CN108876737B - Image denoising method combining residual learning and structural similarity - Google Patents

Image denoising method combining residual learning and structural similarity Download PDF

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CN108876737B
CN108876737B CN201810583825.9A CN201810583825A CN108876737B CN 108876737 B CN108876737 B CN 108876737B CN 201810583825 A CN201810583825 A CN 201810583825A CN 108876737 B CN108876737 B CN 108876737B
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范赐恩
冉杰文
邹炼
马杨
王楠楠
陈丽琼
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Wuhan University WHU
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Abstract

The invention provides an image denoising method combining residual error learning and structural similarity. Selecting a plurality of high-definition images in a BSD database to respectively construct a training data set and a test data set; the method comprises the steps of obtaining a cut training data set by performing center cutting on a high-definition image in a training data set, preprocessing the cut training data set to obtain a preprocessed training data set, and adding Gaussian noise with certain intensity to the preprocessed training data set and a test data set respectively to obtain a noise-containing training data set and a noise-containing test data set; designing a deep convolutional neural network, training the deep convolutional neural network by designing L2 norm and SSIM combined loss function minimization, and obtaining a clear image data set by calculation between a noisy test data set and a noise residual image obtained according to the deep convolutional neural network. The invention has the advantage that the denoising effect is more in line with the visual perception of human eyes.

Description

Image denoising method combining residual learning and structural similarity
Technical Field
The invention belongs to the field of image processing and computer vision, and particularly relates to an image denoising method combining residual learning and structural similarity.
Background
Image denoising has been a hotspot of research in the field of image processing. In practical application, more and more ways of acquiring images are provided, but the images are affected by equipment and external factors in the acquisition and transmission processes, various noises are introduced, so that the post-processing of the images is difficult, and the understanding of human eyes on the image information is seriously affected by the noise information. Therefore, it is important to establish an image denoising method conforming to human visual perception.
The purpose of image denoising is to obtain a denoised clear image from a noisy image to be processed. With the development of the denoising algorithm, a relatively obvious effect is obtained for various types of noise at present. Representative denoising algorithms include a local method, a non-local method, a sparse representation and the like, and the methods have better performance on specific types of noise. However, the noise type of the actual noisy image is complex and difficult to describe by a specific model, so that the traditional method has poor denoising effect in the complex noisy image. In recent years, with the aid of feature learning and nonlinear feature mapping capabilities of convolutional neural networks, an end-to-end image denoising neural network is established, so that denoising effects are further improved.
The evaluation of the performance of the image denoising algorithm is divided into a subjective evaluation mode and an objective evaluation mode, wherein the subjective evaluation mode is that human eyes are used for directly perceiving the image denoising effect; the objective evaluation is mainly evaluated according to the existing indexes such as Mean Square Error (MSE), peak signal-to-noise ratio (PSNR), Structural Similarity (SSIM) and the like. At present, a loss function of a denoising neural network based on deep learning is generally based on an L2 norm, and although the L2 norm is beneficial to the improvement of a peak signal-to-noise ratio (PSNR) index, the PSNR evaluation index is inconsistent with human visual perception, so that the edge and local texture of an image after denoising are generally smoothed, and detail features are lost. Therefore, the SSIM with higher consistency with human visual perception is added into the loss function, so that the consistency with the human visual perception after image denoising is improved.
Through the search of documents in the prior art, Chinese patent application publication No. CN106204468A (published as 2016.12.07) discloses an image denoising method based on a ReLU convolutional neural network, which adopts a ReLU-based convolutional neural network model, uses a plurality of convolutional layers and ReLU active layers, and establishes the mapping from a noise image to a denoised clear image by taking minimum MSE as a loss function. The method has simple model structure, obtains certain denoising effect, but has the following problems: (1) with the increase of the network depth, the model of the clear image after being directly learned and denoised is not easy to be converged; (2) the loss function only considers MSE, and although large noise can be suppressed, the loss function can tolerate small noise, and the effect after denoising is often inconsistent with human eye subjectivity.
Disclosure of Invention
In order to solve the technical problem, the invention discloses an image denoising method combining residual error learning and structural similarity, which designs a network model with noise-containing images as input and noise residual error images as output by utilizing the thought of residual error learning, and enables the denoising effect to be more accordant with human visual perception by optimizing a loss function combining L2 norm and SSIM.
