CN104200439B - Image super-resolution method based on adaptive filtering and regularization constraint - Google Patents

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

Image Super-resolution Method Based on Adaptive Filtering and Regular Constraint

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 canonical constraints in the fields of remote sensing images, video monitoring, and medical images. High-resolution images are reconstructed from high-resolution images and low-resolution medical images to improve the spatial resolution of images and preserve the accuracy of image edge structures to the greatest extent.

Background technique

In the imaging fields of remote sensing images, video surveillance, and medical images, a single image super-resolution reconstruction method that reconstructs a high-resolution image from a low-resolution image is used to improve image resolution. At present, single image is mainly based on sparse representation and regularized constraint methods to achieve super-resolution reconstruction.

Yang, J, Wright, J, Huang, T, Ma, Y. Four people in the literature "Image Super-Resolution ViaSparse Representation" (IEEE Trans. on Image Processing vol.19 no.11 pp.2861-2873 Nov.2010. ) discloses a method for realizing super-resolution reconstruction of a single image based on sparse representation. This method is given a low-resolution image, divides the image into multiple blocks, and sparsely encodes each low-resolution image block, so that it can adaptively find K low-resolution images in the low-resolution data block to minimize the representation error and the representation coefficients are sufficiently sparse, then linearly combine the K high-resolution image blocks corresponding to the low-resolution image blocks, and fuse all the high-resolution image blocks to obtain the final high-resolution image. The disadvantage of this method is that the sparse coding process is computationally complex, and this method does not process the edge and texture of the image.

Zuo, W, Lin, Z in the document "A Generalized Accelerated Accelerated Proximal Gradient Approach for Total-Variation-Based Image Restoration" (IEEE Trans.onImage Processing vol.20 no.10 pp.2748-2759 Oct.2011.) A method for solving super-resolution problems with gradient smoothness constraints is disclosed. This method transforms the super-resolution problem into an optimization problem by adding a penalty function, and obtains the final high-resolution image by solving the optimization problem. The disadvantage of this method is that the model of this method needs to be established under the assumption that the image is sliced and smooth, and such a precondition cannot be satisfied for all images. In addition, this method will also introduce block effects of the image, resulting in super-resolution The image is blurry.

The patent "Image Super-resolution Reconstruction Method Based on Sparse Representation" (application date: 2013.07.16, application number: 201310296581.3 publication number: CN 103366347 A) filed by Suzhou New Vision Culture Technology Development Co., Ltd. discloses a method based on sparse representation Image super-resolution reconstruction method. This method first calculates the gradient information of the low-resolution image and the residual information between the high-resolution image and the low-resolution image, then obtains the low-resolution feature set and the high-resolution feature set through the sparse expression method, and finally obtains the high-resolution feature set The corresponding residual information is found in the set, and the residual information is fused to the low-resolution image to obtain a high-resolution image. The shortcomings of this method are that the sparse representation method for calculating low-resolution feature sets and high-resolution feature sets has high computational complexity, poor real-time performance, and limited practical application range.

Contents of the invention

The purpose of the present invention is to address the deficiencies of the above-mentioned prior art, and propose an image super-resolution method based on adaptive filtering and regular constraints, by optimizing the high-frequency part of the constrained image, the obtained high-resolution image has sharp edges and Rich texture details.

Realize the concrete steps of the present invention as follows:

(1) Obtain the initial high-resolution remote sensing image:

(1a) Input a high-resolution remote sensing image;

(1b) Generate a Gaussian blur matrix with a mean value of 0, a variance of 1.6, and a size of 7×7;

(1c) Convolving the high-resolution remote sensing image with a Gaussian blur matrix to obtain a high-resolution blurred remote sensing image;

(1d) Downsampling the high-resolution fuzzy remote sensing image by 3 times in the horizontal and vertical directions respectively to obtain a low-resolution remote sensing image;

