing the projection of high frequency remote sensing images in the wavelet domain, α2＝3.0e-5；D1And D2Respectively representing horizontal and vertical gradient operators of the remote sensing image; u represents a high-frequency remote sensing image; ΨTA transposed matrix of a wavelet transformation matrix representing the high-frequency remote sensing image, η a penalty factor of the high-frequency remote sensing image constraint, η being 2, u0Representing an initial high-frequency remote sensing image;represents the optimization equation, | ·| luminance12Expressing a normal form operation, | ·| non-conducting phosphor2Expressing a square operation of a norm taking mode;
(4) obtaining an optimal high-resolution remote sensing image:
(4a) obtaining a down-sampling matrix corresponding to the position relation between the pixels of the low-resolution remote sensing image and the pixels of the high-resolution remote sensing image;
(4b) solving the following formula by adopting an optimization equation equivalent transformation solving method to obtain an optimal high-resolution remote sensing image:
the method comprises the following steps of obtaining a high-resolution remote sensing image, obtaining a low-resolution remote sensing image, obtaining a down-sampling matrix, obtaining a Gaussian fuzzy matrix, obtaining a high-resolution remote sensing image, obtaining a self-adaptive filter coefficient matrix, wherein K represents an optimal high-resolution remote sensing image, g represents a low-resolution remote sensing image, W represents a down-sampling matrix, H represents a Gaussian fuzzy matrix, K represents a high-resolution remote sensing image;represents the optimization equation, | ·| luminance2Expressing a normal form operation, | ·| non-conducting phosphor2Expressing a square operation of a norm taking mode;
(5) calculating the relative error between the optimal high-resolution remote sensing image and the initial high-resolution remote sensing image by using the following formula:
wherein gamma represents the relative error between the optimal high-resolution remote sensing image and the initial high-resolution remote sensing image, and K represents the optimal high-resolution remote sensing image; k is a radical of0Representing an initial high resolution remote sensing image; i | · | purple wind2Expressing a model taking operation;
(6) judging whether the relative error meets a termination condition, if so, executing the step (8); otherwise, executing the step (7);
(7) and (3) updating data:
assigning the pixel value of the optimal high-resolution remote sensing image to the pixel of the initial high-resolution remote sensing image, and executing the step (2);
(8) and outputting the optimal high-resolution remote sensing image.
Compared with the prior art, the invention has the following advantages:
firstly, the invention can realize the high-resolution reconstruction of the image only by inputting one image, does not need other conditions when reconstructing the image, overcomes the harsh conditions that the input image needs to be added with segmentation smoothness and the like in the prior art, and improves the universality.
Secondly, because the invention adopts the optimization operation to the high-frequency part of the high-resolution image, the reconstructed image has sharp edges and abundant texture details, and the defect of fuzzy edge of the reconstructed image in the prior art is overcome, so that the invention improves the reconstruction quality of the image.
Thirdly, because the invention reconstructs the high-resolution image by utilizing the optimization operation, the defect of high complexity of sparse coding operation in the prior art is overcome, the invention has low calculation complexity, high convergence rate of the optimization operation and improved efficiency.
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FIG. 1 is a flow chart of the present invention;
FIG. 2 is a schematic diagram of a low resolution image generated in step 1 of the present invention;
FIG. 3 is a diagram showing the effect of simulation experiment 1 according to the present invention;
fig. 4 is a graph showing the effect of simulation experiment 2 of the present invention.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
Referring to fig. 1, the embodiment of the present invention is as follows:
step 1, obtaining an initial high-resolution remote sensing image.
And inputting a high-resolution remote sensing image. The remote sensing image input by the embodiment of the invention is arbitrarily acquired from a network. A gaussian blur matrix with mean 0, variance 1.6, and size 7 × 7 was generated by MATLAB software. And convolving the input high-resolution remote sensing image by using the generated Gaussian blur matrix to obtain the high-resolution blurred remote sensing image. And then, respectively sampling the high-resolution fuzzy remote sensing image by 3 times in the horizontal direction and the vertical direction to obtain a low-resolution remote sensing image.
