A Compressive Sensing Reconstruction Method Based on Learning Sampling and Convolutional Neural Network

Abstract

A compressive sensing reconstruction method based on learning sampling and convolutional neural network can sample and reconstruct a restored image at a low sampling rate through a system model for an image input. The present invention combines the CSNet network and the CombNet network, and uses wavelet transform as a denoising means to achieve maximum reconstruction of the image under the condition of a low sampling rate, which can well improve the signal transmission bandwidth problem, save transmission time and storage space, and enable the compressive sensing technology to have higher efficiency and better performance in the fields of signal transmission and image compression.

Description

Technical Field

[0001] The present invention belongs to the field of artificial intelligence and relates to a compressive sensing reconstruction method based on learning sampling and convolutional neural network. Background Art

[0002] The theory of Compressive Sensing (CS) was proposed by CANDES et al. in 2006. This theory states that when a signal itself or in a transform domain is sparse, the original high-dimensional signal can be projected onto a low-dimensional space through an observation matrix, and by optimizing and solving this sampling equation, the signal can be reconstructed. This technology greatly reduces the storage space of the signal and the transmission cost, and has been widely applied in many fields. However, traditional compressive sensing reconstruction methods require manual design of the observation matrix, the reconstruction method is complex, time-consuming, and the final reconstruction effect is poor, making it difficult to directly adapt to the vast majority of application scenarios. With the development of deep learning in recent years, some scholars have gradually proposed to fuse deep neural networks with compressive sensing technology, using a self-learning sampling matrix as the observation matrix to process the original signal. Among them, the compressive sampling module in CSNet can adaptively learn the sampling matrix from the training set images, and can still better retain the structural information of the image after sampling, improving the image reconstruction effect. The CombNet convolutional neural network structure has good reconstruction effect and the advantage of low complexity, making the reconstruction method light and accurate. Summary of the Invention

[0003] To solve the deficiencies of traditional compressive sensing methods, such as the need to customize the sampling matrix, complex reconstruction algorithms, long time consumption, and poor reconstruction effect, and aiming at deep learning, the present invention proposes an optimized method for compressive sensing image reconstruction. The present invention innovatively combines the CSNet network and the CombNet network, and uses wavelet transform as a denoising means to improve the traditional convex function optimization iterative reconstruction method, realizing the maximum reconstruction of the image under a lower sampling rate, and achieving good applications in the fields of signal transmission and image compression.

[0004] The technical solution adopted by the present invention to solve its technical problems is as follows:

[0005] A compressive sensing reconstruction method based on learning sampling and convolutional neural network, comprising the following steps:

[0006] 1) The operations in the image preprocessing stage are as follows: The image x to be reconstructed 0 is re-constructed into an image matrix x of size 1024×1024 1 , and the original size information of the image is recorded; then the matrix is segmented into standardized image matrix blocks, denoted as Record the position information at the same time. Here, n is the total number of image matrix blocks after the image is segmented according to the specified size;

[0007] 2) In the sampling stage, use learning sampling to replace the traditional fixed observation matrix sampling. Use the learned convolution kernel conv1 to perform matrix sparsification operation on the input image matrix block to obtain the sampling signal y 0 , and then use the convolution kernel conv2 to perform an initial reconstruction operation on the sampling signal y 0 to obtain the signal y 1 . Finally, through recombination and splicing, the image matrix sampling signal is obtained, denoted as y 2 ;

[0008] 3) Input the image sampling output signal y 2 into the trained CombNet network. The CombNet network is composed of a fully connected layer and a convolutional layer. After passing through 1 fully connected layer and 10 convolutional layers, the network finally reconstructs the input image matrix block, denoted as

[0009] 4) After obtaining all the image matrix blocks of this image, through the position information, can be combined into the reconstructed image of the original image, denoted as x′ 1 ;

[0010] 5) The operations in the wavelet denoising stage are as follows: The reconstructed image x′ of the original image obtained 1 is decomposed through the first-level wavelet transform (DWT) to obtain 1 low-frequency signal and 3 high-frequency signals. Among them, the low-frequency signal remains unchanged, while the high-frequency components are denoised separately. The specific operation of denoising is through the first convolutional layer, the nonlinear transformation layer (ReLU), and the second convolutional layer. The three denoised high-frequency components and the untreated low-frequency component are subjected to the inverse wavelet transform IDWT to obtain the denoised reconstructed image x″ of the original image 1 ;

[0011] 6) Finally, reconstruct the original image x″ 0 according to the original image size information, and the method for image compression and reconstruction through the neural network can be realized.