(1e) Enlarge the low-resolution remote sensing image by 3 times by using the interpolation amplification method to obtain the initial high-resolution image;

(2) Calculate the adaptive filter coefficient matrix:

(2a) Using an adaptive filter generation method to generate an adaptive filter for the initial high-resolution remote sensing image, and obtain an adaptive filter coefficient matrix;

(2b) Use the following formula to calculate the initial high-frequency remote sensing image:

u ₀ =k ₀ −Fk ₀

Among them, u ₀ represents the initial high-frequency remote sensing image, k ₀ represents the initial high-resolution remote sensing image, and F represents the adaptive filter coefficient matrix;

(3) Obtain the optimal high-frequency remote sensing image:

(3a) Make a difference between two adjacent columns of pixels in the initial high-resolution remote sensing image to obtain the horizontal gradient operator of the remote sensing image; make a difference between two adjacent rows of pixels in the initial high-resolution remote sensing image, Get the vertical gradient operator of the image;

(3b) Use the following formula to calculate the total variation of the high-frequency remote sensing image:

Among them, Q represents the total variation of high-frequency remote sensing images, D ₁ and D ₂ represent the horizontal and vertical gradient operators of remote sensing images, respectively, and u represents high-frequency remote sensing images;

(3c) performing wavelet domain transformation on the high-frequency remote sensing image to obtain a wavelet transform matrix of the high-frequency remote sensing image;

(3d) Calculate the projection matrix of the high-frequency remote sensing image in the wavelet domain by using the following formula:

B＝ ^ΨTu

Among them, B represents the projection matrix of the high-frequency remote sensing image in the wavelet domain, Ψ ^T represents the transpose matrix of the wavelet transformation matrix of the high-frequency remote sensing image, and u represents the high-frequency remote sensing image;

(3e) Use the optimization equation solution method to solve the following equation to obtain the optimal high-frequency remote sensing image:

Among them, U represents the optimal high-frequency remote sensing image; α ₁ represents the regularization parameter of the total variation of the high-frequency remote sensing image, α ₁ =4.0e ^-5 ; α ₂ represents the regularization parameter of the projection of the high-frequency remote sensing image in the wavelet domain , α ₂ =3.0e ^-5 ; D ₁ and D ₂ represent the horizontal and vertical gradient operators of the remote sensing image respectively; u represents the high-frequency remote sensing image; Ψ ^T represents the transpose matrix of the wavelet transform matrix of the high-frequency remote sensing image; η Represents the penalty factor of high-frequency remote sensing image constraints, η=2; u ₀ represents the initial high-frequency remote sensing image; Indicates the optimization equation, ||·|| ₁₂ represents the normal form operation, ||·|| ² represents the normal form square operation;

(4) Obtain the optimal high-resolution remote sensing image:

(4a) Corresponding to the positional relationship between the pixels of the low-resolution remote sensing image and the pixels of the high-resolution remote sensing image, a downsampling matrix is obtained;

(4b) Use the optimization equation equivalent conversion solution method to solve the following equation to obtain the optimal high-resolution remote sensing image:

Among them, K represents the optimal high-resolution remote sensing image; g represents the low-resolution remote sensing image; W represents the downsampling matrix; H represents the Gaussian blur matrix; k represents the high-resolution remote sensing image; Partial penalty factor, β=2; F represents the adaptive filter coefficient matrix; U represents the optimal high-frequency remote sensing image; Represents the optimization equation, ||·|| ₂ represents the normal form operation, ||·|| ² represents the normal form square operation;

(5) Use the following formula to calculate the relative error between the optimal high-resolution remote sensing image and the initial high-resolution remote sensing image:

Among them, γ represents the relative error between the optimal high-resolution remote sensing image and the initial high-resolution remote sensing image, K represents the optimal high-resolution remote sensing image; k ₀ represents the initial high-resolution remote sensing image; ||·|| ₂ represents the Paradigm operation;

(6) Judging whether the relative error satisfies the termination condition, if yes, execute step (8); otherwise, execute step (7);

(7) Data update:

Assign the pixel value of the optimal high-resolution remote sensing image to the pixel of the initial high-resolution remote sensing image, and perform step (2);

(8) Output the optimal high-resolution remote sensing image.