And amplifying the low-resolution remote sensing image by 3 times by adopting an interpolation amplification method to obtain an initial high-resolution remote sensing image.
The interpolation amplification method is a method for amplifying an image by adopting one of nearest neighbor interpolation and bilinear interpolation. In the embodiment of the invention, the interpolation amplification method adopts a bilinear interpolation method.
And 2, calculating a coefficient matrix of the adaptive filter.
And generating the self-adaptive filter of the initial high-resolution remote sensing image by adopting a self-adaptive filter generation method to obtain a coefficient matrix of the self-adaptive filter.
Using the formula: u. of0＝k0-Fk0Obtaining an initial high-frequency remote sensing image, wherein u0Representing the initial high-frequency remote sensing image, k0Representing the initial high resolution remote sensing image and F representing the adaptive filter coefficient matrix.
The self-adaptive filter generation method is a generation method based on one of a non-local mean method and an image guide method. In an embodiment of the invention a non-local mean method is used.
And 3, obtaining an optimal high-frequency remote sensing image.
And (4) carrying out pairwise difference on two adjacent columns of pixels in the initial high-resolution remote sensing image to obtain a horizontal gradient operator of the remote sensing image. And carrying out pairwise difference on two adjacent lines of pixels in the initial high-resolution remote sensing image to obtain a vertical gradient operator of the remote sensing image.
Using the formula:obtaining the total variation of the high-frequency remote sensing image, wherein Q represents the total variation of the high-frequency remote sensing image, D1And D2And u represents a high-frequency remote sensing image. And performing wavelet domain transformation on the high-frequency remote sensing image to obtain a wavelet transformation matrix of the high-frequency remote sensing image.
Using the formula: b ═ ΨTu, obtaining a projection matrix of the high-frequency remote sensing image in a wavelet domain, wherein B represents the projection matrix of the high-frequency remote sensing image in the wavelet domain, psiTAnd u represents the high-frequency remote sensing image.
Solving the following formula by adopting an optimization equation solving method to obtain an optimal high-frequency remote sensing image:
wherein U represents the optimal high-frequency remote sensing image α1Regularization parameters representing total variation of high frequency remote sensing images, α1＝4.0e-5；α2Regularization parameters representing the projection of high frequency remote sensing images in the wavelet domain, α2＝3.0e-5；D1And D2Respectively representing horizontal and vertical gradient operators of the remote sensing image; u represents a high-frequency remote sensing image; ΨTA transposed matrix of a wavelet transformation matrix representing the high-frequency remote sensing image, η a penalty factor of the high-frequency remote sensing image constraint, η being 2, u0Representing an initial high-frequency remote sensing image;represents the optimization equation, | ·| luminance1,2Expressing a normal form operation, | ·| non-conducting phosphor2Express normThe equation square operation. The optimization equation solving method is any one of a combined alternative iteration method, an iterative shrinkage method, a two-step iterative shrinkage method and a weighted least square method.
The embodiment of the invention adopts a combined alternate iteration method, and the specific steps of the combined alternate iteration method are as follows:
firstly, setting initial parameters and starting iterative operation.
Set the maximum number of iterations to 20 and the threshold to 10-4。
Secondly, calculating an approximation matrix of a high-frequency image gradient domain by using the following formula:
wherein, w1And w2Respectively representing approximation matrixes of horizontal gradient and vertical gradient of the high-frequency remote sensing image; sigma1Representing penalty factors for approximating horizontal and vertical gradients of the high-frequency remote sensing image α1The regularization parameter represents the total variation of the high-frequency remote sensing image; lambda [ alpha ]11And λ12Represents an auxiliary variable, the initial value of which is 0; u represents a high-frequency remote sensing image; d1And D2Respectively representing horizontal and vertical gradient operators of the remote sensing image; | · | represents an absolute value operation; max (·) denotes a max operation; sgn (·) represents the sign operator operation.