In order to achieve the purpose, the technical scheme of the invention comprises the following steps:
step 1: selecting a plurality of high-definition images in a BSD database to respectively construct a training data set and a test data set;
step 2: the method comprises the steps of obtaining a cut training data set by performing center cutting on a high-definition image in a training data set, preprocessing the cut training data set to obtain a preprocessed training data set, and adding Gaussian noise with certain intensity to the preprocessed training data set and a test data set respectively to obtain a noise-containing training data set and a noise-containing test data set;
and step 3: designing a deep convolutional neural network, training the deep convolutional neural network by designing L2 norm and SSIM combined loss function minimization, and obtaining a clear image data set by calculation between a noisy test data set and a noise residual image obtained according to the deep convolutional neural network.
Preferably, the number of the high-definition images in the step 1 is K;
the high-quality image in the step 1 is as follows:
P1,P2,...,PK
wherein the image Pk k∈[1,K]Resolution M N, image Pk k∈[1,K]Has a pixel value of
Pk(i,j)i∈[1,M]j∈[1,N]；
The number of the high-definition images in the training data set in the step 1 is KaSheet, residual Kb＝K-Ka,KbUsing a Zhang high definition image as a test data set;
the high-definition image in the training data set is Pa a∈[1,Ka]Having a pixel value of
Pa(ia,ja)ia∈[1,M]ja∈[1,N]；
The high-definition image in the test data set is Pb b∈[1,Kb]Having a pixel value of
Pb(ib,jb)ib∈[1,M]jb∈[1,N]；
Preferably, the high-definition image in the training data set in step 2 is K in step 1aTraining data is concentrated into high-definition images;
cutting to reserve the central part K of the image in the step 2Z,KZ×KZHigh definition image P in training data set after size and cuttinga′a∈[1,Ka]The pixel values in (1) are:
Figure BDA0001686122770000031
the preprocessing of the training data set after cutting comprises the following steps:
to high definition image P in post-cutting training data seta′a∈[1,Ka]According to step size alpha to KY,KY×KYImage sliding and partitioning of the image block to obtain a horizontal KzColumn,/α, vertical KzImage blocks of/alpha line, in total (K)z/α)2A block;
then, each image is horizontally translated and vertically turned over, and is reduced to 0.8 time of the original image, and is clockwise rotated by 90 degrees to obtain (K)z/α)24 high-definition image blocks;
pre-processed training data set Pc c∈[1,(Kz/α)2*4]Each high definition image consists of (K)z/α)2A KY×KYImage block composition, KY；
In the step 2, adding a certain intensity of gaussian noise to the preprocessed training data set is as follows:
to (K)z/α)2*4*KaAdding Gaussian noise with certain intensity into a training data set after preprocessing of the Zhang HD image blocks to obtain a noise-containing training data set:
Figure BDA0001686122770000032
c∈[1,(Kz/α)2*4]
wherein the content of the first and second substances,
Figure BDA0001686122770000033
for corresponding noisy images, PcFor high-definition images, [ sigma ]pFor noise variance, randn (size (P)c) Is generated with P)cRandom matrices of the same size;
in the step 2, adding a certain intensity of Gaussian noise to the test data set is as follows:
adding Gaussian noise with certain intensity to the test data set in the step 1 to obtain a noise-containing training data set:
Figure BDA0001686122770000034
wherein the content of the first and second substances,
Figure BDA0001686122770000035
for corresponding noisy images, PbFor high-definition images, [ sigma ]pFor noise variance, randn (size (P)b) Is generated and
Figure BDA0001686122770000036
random matrices of the same size;
preferably, the first layer and the second layer of the end-to-end deep convolutional neural network in the step 3 are 3 × 3 convolutional layers, each convolutional layer is composed of a convolutional layer, a batch normalization layer and a ReLU activation layer;