Compared with the prior art, the present invention has the following advantages:

First, because the present invention only needs to input one image to realize the high-resolution reconstruction of the image, no other conditions are needed when reconstructing the image, and it overcomes the harsh conditions of the prior art that need to add segmental smoothness to the input image, making the present invention Invention increases versatility.

Second, because the present invention optimizes the high-frequency part of the high-resolution image, the reconstructed image has sharp edges and rich texture details, which overcomes the shortcomings of the blurred edges of the reconstructed image in the prior art, making the present invention improve image quality. reconstruction quality.

Third, because the present invention reconstructs high-resolution images using optimization operations, it overcomes the disadvantage of high computational complexity of sparse coding in the prior art, so that the present invention has low computational complexity, fast convergence rate of optimization operations, and improved efficiency.

Description of drawings

Fig. 1 is a flowchart of the present invention;

Fig. 2 is the schematic diagram of the low resolution image that step 1 of the present invention generates;

Fig. 3 is the rendering of simulation experiment 1 of the present invention;

FIG. 4 is an effect diagram of simulation experiment 2 of the present invention.

detailed description

The present invention will be further described below in conjunction with the accompanying drawings.

With reference to Fig. 1, the embodiment of the present invention is as follows:

Step 1. Obtain an initial high-resolution remote sensing image.

Input a high-resolution remote sensing image. The remote sensing images input by the embodiments of the present invention are randomly obtained from the Internet. A Gaussian blur matrix with a mean value of 0, a variance of 1.6, and a size of 7×7 was generated by MATLAB software. The input high-resolution remote sensing image is convolved with the generated Gaussian blur matrix to obtain a high-resolution blurred remote sensing image. Then, the high-resolution fuzzy remote sensing image is down-sampled by 3 times in the horizontal direction and vertical direction respectively, and the low-resolution remote sensing image is obtained.

The low-resolution remote sensing image is magnified three times by interpolation amplification method to obtain the initial high-resolution remote sensing image.

The interpolation magnification method refers to a method of image magnification using one of nearest neighbor interpolation and bilinear interpolation. In the embodiment of the present invention, the interpolation amplification method adopts a bilinear interpolation method.

Step 2. Compute the adaptive filter coefficient matrix.

The adaptive filter generation method is used to generate the adaptive filter of the initial high-resolution remote sensing image, and the adaptive filter coefficient matrix is obtained.

The initial high-frequency remote sensing image is obtained by using the formula: u ₀ =k ₀ -Fk ₀ , where u ₀ represents the initial high-frequency remote sensing image, k ₀ represents the initial high-resolution remote sensing image, and F represents the adaptive filter coefficient matrix.

The adaptive filter generation method refers to a generation method using a non-local mean method and an image-guided method. In an embodiment of the present invention a non-local mean method is employed.

Step 3. Obtain the optimal high-frequency remote sensing image.

The horizontal gradient operator of the remote sensing image is obtained by taking the difference between two adjacent columns of pixels in the initial high-resolution remote sensing image. The vertical gradient operator of the remote sensing image is obtained by taking the difference between two adjacent rows of pixels in the initial high-resolution remote sensing image.

Use the formula: The total variation of the high-frequency remote sensing image is obtained, where Q represents the total variation of the high-frequency remote sensing image, D ₁ and D ₂ represent the horizontal and vertical gradient operators of the remote sensing image, and u represents the high-frequency remote sensing image. The wavelet domain transform is carried out on the high-frequency remote sensing image, and the wavelet transform matrix of the high-frequency remote sensing image is obtained.