Thirdly, calculating an approximation matrix of the wavelet transform coefficient of the high-frequency remote sensing image by using the following formula:
wherein z represents an approximation matrix of wavelet transform coefficients of the high-frequency remote sensing image; ΨTConversion of wavelet transformation matrix representing high frequency remote sensing imageArranging a matrix; u represents a high-frequency remote sensing image; sigma2Representing penalty factors when approximating wavelet transform coefficients of the high-frequency remote sensing image α2Representing regularization parameters of the projection of the high-frequency remote sensing image in a wavelet domain; lambda [ alpha ]2Represents an auxiliary variable, the initial value of which is 0; | · | represents an absolute value operation; max (·) denotes a max operation; sgn (·) represents the sign operator operation.
Solving the optimal equation of the optimal high-frequency remote sensing image is equivalent to solving the following linear equation of unity:
the one-dimensional equations described above can be efficiently solved using a two-dimensional fast discrete fourier transform and inverse transform, wherein,represents a merge D1Matrix sum D2Matrix, D1And D2Respectively representing horizontal and vertical gradient operators of the remote sensing image;represents a merge w1Matrix sum w2Matrix, w1And w2Respectively representing approximation matrixes of horizontal gradient and vertical gradient of the high-frequency remote sensing image; sigma1Representing penalty factors, σ, approximating horizontal and vertical gradients of the high-frequency remote sensing image2Representing a penalty factor when approaching a wavelet transform coefficient of the high-frequency remote sensing image; u represents a high-frequency remote sensing image; psi represents a wavelet transformation matrix of the high-frequency remote sensing image; z represents an approximation matrix of the wavelet transform coefficient of the high-frequency remote sensing image; lambda [ alpha ]2Representing auxiliary variables, η representing penalty factors of high-frequency remote sensing image constraint, u0Representing the initial high frequency remote sensing image.
Step four, updating parameters:
the parameters are updated using the following equations:
wherein,andthe parameter value representing the k-th iteration,anda parameter value representing the (k + 1) th iteration;andparameter values representing the kth and the (k + 1) th iterations, respectively;represents a fixed parameter, in the example, 1.618; d1And D2Respectively representing horizontal and vertical gradient operators of the remote sensing image; w is a1And w2Respectively representing approximation matrixes of horizontal gradient and vertical gradient of the high-frequency remote sensing image; u represents a high-frequency remote sensing image; ΨTWavelet representing high frequency remote sensing imageTransforming a transpose of the matrix; z represents an approximation matrix of the wavelet transform coefficient of the high-frequency remote sensing image;a fixed parameter is indicated, and μ ═ 1.022 is taken in the examples.
And fifthly, judging whether to terminate the iteration by using the following joint alternate iteration termination conditions:
a joint alternate iteration termination condition 1 is reached, wherein the maximum iteration number is initially set, and the maximum iteration number is 20 in the embodiment of the invention;
and (2) judging whether the relative change rate of the high-frequency information in two adjacent iterations is less than or equal to a given threshold value by using the following formula:
wherein u iskHigh-frequency remote sensing image, u, representing the kth iterationk+1The high-frequency remote sensing image representing the k +1 th iteration is represented by zeta representing a threshold, and zeta is 10 in the embodiment-4，||·||2A canonical operation is shown.
And (4) as long as any one of the joint alternation iteration termination condition 1 and the joint alternation iteration termination condition 2 is met, terminating the iteration and turning to the step 4, otherwise, turning to the second step and continuing the iteration.
And 4, obtaining an optimal high-resolution remote sensing image.
And obtaining a down-sampling matrix corresponding to the position relation between the pixels of the low-resolution remote sensing image and the pixels of the high-resolution remote sensing image.
Solving the following formula by adopting an optimization equation equivalent transformation solving method to obtain an optimal high-resolution remote sensing image:
the self-adaptive filter comprises a high-resolution remote sensing image, a low-resolution remote sensing image, a down-sampling matrix, a Gaussian fuzzy matrix, a high-resolution remote sensing image, a penalty factor, β to 2, a self-adaptive filter coefficient matrix and a self-adaptive filter coefficient matrix, wherein K represents an optimal high-resolution remote sensing image, g represents a low-resolution remote sensing image, W represents a down-sampling matrix, H represents a Gaussian fuzzy matrix, K represents a high-resolution remote sensing image, β represents a penalty;represents the optimization equation, | ·| luminance2Expressing a normal form operation, | ·| non-conducting phosphor2Representing a norm squaring operation. The optimization equation equivalence transformation solving method is a method for transforming an optimization equation into a linear equation by adopting an equivalence transformation method.