the end-to-end deep convolutional neural network comprises a second layer and a ninth layer, wherein each layer consists of a 1 × 1 convolutional layer, a 3 × 3 convolutional layer and a maximum pooling layer which are branched in parallel to form an increment module;
the tenth layer of the end-to-end deep convolution neural network is 3 multiplied by 3 convolution, a noise residual image is output, and a mapping v from a noise-containing image X to the noise residual image v is established to be F (X, W), wherein F (X, W) is a nonlinear mapping function of the whole network;
designing a joint loss function of the L2 norm and SSIM, and training the deep convolutional neural network by minimizing the joint loss function:
Figure BDA0001686122770000041
wherein the content of the first and second substances,
Figure BDA0001686122770000042
in order to be a function of the loss,
Figure BDA0001686122770000043
the method comprises the following steps that (1) a real noise-free image and a denoised image are respectively obtained, W is a parameter needing to be learned by a neural network, and alpha controls the influence degree of SSIM loss on the whole loss function;
further, in the present invention,
Figure BDA0001686122770000044
x is the input noisy image which is the noisy training data set in the step 2
Figure BDA0001686122770000045
c∈[1,(Kz/α)2*4]V is the noise residual image, F (X, W) is the network learning process,
Figure BDA0001686122770000046
wherein SSIM (x, y) is a structural similarity index, image quality is measured from three aspects of brightness, contrast and structure, and the value range is [0,1 ]]A larger value indicates a higher image quality;
the specific formula for SSIM is as follows:
Figure BDA0001686122770000047
wherein u isx,uyThe mean values of the images x, y,
Figure BDA0001686122770000048
variance, σ, of the images x, y, respectivelyxyIs the covariance of the images x, y, C1, C2 are constants;
optimizing a joint loss function by adopting an Adam method to obtain a network optimization parameter W;
k in the noisy test data set in the step 2bOpening noisy image
Figure BDA0001686122770000049
Inputting the data into a deep convolutional neural network, and outputting to obtain a noise residual image v;
using noisy images in noisy test data sets
Figure BDA00016861227700000410
Subtracting the noise residual image v to obtain a denoised clear image:
Figure BDA0001686122770000051
wherein, KbThe number of noisy images in the noisy test data set.
Compared with the prior art, the invention has the advantages that:
the method utilizes residual learning to construct an end-to-end convolutional neural network with input of a noisy image and output of a noisy residual image, reduces network parameters while capturing local detail characteristics of the image through small-scale convolution, and accelerates convergence of a model by adding a batch normalization layer; the size of the characteristic graph is kept consistent in the whole convolution process, and image edge information is kept;
according to the invention, a loss function combining the L2 norm and the SSIM is designed for network parameter learning, and as the PSNR does not consider the visual characteristics of human eyes, the SSIM has higher consistency in image quality perception and human eye vision from three aspects of brightness, contrast and structure. Therefore, the optimization of the loss function with SSIM is beneficial to improving the consistency of the denoised image and the subjective perception of human eyes.
Drawings
FIG. 1: the overall flow diagram of the invention;
FIG. 2: the detailed structure diagram of the network sub-module inclusion;
FIG. 3: the overall structure diagram of the network model;
FIG. 4: the image size and the number of channels of each layer of the network are set.
Detailed Description
In order to facilitate the understanding and implementation of the present invention for those of ordinary skill in the art, the present invention is further described in detail with reference to the accompanying drawings and examples, it is to be understood that the embodiments described herein are merely illustrative and explanatory of the present invention and are not restrictive thereof.