[0012] Furthermore, the processing process of step 1) is as follows: For the image x to be reconstructed 0 record the number of pixel points in the length and width, and then use the bilinear interpolation method to reconstruct the image size. The formula of the bilinear interpolation method is as follows:

[0013]

[0014]

[0015]

[0016] x: The x - coordinate of the pixel point for interpolation operation;

[0017] y: The y - coordinate of the pixel point for interpolation operation;

[0018] x 1 : The x - coordinates of the two left adjacent pixels;

[0019] x 2 : The x - coordinates of the two right adjacent pixels;

[0020] y 1 : The y - coordinates of the two upper adjacent pixels;

[0021] y 2 : The y - coordinates of the two lower adjacent pixels;

[0022] Q 11 : The pixel value of the upper - left adjacent pixel;

[0023] Q 12 : The pixel value of the upper - right adjacent pixel;

[0024] Q 21 : The pixel value of the lower - left adjacent pixel;

[0025] Q 22 : The pixel value of the lower - right adjacent pixel;

[0026] Then, for the 1024×1024 image x 1 is divided into 1024 image blocks of size 32×32 from left to right and top to bottom, that is, n = 1024, and records the position information according to which block of the original image the image block is, for subsequent image reconstruction.

[0027] Furthermore, in step 2), the learning sampling process is as follows: Design a convolutional kernel conv1 with a size of 32×32, a stride of 32, and a number of n. After performing convolutional sampling operation, the sampling output is y 0 , and then through the convolutional kernel conv2 and recombination and splicing operations, the sampling signal y 2 is obtained. The number of conv2 convolutional kernels is 1024, with a size of 1×1 and a stride of 1. Both of these two convolutional layers can achieve end - to - end learning. The random gradient descent (SGD) training algorithm is adopted. This sampling process is represented by the following formula:

[0028]

[0029] It is the mapping of the convolution sampling operation of the convolution kernel conv1.

[0030] It is the mapping of the convolution sum and recombination splicing operation of the convolution kernel conv2.

[0031] Among them, the size of n is set according to the sampling rate, and there is the following formula:

[0032] Sr = n / 1024 (5)

[0033] Sr: The sampling rate set for compressive sensing.

[0034] Furthermore, in step 3), the image reconstruction process is as follows: The image sampling output signal y 2 is first input into the fully connected layer, where the signal y 2 has a dimension of n×1. The fully connected layer is connected to 1024 neurons one by one, and then passes through 10 convolutional layers to obtain the final 32×32 reconstructed image matrix block The structures of these convolutional layers are as follows: The first and second layers use convolutional kernels of size 1×1, and the outputs are 128 and 64 feature matrices respectively; the third layer uses a convolutional kernel of size 9×9, and the output is 64 feature matrices; the fourth layer uses a convolutional kernel of size 7×7, and the output is 32 feature matrices; the fifth and sixth layers use convolutional kernels of size 3×3 and 1×1 respectively, and the output is 16 feature matrices; the seventh, eighth, and ninth layers use convolutional kernels of size 3×3, 5×5, and 3×3 respectively, and the outputs are all 1 feature matrix; the tenth layer uses a convolutional kernel of size 3×3 and outputs the image reconstruction block Among them, after passing through each convolutional layer, a non-linear transformation layer (ReLU) is required. The loss function during network training is expressed by the following formula:

[0035]

[0036] m: The total number of image blocks in the training set;

[0037] y i : The low-resolution reconstructed image in the image block;

[0038] x i : The high-resolution original image in the image block;

[0039] The training of the network also adopts the stochastic gradient descent (SGD) training algorithm. In addition, the convolution operation can be expressed by the following formula:

[0040]

[0041] Wi : represents the weight vector of the convolutional kernel in the i-th layer;

[0042] represents the inner product operation;

[0043] b i : represents the offset vector of the i-th layer;

[0044] f(x): represents the non-linear activation function;

[0045] H i : represents the feature map vector representation of the i-th layer.