And 5, calculating the relative error between the optimal high-resolution remote sensing image and the initial high-resolution remote sensing image by using the following formula.
Wherein gamma represents the relative error between the optimal high-resolution remote sensing image and the initial high-resolution remote sensing image, and K represents the optimal high-resolution remote sensing image; k is a radical of0Representing an initial high resolution remote sensing image; i | · | purple wind2A canonical operation is shown.
Step 6, judging whether the relative error meets a termination condition, if so, executing step 8; otherwise, step 7 is performed.
The termination condition set by the invention is that gamma is less than or equal to a tolerance limit, and the value range is ∈ (10)-6,10-2) Positive number of (c). In the examples of the present invention, 10 is taken-4。
And 7, updating the data.
And (3) assigning the pixel value of the optimal high-resolution remote sensing image to the pixel of the initial high-resolution remote sensing image, and executing the step 2.
And 8, outputting the optimal high-resolution remote sensing image.
The super-resolution effect of the image of the present invention is further described below with reference to the following embodiments:
1. simulation experiment conditions are as follows:
the simulation experiment running system adopts an Intel (R) core (TM) i7-2600 CPU 650@3.40GHz 64-bit Windows operating system, and simulation software adopts MATLAB (R2013 b).
2. Simulation experiment contents:
in the embodiment of the present invention, the parameters are uniformly set to be fixed values, so that α1＝4.0e-5，α2＝3.0e-5，η＝2，β＝2，＝10-5。
Fig. 2 is a schematic diagram of two low resolution remote sensing images. And randomly downloading two gray remote sensing images from the network to serve as high-resolution remote sensing images of the simulation experiment. And respectively convolving the two high-resolution remote sensing images by using the Gaussian fuzzy matrix to obtain two high-resolution fuzzy remote sensing images. And then, respectively sampling the high-resolution fuzzy remote sensing image by 3 times in the horizontal direction and the vertical direction to obtain two low-resolution remote sensing images. Fig. 2(a) is used for simulation experiment 1, and fig. 2(b) is used for simulation experiment 2.
Fig. 3 is a graph showing the effect of simulation experiment 1. Fig. 3(a) is an optimal high resolution image obtained using prior art bilinear interpolation. FIG. 3(b) is an optimal high-resolution Image obtained by using the Image super-resolution method proposed by Zuo, W, Lin, Z in the document "A Generalized additive accelerated sequential Gradient Image application for Total-Variation-Based Image retrieval" (IEEE trans. on Image Processing vol.20 No.10 pp.2748-2759 Oct.2011.). Fig. 3(c) is an optimum high-Resolution Image obtained by the Super-Resolution method proposed in "Image Super-Resolution Via sparse representation" (IEEE trans. on Image Processing vol.19 No.11 pp.2861-2873 nov.2010) by four people, Yang, J, Wright, J, Huang, T, Ma, y. Fig. 3(d) is an optimal high resolution image obtained using the method of the present invention.
Fig. 4 is a graph showing the effect of simulation experiment 2. Fig. 4(a) is an optimal high resolution image obtained using prior art bilinear interpolation. FIG. 4(b) is an optimal high-resolution Image obtained by using the Image super-resolution method proposed by Zuo, W, Lin, Z in the document "A Generalized additive accelerated sequential Gradient Image application for Total-Variation-Based Image retrieval" (IEEE trans. on Image Processing vol.20 No.10 pp.2748-2759 Oct.2011.). Fig. 4(c) is an optimum high-Resolution Image obtained by the Super-Resolution method proposed in "Image Super-Resolution Via sparse representation" (IEEE trans. on Image Processing vol.19 No.11 pp.2861-2873 nov.2010) by four people, Yang, J, Wright, J, Huang, T, Ma, y. Fig. 4(d) is an optimal high resolution image obtained using the method of the present invention.