FIG. 1 is a general flow diagram of the present invention;
fig. 2 is a detailed structural diagram of the networking sub-module inclusion, where the tensor output of the upper layer is B × C × W × H, where C denotes the number of channels, B denotes the size of the batch, and W, H denotes the width and height of the feature map, respectively; the middle part is a convolution layer of filters with different sizes, F represents the size of a convolution kernel, S represents the step length of convolution, and P represents the boundary filling quantity; finally, the output connects the characteristics through filter aggregation operation, and 256 channel characteristic graphs are output; the increment module consists of a plurality of parallel branches such as 1 × 1 convolution, 3 × 3 convolution and a maximum pooling layer, and the network width is expanded; the feature fusion of each feature map channel is effectively realized by using 1 × 1 convolution, and the channel dimension can be reduced and the parameter number can be reduced; the two 3 × 3 convolution cascades are equivalent to realizing 5 × 5 convolution, so that the number of parameters is reduced while the receptive field is enlarged; finally, connecting a plurality of branches on the channel dimension to realize the fusion of feature maps on different receptive fields; in addition, the whole module ensures the consistency of the scale when the final channels are fused through different filling quantities;
FIG. 3 is a diagram of an overall structure of a network model, the overall structure being used for learning noise by residual error to establish a mapping from an input noisy image to an output noisy residual image, the overall network being used for learning noise; in the network design process, with the help of an inclusion module, convolution kernels with different sizes are used for extracting detail features of the image in different receptive fields;
FIG. 4 is the input tensor and output channel number of each layer of the eigen map in the network structure; during training, a network inputs a 64 × 64 image, the image is convolved twice by 3 × 3 to become 64 channels, then the image passes through an increment module for 8 times, and finally the image is convolved by 3 × 3 to obtain a noise residual image v. Setting the network batch size to be 128, completely training for 50 times, finishing training, initially setting the learning rate to be 0.0001, and attenuating the iteration attenuation of each 10 times to be 0.1 time of the original iteration attenuation; the Adam optimization method is adopted in the whole training process, and the momentum is 0.9.
Embodiments of the present invention will be described below with reference to fig. 1 to 4. The implementation mode of the invention comprises the following steps: step 1: selecting a plurality of high-definition images in a BSD database to respectively construct a training data set and a test data set;
the number of the high-definition images in the step 1 is K equal to 500;
the high-quality image in the step 1 is as follows:
P1,P2,...,PK
wherein the image Pk k∈[1,K]Resolution M N, image Pk k∈[1,K]Has a pixel value of
Pk(i,j)i∈[1,M]j∈[1,N]；
The number of the high-definition images in the training data set in the step 1 is Ka400 pieces, the rest Kb＝K-Ka,KbTaking 100 high-definition images as a test data set;
the high-definition image in the training data set is Pa a∈[1,Ka]Having a pixel value of
Pa(ia,ja)ia∈[1,M]ja∈[1,N]；
The high-definition image in the test data set is Pb b∈[1,Kb]Having a pixel value of
Pb(ib,jb)ib∈[1,M]jb∈[1,N]；
Step 2: the method comprises the steps of obtaining a cut training data set by performing center cutting on a high-definition image in a training data set, preprocessing the cut training data set to obtain a preprocessed training data set, and adding Gaussian noise with certain intensity to the preprocessed training data set and a test data set respectively to obtain a noise-containing training data set and a noise-containing test data set;
the high-definition image in the training data set in the step 2 is K in the step 1a400 training data sets with high definition images;
cutting to reserve the central part K of the image in the step 2Z＝256,KZ×KZHigh definition image P in training data set after size and cuttinga′a∈[1,Ka]Has a pixel value of
Figure BDA0001686122770000071
The preprocessing of the training data set after cutting comprises the following steps:
to high definition image P in post-cutting training data seta′a∈[1,Ka]According to the step length alpha, 16 pairs are divided by KY＝64,KY×KYImage sliding and partitioning of the image block to obtain a horizontal Kz16 columns,/α, vertical Kz16 rows of image blocks, for a total of 256 (K)z/α)2A block;