[0046] Furthermore, in step 4), the combination operation of the image matrix blocks can be expressed as follows: Using the image position information recorded in the previous steps, the reconstructed image matrix blocks are arranged in order to form a complete 1024×1024 picture x'. 1 .

[0047] Further, in step 5), the wavelet transform denoising operation for the image can be expressed as follows: The obtained picture x' 1 is subjected to discrete wavelet transform DWT according to the power series. First, wavelet transform is performed on each row of the image to obtain the low-frequency component L and high-frequency component H in the horizontal direction of the image. Then, wavelet transform is performed on each column of the transformed data to obtain the low-frequency component LL, horizontal high-frequency component LH, vertical high-frequency component HL, and diagonal high-frequency component HH of the original image in the horizontal and vertical directions. After that, one low-frequency component is kept unchanged, and the three high-frequency components are denoised. The specific operation is to make the high-frequency signals pass through a convolutional layer containing 32 3×2×1 convolutional kernels, a non-linear transformation layer, and another convolutional layer containing 1 3×3×32 convolutional kernel in sequence. Finally, the low-frequency component and the three processed high-frequency components are subjected to inverse wavelet transform to obtain the reconstructed image x'' 1 .

[0048] The corresponding wavelet transform reconstruction process is described as: First, perform inverse discrete wavelet transform on each column of the transform result, and then perform one-dimensional inverse discrete wavelet transform on each row of the transformed data to obtain the reconstructed image;

[0049] The steps of wavelet transform are as follows:

[0050] 5.1. Compare the start part of the wavelet w(t) with the original function f(t), and calculate the similarity degree between this part of the function and the wavelet;

[0051] 5.2. Shift the wavelet to the right by k units to get the wavelet w(t - k), and repeat 5.1. Repeat this step until the function f ends;

[0052] 5.3. Expand the wavelet w(t) to obtain the wavelet w(t / 2), and repeat steps 5.1 and 5.2;

[0053] 5.4. Continuously expand the wavelet and repeat 5.1, 5.2, and 5.3;

[0054] The implementation of the DWT discrete wavelet transform is expressed by the following formula:

[0055]

[0056] x(m,n): The wavelet basis transform scale component of the original image.

[0057] x(t): The time-domain feature quantity of the original image.

[0058] ψ(t): The wavelet basis transform function.

[0059] The beneficial effects of the present invention are as follows: The present invention innovatively combines the CSNet convolutional sampling neural network and the CombNet convolutional reconstruction neural network, improves the traditional optimization iteration model based on machine learning, achieves a better compression and reconstruction effect, and makes this technology universal in the fields of information transmission and image compression. Brief Description of the Drawings

[0060] Figure 1 It is a schematic diagram of an image compression sampling model based on the CSNet convolutional sampling network, mainly composed of a bilinear interpolation image normalization module, an image segmentation module, a convolutional sampling module, and an initial reconstruction module. The convolutional sampling module and the initial sampling module include the following parts: the CSNet convolutional sampling model;

[0061] Figure 2 It is a schematic diagram of an image perception reconstruction model based on the CombNet convolutional reconstruction network, mainly composed of a fully connected layer, a convolutional layer, and an image recombination module;

[0062] Figure 3 It is a schematic diagram of an image denoising model based on wavelet transform, mainly composed of a wavelet transform denoising module and an image size reduction module. The wavelet transform denoising module includes the following parts: the wavelet basis transform reconstruction model. Detailed Embodiment

[0063] The present invention will be further described in detail below with reference to the accompanying drawings.