Using the formula: B = Ψ ^T u, the projection matrix of the high-frequency remote sensing image in the wavelet domain is obtained, where B represents the projection matrix of the high-frequency remote sensing image in the wavelet domain, and Ψ ^T represents the transposition matrix of the wavelet transform matrix of the high-frequency remote sensing image , u represents the high-frequency remote sensing image.

The optimal high-frequency remote sensing image is obtained by solving the following formula with the optimization equation solution method:

Among them, U represents the optimal high-frequency remote sensing image; α ₁ represents the regularization parameter of the total variation of the high-frequency remote sensing image, α ₁ =4.0e ^-5 ; α ₂ represents the regularization parameter of the projection of the high-frequency remote sensing image in the wavelet domain , α ₂ =3.0e ^-5 ; D ₁ and D ₂ represent the horizontal and vertical gradient operators of the remote sensing image respectively; u represents the high-frequency remote sensing image; Ψ ^T represents the transpose matrix of the wavelet transform matrix of the high-frequency remote sensing image; η Represents the penalty factor of high-frequency remote sensing image constraints, η=2; u ₀ represents the initial high-frequency remote sensing image; Represents the optimization equation, ||·|| _1,2 represents the normal form operation, ||·|| ² represents the normal form square operation. The method of solving the optimization equation refers to the use of any one of the joint alternate iteration method, iterative contraction method, two-step iterative contraction method, and weighted least squares method.

Embodiments of the present invention adopt the joint alternate iteration method, and the specific steps of the joint alternate iteration are the following five steps:

The first step is to set the initial parameters and start the iterative operation.

Set the maximum number of iterations to 20, and set the threshold to 10 ^-4 .

In the second step, the approximation matrix of the high-frequency image gradient domain is calculated using the following formula:

Among them, w ₁ and w ₂ represent the approximation matrix of the horizontal gradient and vertical gradient of the high-frequency remote sensing image respectively; σ ₁ represents the penalty factor when approximating the horizontal gradient and vertical gradient of the high-frequency remote sensing image; α ₁ represents the full Variational regularization parameters; λ ₁₁ and λ ₁₂ represent auxiliary variables, whose initial value is 0; u represents high-frequency remote sensing images; D ₁ and D ₂ represent the horizontal and vertical gradient operators of remote sensing images, respectively; |·| Take the absolute value operation; max(·) means take the maximum value operation; sgn(·) means take the sign operator operation.

The third step is to calculate the approximation matrix of the wavelet transform coefficients of the high-frequency remote sensing image using the following formula:

Among them, z represents the approximation matrix of the wavelet transform coefficient of the high _- frequency remote sensing image; Ψ ^T represents the transpose matrix of the wavelet transform matrix of the high-frequency remote sensing image; u represents the high-frequency remote sensing image; α ₂ represents the regularization parameter of the projection of high-frequency remote sensing images in the wavelet domain; λ ₂ represents the auxiliary variable, whose initial value is 0; |·| represents the absolute value operation; max(·) represents the maximum value operation; sgn(·) represents the symbolic operator operation.

The optimization equation for solving the optimal high-frequency remote sensing image is equivalent to solving the following linear equation in one variable:

The above one-dimensional linear equation can be efficiently solved by using two-dimensional fast discrete Fourier transform and inverse transform, where, Indicates the combination of D ₁ matrix and D ₂ matrix, D ₁ and D ₂ respectively represent the horizontal and vertical gradient operators of the remote sensing image; Represents the combination of w ₁ matrix and w ₂ matrix, w ₁ and w ₂ represent the approximation matrix of the horizontal gradient and vertical gradient of high-frequency remote sensing images respectively; σ ₁ represents the penalty factor when approximating the horizontal gradient and vertical gradient of high-frequency remote sensing images, σ ₂ represents the penalty factor when approaching the wavelet transform coefficients of high-frequency remote sensing images; u represents high-frequency remote sensing images; Ψ represents the wavelet transform matrix of high-frequency remote sensing images; z represents the approximation matrix of wavelet transform coefficients of high-frequency remote sensing images _; Auxiliary variable; η represents the penalty factor of high-frequency remote sensing image constraints; u ₀ represents the initial high-frequency remote sensing image.