then, each image is horizontally translated and vertically turned over, the image is reduced to 0.8 time of the original image, and the image is clockwise rotated by 90 degrees to obtain 1024 ═ Kz/α)24 high-definition image blocks;
pre-processed training data set Pc c∈[1,(Kz/α)2*4]Each high definition image consists of (K)z/α)2256 of KY×KYImage block composition, KY＝64；
In the step 2, adding a certain intensity of gaussian noise to the preprocessed training data set is as follows:
to (K)z/α)2*4*KaAdding Gaussian noise with certain intensity into a training data set after preprocessing of the Zhang HD image blocks to obtain a noise-containing training data set:
Figure BDA0001686122770000072
c∈[1,(Kz/α)2*4]
wherein the content of the first and second substances,
Figure BDA0001686122770000073
for corresponding noisy images, PcFor high-definition images, [ sigma ]pFor noise variance, randn (size (P)c) Is generated with P)cRandom matrices of the same size;
in the step 2, adding a certain intensity of Gaussian noise to the test data set is as follows:
adding Gaussian noise with certain intensity to the test data set in the step 1 to obtain a noise-containing training data set:
Figure BDA0001686122770000074
wherein the content of the first and second substances,
Figure BDA0001686122770000075
for corresponding noisy images, PbFor high-definition images, [ sigma ]pFor noise variance, randn (size (P)b) Is generated and
Figure BDA0001686122770000076
random matrices of the same size;
and step 3: designing a deep convolutional neural network, training the deep convolutional neural network by designing L2 norm and SSIM combined loss function minimization, and obtaining a clear image data set by calculation between a noisy test data set and a noise residual image obtained according to the deep convolutional neural network;
in step 3, the first layer and the second layer of the end-to-end deep convolutional neural network are 3 multiplied by 3 convolutional layers, and each convolutional layer consists of a convolutional layer, a batch normalization layer and a ReLU activation layer;
the end-to-end deep convolutional neural network comprises a second layer and a ninth layer, wherein each layer consists of a 1 × 1 convolutional layer, a 3 × 3 convolutional layer and a maximum pooling layer which are branched in parallel to form an increment module;
the tenth layer of the end-to-end deep convolution neural network is 3 multiplied by 3 convolution, a noise residual image is output, and a mapping v from a noise-containing image X to the noise residual image v is established to be F (X, W), wherein F (X, W) is a nonlinear mapping function of the whole network;
designing a joint loss function of the L2 norm and SSIM, and training the deep convolutional neural network by minimizing the joint loss function:
Figure BDA0001686122770000081
wherein the content of the first and second substances,
Figure BDA0001686122770000082
in order to be a function of the loss,
Figure BDA0001686122770000083
the method comprises the following steps that (1) a real noise-free image and a denoised image are respectively obtained, W is a parameter needing to be learned by a neural network, and alpha controls the influence degree of SSIM loss on the whole loss function;
further, in the present invention,
Figure BDA0001686122770000084
x is the input noisy image which is the noisy training data set in the step 2
Figure BDA0001686122770000085
c∈[1,(Kz/α)2*4]Kz16, v is the noise residual image, F (X, W) is the network learning process,
Figure BDA0001686122770000086
wherein SSIM (a)x, y) is a structural similarity index, the image quality is respectively measured from three aspects of brightness, contrast and structure, and the value range is [0, 1%]A larger value indicates a higher image quality;
the specific formula for SSIM is as follows:
Figure BDA0001686122770000087
wherein u isx,uyThe mean values of the images x, y,
Figure BDA0001686122770000088
variance, σ, of the images x, y, respectivelyxyIs the covariance of the images x, y, C1, C2 are constants;
optimizing a joint loss function by adopting an Adam method to obtain a network optimization parameter W;
k in the noisy test data set in the step 2b100 noisy images
Figure BDA0001686122770000089
Inputting the data into a deep convolutional neural network, and outputting to obtain a noise residual image v;
using noisy images in noisy test data sets
Figure BDA0001686122770000091
Subtracting the noise residual image v to obtain a denoised clear image:
Figure BDA0001686122770000092
wherein, Kb100 is the number of noisy images in the noisy test data set.
It should be understood that parts of the specification not set forth in detail are well within the prior art.