[0064] Refer to Figures 1 to 3 , a compressive sensing reconstruction method based on learning sampling and convolutional neural network. Implementing this method can reconstruct the image after compressive sampling to the greatest extent. The present invention can be applied to the fields of image and communication, such as Figure 1As shown in the figure, the convolution sampling method for the original image includes the following steps:

[0065] 1) The operations in the image preprocessing stage are as follows: The image x to be reconstructed 0 is reconstructed into an image matrix x of size 1024×1024 using bilinear interpolation method 1 , and the original size information of the image is recorded; then the matrix is divided from top to bottom and from left to right into standard 32×32-sized image matrix blocks, denoted as At the same time, the position information is recorded for subsequent image reconstruction;

[0066] The formula of the bilinear interpolation method is as follows:

[0067]

[0068]

[0069]

[0070] x: The x coordinate of the pixel point to perform the interpolation operation;

[0071] y: The y coordinate of the pixel point to perform the interpolation operation;

[0072] x 1 : The x coordinates of the two left neighboring pixel points;

[0073] x 2 : The x coordinates of the two right neighboring pixel points;

[0074] y 1 : The y coordinates of the two upper neighboring pixel points;

[0075] y 2 : The y coordinates of the two lower neighboring pixel points;

[0076] Q 11 : The pixel value of the upper left neighboring pixel point;

[0077] Q 12 : The pixel value of the upper right neighboring pixel point;

[0078] Q 21 : The pixel value of the lower left neighboring pixel point;

[0079] Q 22 : The pixel value of the lower right neighboring pixel point;

[0080] 2) In the sampling stage, learning sampling is adopted instead of traditional fixed observation matrix sampling, and the learned convolution kernel conv1 is used to perform matrix sparsification operation on the input image matrix block to obtain the sampling signal y0 , and then the sampled signal y is initially reconstructed using the convolution kernel conv2 0 to obtain the signal y 1 , and finally, through recombination and splicing, the image matrix sampling signal is obtained, denoted as y 2 . Among them, the convolution kernel conv1 has a size of 32×32, a stride of 32, and a number of n. The number of conv2 convolution kernels is 1024, the size is 1×1, and the stride is 1. Both of these two convolutional layers can achieve end-to-end learning, and the stochastic gradient descent (SGD) training algorithm is adopted. This sampling process can be expressed by the following formula:

[0081]

[0082] is the mapping of the convolution sampling operation of the convolution kernel conv1.

[0083] is the mapping of the convolution, recombination, and splicing operations of the convolution kernel conv2.

[0084] Among them, the size of n can be set according to the sampling rate, and there is the following formula:

[0085] Sr = n / 1024 (5)

[0086] Sr: is the sampling rate set for compressive sensing.

[0087] As Figure 2 shown, the convolutional reconstruction method for the sampled image includes the following steps:

[0088] 3) Input the image sampling output signal y 2 into the trained CombNet network. The CombNet network consists of a fully connected layer and convolutional layers. After passing through 1 fully connected layer and 10 convolutional layers, the network finally reconstructs the input image matrix block, denoted as

[0089] The signal y 2 has a dimension of n×1. The fully connected layer is connected to 1024 neurons one by one, and then passes through 10 convolutional layers. The specific structures of these convolutional layers are as follows: The first and second layers use convolutional kernels with a size of 1×1, and the outputs are 128 and 64 feature matrices respectively; the third layer uses a convolutional kernel with a size of 9×9, and the output is 64 feature matrices; the fourth layer uses a convolutional kernel with a size of 7×7, and the output is 32 feature matrices; the fifth and sixth layers use convolutional kernels with sizes of 3×3 and 1×1 respectively, and the output is 16 feature matrices; the seventh, eighth, and ninth layers use convolutional kernels with sizes of 3×3, 5×5, and 3×3 respectively, and the outputs are all 1 feature matrix; the tenth layer uses a convolutional kernel with a size of 3×3, and outputs the image reconstruction block After each convolutional layer, a non-linear transformation layer (ReLU) is required. The loss function during network training is expressed by the following formula:

[0090]

[0091] m: The total number of image patches in the training set.