3. And (3) simulation result analysis:
in the embodiment of the invention, the peak signal-to-noise ratio index is adopted to evaluate the experimental result:
where PSNR represents the peak signal-to-noise ratio, K represents the optimal high resolution image, and K0Expressed as a high resolution image, log, obtained by super-resolution amplification using the observed low resolution image10(. h) represents a logarithmic operation, ∑ (& gth) represents a summation operation, | & lt| & gtL & gtO & lt2A canonical operation is shown.
The peak signal-to-noise ratio of each image in fig. 3 is (in dB) in order: 25.08, 29.49, 25.34, 32.42.
The peak signal-to-noise ratio of each image in fig. 4 is (in dB) in order: 21.86, 24.65, 22.13, 26.36.
The larger the peak signal-to-noise ratio value, the better the performance of the super-resolution method. The peak snr of fig. 3(d) is greater than that of fig. 3(a), 3(b) and 3(c), and the peak snr of fig. 4(d) is greater than that of fig. 4(a), 4(b) and 4(c), so that it can be seen that the super-resolution method of the present invention is better than the other three prior arts.
As can be further seen from fig. 3 and 4, the visual effects of fig. 3(a) and 4(a) are the worst. The images of fig. 3(b) and fig. 4(b) are relatively clear, but the blocking effect of the edge of the object is relatively obvious. The blocking effect of the images in fig. 3(c) and 4(c) is suppressed as compared with that in fig. 3(b) and 4(b), but the images are blurred as a whole and the edges are not sharp enough. The images in fig. 3(d) and fig. 4(d) have substantially no blockiness effect, the texture of the images is clear, the edge effect is good, and the high-frequency information of the images is better recovered.
In conclusion, the image super-resolution method provided by the invention has the advantages that the peak signal-to-noise ratio result is better, and the visual effect is also good.
Claims (6)
1. An image super-resolution method based on adaptive filtering and regular constraint comprises the following steps:
(1) obtaining an initial high-resolution remote sensing image:
(1a) inputting a high-resolution remote sensing image;
(1b) generating a Gaussian blur matrix with the mean value of 0, the variance of 1.6 and the size of 7 multiplied by 7;
(1c) convolving the high-resolution remote sensing image by using a Gaussian fuzzy matrix to obtain a high-resolution fuzzy remote sensing image;
(1d) respectively sampling the high-resolution fuzzy remote sensing image by 3 times in the horizontal direction and the vertical direction to obtain a low-resolution remote sensing image;
(1e) amplifying the low-resolution remote sensing image by 3 times by adopting an interpolation amplification method to obtain an initial high-resolution remote sensing image;
(2) calculating an adaptive filter coefficient matrix:
(2a) generating a self-adaptive filter of the initial high-resolution remote sensing image by adopting a self-adaptive filter generation method to obtain a coefficient matrix of the self-adaptive filter;
(2b) calculating an initial high frequency remote sensing image by using the following formula:
u0＝k0-Fk0
wherein u is0Representing the initial high-frequency remote sensing image, k0Representing an initial high-resolution remote sensing image, and F representing a coefficient matrix of an adaptive filter;
(3) obtaining an optimal high-frequency remote sensing image:
(3a) two adjacent columns of pixels in the initial high-resolution remote sensing image are subjected to pairwise difference to obtain a horizontal gradient operator of the remote sensing image; carrying out pairwise difference on two adjacent lines of pixels in the initial high-resolution remote sensing image to obtain a vertical gradient operator of the remote sensing image;
(3b) calculating the total variation of the high-frequency remote sensing image by using the following formula:
wherein Q represents the total variation of the high-frequency remote sensing image, D1And D2Respectively representing horizontal and vertical gradient operators of the remote sensing image, and u represents a high-frequency remote sensing image;
(3c) performing wavelet domain transformation on the high-frequency remote sensing image to obtain a wavelet transformation matrix of the high-frequency remote sensing image;
(3d) calculating a projection matrix of the high-frequency remote sensing image in a wavelet domain by using the following formula:
B＝ΨTu
wherein, B represents a projection matrix of the high-frequency remote sensing image in a wavelet domain, psiTA transposed matrix representing a wavelet transformation matrix of the high-frequency remote sensing image, and u represents the high-frequency remote sensing image;