The fourth step is to update the parameters:

The parameters are updated using the following formulas:

in, with Indicates the parameter value of the kth iteration, with Indicates the parameter value of the k+1th iteration; with Represent the parameter values of the kth and k+1th iterations, respectively; Represents a fixed parameter, ρ=1.618 in the embodiment; D ₁ and D ₂ represent the horizontal and vertical gradient operators of the remote sensing image respectively; w ₁ and w ₂ represent the approximation of the horizontal gradient and the vertical gradient of the high-frequency remote sensing image respectively matrix; u represents the high-frequency remote sensing image; Ψ ^T represents the transpose matrix of the wavelet transform matrix of the high-frequency remote sensing image; z represents the approximation matrix of the wavelet transform coefficient of the high-frequency remote sensing image; represents a fixed parameter, and μ=1.022 is taken in the embodiment.

The fifth step is to use the following joint alternate iteration termination conditions to determine whether to terminate the iteration:

Joint alternate iteration termination condition 1. reaches the maximum number of iterations initially set, and the maximum number of iterations is 20 times in the embodiment of the present invention;

Joint alternate iteration termination condition 2. Use the following formula to determine whether the relative change rate of high-frequency information is less than or equal to a given threshold during two adjacent iterations:

Among them, u ^k represents the high-frequency remote sensing image of the k-th iteration, u ^k+1 represents the high-frequency remote sensing image of the k+1-th iteration, ζ represents the threshold, and in the embodiment, ζ=10 ^-4 , ||·| | ₂ means to take the normal form operation.

As long as any one of joint alternating iteration termination condition 1 and joint alternating iteration termination condition 2 is satisfied, the iteration is terminated and go to step 4, otherwise, go to the second step and continue iteration.

Step 4. Obtain the optimal high-resolution remote sensing image.

Corresponding to the positional relationship between the pixels of the low-resolution remote sensing image and the pixels of the high-resolution remote sensing image, the downsampling matrix is obtained.

The optimal high-resolution remote sensing image is obtained by solving the following equation by using the optimization equation equivalent conversion solution method:

Among them, K represents the optimal high-resolution remote sensing image; g represents the low-resolution remote sensing image; W represents the downsampling matrix; H represents the Gaussian blur matrix; k represents the high-resolution remote sensing image; β represents the penalty of the high-resolution remote sensing image constraint Factor, β=2; F represents the adaptive filter coefficient matrix; U represents the optimal high-frequency remote sensing image; Indicates the optimization equation, ||·|| ₂ represents the normal form operation, and ||·|| ² represents the normal form square operation. The optimization equation equivalent conversion solution method refers to the method of converting the optimization equation into a linear equation by using the equivalent conversion method.

Step 5. Using the following formula, calculate the relative error between the optimal high-resolution remote sensing image and the initial high-resolution remote sensing image.

Among them, γ represents the relative error between the optimal high-resolution remote sensing image and the initial high-resolution remote sensing image, K represents the optimal high-resolution remote sensing image; k ₀ represents the initial high-resolution remote sensing image; ||·|| ₂ represents the Paradigm operation.

Step 6. Judging whether the relative error satisfies the termination condition, if yes, execute step 8; otherwise, execute step 7.

The termination condition set in the present invention is: γ≤ε, where ε is a tolerance limit, and its value range is a positive number of ε∈(10 ⁻⁶ , 10 ⁻² ). In the embodiment of the present invention, ε=10 ^-4 is taken.

Step 7. Data update.

Assign the pixel values of the optimal high-resolution remote sensing image to the pixels of the initial high-resolution remote sensing image, and perform step 2.