[0092] y i : The reconstructed low-resolution image in the image patch.

[0093] x : The original high-resolution image in the image patch.

[0094] The network is also trained using the Stochastic Gradient Descent (SGD) training algorithm. Additionally, the convolution operation can be expressed by the following formula:

[0095]

[0096] W i : Represents the weight vector of the convolutional kernel in the i-th layer.

[0097] Denotes the inner product operation.

[0098] b i : Represents the bias vector in the i-th layer.

[0099] f(x): Represents the non-linear activation function.

[0100] H i : Represents the feature map vector representation in the i-th layer.

[0101] 4) After obtaining all the image matrix patches of the image, through the position information, can be combined in order to form the reconstructed image of the original image, denoted as x' 1 .

[0102] As Figure 3 shown, the wavelet transform denoising method for the reconstructed image includes the following steps:

[0103] 5) The operations in the wavelet denoising stage are as follows: The obtained picture x' 1Perform discrete wavelet transform (DWT) according to the power series. First, perform wavelet transform on each row of the image to obtain the low-frequency component L and high-frequency component H in the horizontal direction of the image. Then, perform wavelet transform on each column of the transformed data to obtain the low-frequency component LL, horizontal high-frequency component LH, vertical high-frequency component HL, and diagonal high-frequency component HH in the horizontal and vertical directions of the original image. After that, keep one low-frequency component unchanged and denoise the three high-frequency components. The specific operation is to make the high-frequency signal pass through a convolutional layer containing 32 convolution kernels of 3×2×1, a non-linear transformation layer, and another convolutional layer containing 1 convolution kernel of 3×3×32 in sequence. Finally, perform inverse wavelet transform on the low-frequency component and the three processed high-frequency components to obtain the reconstructed image x″ 1 。

[0104] The corresponding wavelet transform reconstruction process can be described as follows: First, perform inverse discrete wavelet transform on each column of the transformation result, and then perform one-dimensional inverse discrete wavelet transform on each row of the transformed data to obtain the reconstructed image.

[0105] The steps of wavelet transform can be expressed as follows:

[0106] 5.1) Compare the start part of the wavelet w(t) and the original function f(t), and calculate the similarity degree between this part of the function and the wavelet;

[0107] 5.2) Shift the wavelet to the right by k units to get the wavelet w(t - k), and repeat 5.1. Repeat this step until the function f ends;

[0108] 5.3) Expand the wavelet w(t) to get the wavelet w(t / 2), and repeat steps 5.1 and 5.2;

[0109] 5.4) Continuously expand the wavelet and repeat 5.1, 5.2, and 5.3;

[0110] The implementation of DWT discrete wavelet transform can be expressed by the following formula:

[0111]

[0112] x(m,n): The wavelet basis transform scale component of the original image.

[0113] x(t): The time-domain characteristic quantity of the original image.

[0114] ψ(t): The wavelet basis transform function.

[0115] 6) Finally, reconstruct the original image x″ according to the original image size information 0 ,and the method of image compression and reconstruction through neural network can be realized.

[0116] The content described in the embodiments of this specification is only a list of implementation forms of the inventive concept and is for illustrative purposes only. The protection scope of the present invention should not be regarded as limited to the specific forms stated in this embodiment, and the protection scope of the present invention also extends to equivalent technical means that can be conceived by those of ordinary skill in the art based on the inventive concept of the present invention.