(3e) solving the following formula by adopting an optimization equation solving method to obtain an optimal high-frequency remote sensing image:
wherein U represents the optimal high-frequency remote sensing image α1Regularization parameters representing total variation of high frequency remote sensing images, α1＝4.0e-5；α2Regularization parameters representing the projection of high frequency remote sensing images in the wavelet domain, α2＝3.0e-5；D1And D2Representing horizontal and vertical, respectively, of remote-sensed imagesGradient operator; u represents a high-frequency remote sensing image; ΨTA transposed matrix of a wavelet transformation matrix representing the high-frequency remote sensing image, η a penalty factor of the high-frequency remote sensing image constraint, η being 2, u0Representing an initial high-frequency remote sensing image;represents the optimization equation, | ·| luminance1,2Expressing a normal form operation, | ·| non-conducting phosphor2Expressing a square operation of a norm taking mode;
(4) obtaining an optimal high-resolution remote sensing image:
(4a) obtaining a down-sampling matrix corresponding to the position relation between the pixels of the low-resolution remote sensing image and the pixels of the high-resolution remote sensing image;
(4b) solving the following formula by adopting an optimization equation equivalent transformation solving method to obtain an optimal high-resolution remote sensing image:
the method comprises the steps of obtaining a high-resolution remote sensing image, obtaining a low-resolution remote sensing image, obtaining a down-sampling matrix, obtaining a Gaussian fuzzy matrix, obtaining a high-resolution remote sensing image, obtaining a high-frequency part constraint penalty factor of the high-resolution remote sensing image by using K, obtaining a self-adaptive filter coefficient matrix by using β -2, obtaining a self-adaptive filterAn optimal high-frequency remote sensing image;represents the optimization equation, | ·| luminance2Expressing a normal form operation, | ·| non-conducting phosphor2Expressing a square operation of a norm taking mode;
(5) calculating the relative error between the optimal high-resolution remote sensing image and the initial high-resolution remote sensing image by using the following formula:
wherein gamma represents the relative error between the optimal high-resolution remote sensing image and the initial high-resolution remote sensing image, and K represents the optimal high-resolution remote sensing image; k is a radical of0Representing an initial high resolution remote sensing image; i | · | purple wind2Expressing a model taking operation;
(6) judging whether the relative error meets a termination condition, if so, executing the step (8); otherwise, executing the step (7);
(7) and (3) updating data:
assigning the pixel value of the optimal high-resolution remote sensing image to the pixel of the initial high-resolution remote sensing image, and executing the step (2);
(8) and outputting the optimal high-resolution remote sensing image.
2. The image super-resolution method based on adaptive filtering and regular constraint according to claim 1, wherein the interpolation amplification method in step (1e) is a method for amplifying the remote sensing image by adopting one of nearest neighbor interpolation and bilinear interpolation.
3. The image super-resolution method based on adaptive filtering and regularization constraint according to claim 1, wherein the adaptive filter generation method in step (2a) is a non-local mean method.
4. The image super-resolution method based on adaptive filtering and regularization constraint according to claim 1, wherein the solution method of the optimization equation in the step (3e) is any one of a joint alternating iteration method, an iterative shrinkage method and a weighted least square method.
5. The image super-resolution method based on adaptive filtering and regularization constraint according to claim 1, wherein said optimization equation equivalence transformation solving method in step (4b) is a method of transforming optimization equations into linear equations by using an equivalence transformation method.
6. The image super-resolution method based on adaptive filtering and regularization constraint according to claim 1, wherein the termination condition in step (6) is γ ≦ wherein γ represents the relative error between the optimal high resolution remote sensing image and the initial high resolution remote sensing image, represents the tolerance limit, and has a value ranging from ∈ (10)-6,10-2) Positive number of (c).
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