Step 8. Output the optimal high-resolution remote sensing image.

The image super-resolution effect of the present invention will be further described below in conjunction with the embodiments:

1. Simulation experiment conditions:

The simulation experiment operating system of the present invention adopts Intel(R) Core(TM) i7-2600 CPU 650@3.40GHz, 64-bit Windows operating system, and the simulation software adopts MATLAB(R2013b).

2. Simulation experiment content:

In the embodiment of the present invention, the uniformly set parameters are fixed values, such that α ₁ =4.0e ^-5 , α ₂ =3.0e ^-5 , η=2, β=2, ε=10 ^-5 .

Figure 2 is a schematic diagram of two low-resolution remote sensing images. Two grayscale remote sensing images are downloaded from the Internet as high-resolution remote sensing images for the simulation experiment. Two high-resolution remote sensing images are convoluted with Gaussian blur matrix to obtain two high-resolution blurred remote sensing images. Next, the high-resolution fuzzy remote sensing image is down-sampled by 3 times in the horizontal direction and vertical direction respectively, and two low-resolution remote sensing images are obtained. Figure 2(a) is used for simulation experiment 1, and Figure 2(b) is used for simulation experiment 2.

Fig. 3 is the effect diagram of simulation experiment 1. Figure 3(a) is the optimal high-resolution image obtained by bilinear interpolation in the prior art. Figure 3(b) is based on Zuo, W, Lin, and Z in the literature "A Generalized Accelerated Accelerated Proximal Gradient Approach for Total-Variation-Based Image Restoration" (IEEE Trans.on Image Processing vol.20 no.10 pp.2748- 2759Oct.2011.) The optimal high-resolution image obtained by the image super-resolution method proposed in 2759Oct.2011.). Figure 3(c) is based on Yang, J, Wright, J, Huang, T, Ma, Y. Four people in the document "Image Super-Resolution Via Sparse Representation" (IEEE Trans. on Image Processing vol.19 no.11 pp. 2861-2873Nov.2010.) The optimal high-resolution image obtained by the super-resolution method proposed in 2861-2873Nov.2010.). Fig. 3(d) is the optimal high-resolution image obtained by the method of the present invention.

FIG. 4 is an effect diagram of simulation experiment 2. Fig. 4(a) is the optimal high-resolution image obtained by bilinear interpolation in the prior art. Figure 4(b) is based on Zuo, W, Lin, and Z in the literature "A Generalized Accelerated Accelerated Proximal Gradient Approach for Total-Variation-Based Image Restoration" (IEEE Trans.on Image Processing vol.20 no.10 pp.2748- 2759Oct.2011.) The optimal high-resolution image obtained by the image super-resolution method proposed in 2759Oct.2011.). Figure 4(c) is based on Yang, J, Wright, J, Huang, T, Ma, Y. Four people in the document "Image Super-Resolution Via Sparse Representation" (IEEE Trans. on Image Processing vol.19 no.11 pp. 2861-2873Nov.2010.) The optimal high-resolution image obtained by the super-resolution method proposed in 2861-2873Nov.2010.). Fig. 4(d) is the optimal high-resolution image obtained by the method of the present invention.

3. Simulation result analysis:

In the embodiments of the present invention, the peak signal-to-noise ratio index is used to evaluate the experimental results:

Among them, PSNR represents the peak signal-to-noise ratio, K represents the optimal high-resolution image, k ₀ represents the high-resolution image obtained by super-resolution amplification using the observed low-resolution image, and log ₁₀ ( ) represents the logarithm operation, ∑(·) represents the sum operation, ||·|| ₂ represents the normal form operation.

The peak signal-to-noise ratios of each image in Fig. 3 are (in dB): 25.08, 29.49, 25.34, 32.42.

The peak signal-to-noise ratios of the images in Fig. 4 are (in dB): 21.86, 24.65, 22.13, and 26.36.