Claims

1. A compressive sensing reconstruction method based on learning sampling and convolutional neural network, characterized in that, the method comprises the following steps: 1) The operations in the image preprocessing stage are as follows: the image x to be reconstructed 0 is reconstructed into an image matrix x of size 1024×1024 1 , and the original size information of the image is recorded; then the matrix is segmented into standardized image matrix blocks, denoted as i ∈ [1, n], and the position information is recorded at the same time, where n is the total number of image matrix blocks after the image is segmented according to the specified size; 2) In the sampling stage, learning sampling is used instead of traditional fixed observation matrix sampling. The learned convolution kernel conv1 is used to perform matrix sparsification on the input image matrix block to obtain the sampling signal y 0 . Then, the convolution kernel conv2 is used to perform initial reconstruction on the sampling signal y 0 to obtain the signal y 1 . Finally, through recombination and splicing, the image matrix sampling signal is obtained, denoted as y 2 ; 3) Input the image sampling output signal y 2 into the trained CombNet network. The CombNet network consists of a fully connected layer and convolutional layers. After passing through 1 fully connected layer and 10 convolutional layers, the network finally reconstructs the input image matrix block, denoted as 4) After obtaining all the image matrix blocks of the image, according to the position information, are combined into a reconstructed graph of the original image, where i ∈ [1, n], denoted as x′ 1 ; 5) The operations in the wavelet denoising stage are as follows: the reconstructed image x' of the obtained original image 1 After the first-level wavelet transform DWT, it is decomposed into 1 low-frequency signal and 3 high-frequency signals. Among them, the low-frequency signal is kept unchanged, while the high-frequency components are denoised respectively. The specific operation of denoising is through the first convolutional layer, the non-linear transformation layer ReLU, and the second convolutional layer. The three denoised high-frequency components and the untreated low-frequency component are subjected to the inverse wavelet transform IDWT to obtain the denoised reconstructed image x″ of the original image 1 , 6) Finally, reconstruct the original image x″ according to the original image size information 0 , and the method of image compression and reconstruction through the neural network can be realized; In step 3), the image reconstruction process is as follows: The image sampling output signal y 2 is first input into the fully connected layer, where the signal y 2 has a dimension of n×1. The fully connected layer is connected to 1024 neurons one by one, and then passes through 10 convolutional layers to obtain the final 32×32 reconstructed image matrix block The structures of these convolutional layers are as follows: The first and second layers use convolutional kernels of size 1×1, and the outputs are 128 and 64 feature matrices respectively; The third layer uses a convolutional kernel of size 9×9, and the output is 64 feature matrices. The fourth layer uses a convolutional kernel of size 7×7, and the output is 32 feature matrices; The fifth and sixth layers use convolutional kernels of size 3×3 and 1×1 respectively, and the output is 16 feature matrices; The seventh, eighth, and ninth layers use convolutional kernels of size 3×3, 5×5, and 3×3 respectively, and the outputs are all 1 feature matrix; The tenth layer uses a convolutional kernel of size 3×3 and outputs the image reconstruction block Among them, after passing through each convolutional layer, a non-linear transformation layer ReLU is required. The loss function during network training is expressed by the following formula: m: the total number of image patches in the training set; y i : The reconstructed image with low resolution in the image block; x i : The original high-resolution image in the image block; The training of the network also adopts the stochastic gradient descent (SGD) training algorithm, and the convolution operation is expressed by the following formula: W i : represents the weight vector of the convolutional kernel in the i-th layer; Indicates an inner product operation; b i : represents the offset vector of the i-th layer; f(x): represents the non-linear activation function; H i : represents the feature map vector representation of the i-th layer.

2. The compressive sensing reconstruction method based on learning sampling and convolutional neural network according to claim 1, characterized in that, The processing procedure of step 1) is as follows: for the image x to be reconstructed 0 After recording the number of pixels in length and width, the image size is reconstructed using the bilinear interpolation method. The bilinear interpolation method formula is as follows: x: the x coordinate of the pixel point to be interpolated; y: the y coordinate of the pixel point to be interpolated; x 1 : The x coordinates of the two left adjacent pixels; x 2 : The x coordinates of the two pixel points on the right side of the perimeter; y 1 : The y coordinates of the two upper pixels around; y 2 : The y coordinates of the two pixel points below on the periphery; Q 11 : Pixel value of the pixel points in the upper left vicinity; Q 12 : Pixel value of the upper right surrounding pixel points; Q 21 : Pixel value of the pixel points in the lower left around; Q 22 : Pixel value of the pixel points in the lower right around; Then, for the 1024×1024 image x 1 Divide it into image blocks of size 32×32 from left to right and top to bottom. A total of 1024 blocks are obtained, that is, n = 1024, and we get i ∈ [1, 1024], and record the position information according to which block the image block is in the original image for subsequent image reconstruction.