The larger the peak signal-to-noise ratio, the better the performance of the super-resolution method. The peak signal-to-noise ratio of Figure 3(d) is greater than that of Figure 3(a), Figure 3(b), and Figure 3(c), and the peak signal-to-noise ratio of Figure 4(d) is greater than that of Figure 4(a), Figure 4(b ), Fig. 4(c), it can be seen that the super-resolution method of the present invention is better than the other three prior art methods.

It can be further seen from Figure 3 and Figure 4 that the visual effects of Figure 3(a) and Figure 4(a) are the worst. The images in Figure 3(b) and Figure 4(b) are relatively clear, but the block effect at the edge of the object is more obvious. The blocky effect of the image in Figure 3(c) and Figure 4(c) is suppressed compared with that in Figure 3(b) and Figure 4(b), but the overall image is somewhat blurred and the edges are not clear enough. The images in Figure 3(d) and Figure 4(d) basically have no block effect, the texture of the image is clear, the edge effect is good, and the high-frequency information of the image is restored well.

To sum up, the image super-resolution method of the present invention not only has better peak signal-to-noise ratio results, but also has good visual effects.

Claims (6)

1. An image super-resolution method based on adaptive filtering and regular constraints, comprising the following steps: (1) Obtain the initial high-resolution remote sensing image: (1a) Input a high-resolution remote sensing image; (1b) Generate a Gaussian blur matrix with a mean value of 0, a variance of 1.6, and a size of 7×7; (1c) Convolving the high-resolution remote sensing image with a Gaussian blur matrix to obtain a high-resolution blurred remote sensing image; (1d) Downsampling the high-resolution fuzzy remote sensing image by 3 times in the horizontal and vertical directions respectively to obtain a low-resolution remote sensing image; (1e) Enlarge the low-resolution remote sensing image by 3 times by using the interpolation amplification method to obtain the initial high-resolution remote sensing image; (2) Calculate the adaptive filter coefficient matrix: (2a) Using an adaptive filter generation method to generate an adaptive filter for the initial high-resolution remote sensing image, and obtain an adaptive filter coefficient matrix; (2b) Use the following formula to calculate the initial high-frequency remote sensing image: u ₀ =k ₀ −Fk ₀ Among them, u ₀ represents the initial high-frequency remote sensing image, k ₀ represents the initial high-resolution remote sensing image, and F represents the adaptive filter coefficient matrix; (3) Obtain the optimal high-frequency remote sensing image: (3a) Make a difference between two adjacent columns of pixels in the initial high-resolution remote sensing image to obtain the horizontal gradient operator of the remote sensing image; make a pairwise difference between two adjacent rows of pixels in the initial high-resolution remote sensing image, Obtain the vertical gradient operator of the remote sensing image; (3b) Use the following formula to calculate the total variation of the high-frequency remote sensing image: $\mathrm{<span\; class="notranslate">\; Q</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 2</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 1</span>}}$ Among them, Q represents the total variation of high-frequency remote sensing images, D ₁ and D ₂ represent the horizontal and vertical gradient operators of remote sensing images, respectively, and u represents high-frequency remote sensing images; (3c) performing wavelet domain transformation on the high-frequency remote sensing image to obtain a wavelet transform matrix of the high-frequency remote sensing image; (3d) Calculate the projection matrix of the high-frequency remote sensing image in the wavelet domain by using the following formula: B＝ ^ΨTu Among them, B represents the projection matrix of the high-frequency remote sensing image in the wavelet domain, Ψ ^T represents the transpose matrix of the wavelet transformation matrix of the high-frequency remote sensing image, and u represents the high-frequency remote sensing image; (3e) Use the optimization equation solution method to solve the following equation to obtain the optimal high-frequency remote sensing image: $\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arg</span>}\underset{\mathrm{<span\; class="notranslate">\; u</span>}}{\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; \{</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 2</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; \&Psi;</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \}</span>$ Among them, U represents the optimal high-frequency remote sensing image; α ₁ represents the regularization parameter of the total variation