3. The compressive sensing reconstruction method based on learning sampling and convolutional neural network according to claim 1 or 2, characterized in that, In step 2), the learning sampling process is as follows: Design a convolutional kernel conv1 with a size of 32×32, a stride of 32, and a number of n. After performing convolution sampling operation on the sampling output obtained is y 0 , and then through the convolutional kernel conv2 and the recombination and splicing operations, the sampling signal y 2 is obtained. The number of convolutional kernels of conv2 is 1024, the size is 1×1, and the stride is 1. Both of these two convolutional layers can achieve end-to-end learning. The random gradient descent SGD training algorithm is adopted. This sampling process is represented by the following formula: Mapping for the convolution sampling operation of convolution kernel conv1; Mapping for the convolution sum and recombination splicing operations of convolution kernel conv2; where the size of n is set according to the sampling rate, and there is the following formula: Sr = n / 1024 (5) Sr: the sampling rate set for compressive sensing.

4. The compressive sensing reconstruction method based on learning sampling and convolutional neural network according to claim 1 or 2, characterized in that, In the said step 4), the combination operation of the image matrix blocks can be expressed as follows: Using the image position information recorded in the previous steps, the reconstructed image matrix blocks are arranged in sequence, where i ∈ [1, n], to form a complete 1024×1024 picture x'. 1 .

5. A compressive sensing reconstruction method based on learning sampling and convolutional neural network according to claim 1 or 2, characterized in that, in the step 5), the wavelet transform denoising operation for the image can be expressed as follows: the obtained picture x′ 1 is subjected to discrete wavelet transform DWT according to the power series. First, wavelet transform is performed on each row of the image to obtain the low-frequency component L and high-frequency component H in the horizontal direction of the image. Then, wavelet transform is performed on each column of the transformed data to obtain the low-frequency component LL, horizontal high-frequency component LH, vertical high-frequency component HL, and diagonal high-frequency component HH in the horizontal and vertical directions of the original image. After that, one low-frequency component is kept unchanged, and the three high-frequency components are denoised. The specific operation is to make the high-frequency signal pass through a convolutional layer containing 32 convolutional kernels of 3×2×1, a non-linear transformation layer, and another convolutional layer containing 1 convolutional kernel of 3×3×32 in sequence. Finally, the low-frequency component and the three processed high-frequency components are subjected to inverse wavelet transform to obtain the reconstructed image x″ 1 ; The corresponding wavelet transform reconstruction process is described as follows: First, perform the inverse discrete wavelet transform on each column of the transform result, and then perform the one-dimensional inverse discrete wavelet transform on each row of the data obtained by the transform, and the reconstructed image can be obtained; The steps of the wavelet transform are as follows: 5.

1. Compare the start part of the wavelet w(t) and the original function f(t), and calculate the similarity degree between this part of the function and the wavelet; 5.

2. Shift the wavelet to the right by k units to obtain the wavelet w(t - k), repeat 5.1, and repeat this step until the function f ends; 5.

3. Expand the wavelet w(t) to obtain the wavelet w(t / 2), and repeat steps 5.1 and 5.2; 5.

4. Continuously expand the wavelet and repeat 5.1, 5.2, and 5.3; The implementation of the DWT (Discrete Wavelet Transform) is expressed by the following formula: x(m, n): the wavelet basis transform scale component of the original image; x(t): the time domain feature quantity of the original image; ψ(t): the wavelet basis transform function.

Images