of the high-frequency remote sensing image, α ₁ =4.0e ^-5 ; α ₂ represents the regularization parameter of the projection of the high-frequency remote sensing image in the wavelet domain , α ₂ =3.0e ^-5 ; D ₁ and D ₂ represent the horizontal and vertical gradient operators of the remote sensing image respectively; u represents the high-frequency remote sensing image; Ψ ^T represents the transpose matrix of the wavelet transform matrix of the high-frequency remote sensing image; η Represents the penalty factor of high-frequency remote sensing image constraints, η=2; u ₀ represents the initial high-frequency remote sensing image; Represents the optimization equation, ||·|| _{1, 2} represents the normal form operation, ||·|| ² represents the normal form square operation; (4) Obtain the optimal high-resolution remote sensing image: (4a) Corresponding to the positional relationship between the pixels of the low-resolution remote sensing image and the pixels of the high-resolution remote sensing image, a downsampling matrix is obtained; (4b) Use the optimization equation equivalent conversion solution method to solve the following equation to obtain the optimal high-resolution remote sensing image: $\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arg</span>}\underset{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; \{</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; g</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; W</span>}\mathrm{<span\; class="notranslate">\; h</span>}\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; f</span>}\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \}</span>$ Among them, K represents the optimal high-resolution remote sensing image; g represents the low-resolution remote sensing image; W represents the downsampling matrix; H represents the Gaussian blur matrix; k represents the high-resolution remote sensing image; Partial penalty factor, β=2; F represents the adaptive filter coefficient matrix; U represents the optimal high-frequency remote sensing image; Represents the optimization equation, ||·|| ₂ represents the normal form operation, ||·|| ² represents the normal form square operation; (5) Use the following formula to calculate the relative error between the optimal high-resolution remote sensing image and the initial high-resolution remote sensing image: $\mathrm{<span\; class="notranslate">\; \&gamma;</span>}<span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}$ Among them, γ represents the relative error between the optimal high-resolution remote sensing image and the initial high-resolution remote sensing image, K represents the optimal high-resolution remote sensing image; k ₀ represents the initial high-resolution remote sensing image; ||·|| ₂ represents the Paradigm operation; (6) Judging whether the relative error satisfies the termination condition, if yes, execute step (8); otherwise, execute step (7); (7) Data update: Assign the pixel value of the optimal high-resolution remote sensing image to the pixel of the initial high-resolution remote sensing image, and perform step (2); (8) Output the optimal high-resolution remote sensing image. 2. The image super-resolution method based on adaptive filtering and regular constraints according to claim 1, characterized in that, the interpolation amplification method described in step (1e) refers to the use of nearest neighbor interpolation, bilinear interpolation A method for zooming in on remote sensing images. 3. The image super-resolution method based on adaptive filtering and regular constraints according to claim 1, characterized in that the adaptive filter generation method described in step (2a) refers to the use of a non-local mean method. 4. the image superresolution method based on adaptive filtering and regular constraint according to claim 1, is characterized in that, the optimization equation solution method described in step (3e) refers to, adopts joint alternating iteration method, iterative contraction method , any one of the weighted least squares methods. 5. the image super-resolution method based on adaptive filtering and regular constraint according to claim 1, is characterized in that, the optimization equation described in the step (4b) is equivalent to conversion solution method refers to, adopts equivalent conversion method, A method for converting an optimization equation into a linear equation. 6. The image super-resolution method based on adaptive filtering and regular constraints according to claim 1, wherein the termination condition described in step (6) refers to γ≤ε, where γ represents the optimal high-resolution The relative error between the remote sensing image and the initial high-resolution remote sensing image, ε represents the tolerance limit, and its value range is a positive number of ε∈(10 ^-6 ,10 ^-2 ).