It should be understood that the above description of the preferred embodiments is given for clarity and not for any purpose of limitation, and that various changes, substitutions and alterations can be made herein without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (3)

1. An image denoising method combining residual learning and structural similarity is characterized by comprising the following steps:
step 1: selecting a plurality of high-definition images in a BSD database to respectively construct a training data set and a test data set;
step 2: the method comprises the steps of obtaining a cut training data set by performing center cutting on a high-definition image in a training data set, preprocessing the cut training data set to obtain a preprocessed training data set, and adding Gaussian noise with certain intensity to the preprocessed training data set and a test data set respectively to obtain a noise-containing training data set and a noise-containing test data set;
and step 3: designing a deep convolutional neural network, training the deep convolutional neural network by designing L2 norm and SSIM combined loss function minimization, and obtaining a clear image data set by calculation between a noisy test data set and a noise residual image obtained according to the deep convolutional neural network; in the step 3, the first layer and the second layer of the deep convolutional neural network are 3 multiplied by 3 convolutional layers, and each convolutional layer consists of a convolutional layer, a batch normalization layer and a ReLU activation layer;
the end-to-end deep convolutional neural network comprises a second layer and a ninth layer, wherein each layer consists of a 1 × 1 convolutional layer, a 3 × 3 convolutional layer and a maximum pooling layer which are branched in parallel to form an increment module;
the tenth layer of the end-to-end deep convolution neural network is 3 multiplied by 3 convolution, a noise residual image is output, and a mapping v from a noise-containing image X to the noise residual image v is established to be F (X, W), wherein F (X, W) is a nonlinear mapping function of the whole network;
designing a joint loss function of the L2 norm and SSIM, and training the deep convolutional neural network by minimizing the joint loss function:
Figure FDA0003116790530000011
wherein the content of the first and second substances,
Figure FDA0003116790530000012
the loss function, Y,
Figure FDA0003116790530000013
the method comprises the following steps that (1) a real noise-free image and a denoised image are respectively obtained, W is a parameter needing to be learned by a neural network, and alpha controls the influence degree of SSIM loss on the whole loss function;
further, in the present invention,
Figure FDA0003116790530000014
x is the input noisy image which is the noisy training data set in the step 2
Figure FDA0003116790530000015
v is the noise residual image, F (X, W) is the net learning process,
Figure FDA0003116790530000016
wherein SSIM (x, y) is a structural similarity index, image quality is measured from three aspects of brightness, contrast and structure, and the value range is [0,1 ]]A larger value indicates a higher image quality; kZFor the step 2, cutting to reserve the central part of the image, and alpha is the step length;
the specific formula for SSIM is as follows:
Figure FDA0003116790530000021
wherein u isx，uyThe mean values of the images x, y,
Figure FDA0003116790530000022
the variance of the images x, y,σxyis the covariance of the images x, y, C1, C2 are constants;
optimizing a joint loss function by adopting an Adam method to obtain a network optimization parameter W;
k in the noisy test data set in the step 2bOpening noisy image
Figure FDA0003116790530000023
Inputting the data into a deep convolutional neural network, and outputting to obtain a noise residual image v;
using noisy images in noisy test data sets
Figure FDA0003116790530000024
Subtracting the noise residual image v to obtain a denoised clear image:
Figure FDA0003116790530000025
wherein, KbThe number of noisy images in the noisy test data set.
2. The method for image denoising in joint residual learning and structural similarity according to claim 1, wherein the number of the high definition images in step 1 is K;
in the step 1, the high-definition image is as follows:
P1，P2，...，PK
wherein the image Pk，k∈[1，K]Resolution M N, image Pk，k∈[1，K]Has a pixel value of Pk(i，j)，i∈[1，M]，j∈[1，N]；
The number of the high-definition images in the training data set in the step 1 is KaSheet, residual Kb＝K-Ka，KbUsing a Zhang high definition image as a test data set;
the high-definition image in the training data set is Pa，a∈[1，Ka]Having a pixel value of
Pa(ia，ja)，ia∈[1，M]，ja∈[1，N]；
The high-definition image in the test data set is Pb，b∈[1，Kb]Having a pixel value of
Pb(ib，jb)，ib∈[1，M]，jb∈[1，N]。
3. The method of claim 2, wherein the high-definition image in the training data set in step 2 is K in step 1aTraining data is concentrated into high-definition images;
cutting to reserve the central part K of the image in the step 2Z，KZ×KZSize, high definition image P 'in post-clip training data set'a，a∈[1，Ka]The pixel values in (1) are:
Figure FDA0003116790530000031
the preprocessing of the training data set after cutting comprises the following steps:
concentrating high-definition image P 'in clipped training data'a，a∈[1，Ka]According to step size α to KY×KYImage sliding and partitioning of the image block to obtain a horizontal KzColumn,/α, vertical KzImage blocks of/alpha line, in total (K)z/α)2A block;
then, each image is horizontally translated and vertically turned over, and is reduced to 0.8 time of the original image, and is clockwise rotated by 90 degrees to obtain (K)z/α)24 high-definition image blocks;
pre-processed training data set Pc，c∈[1，(Kz/α)2*4]Each high definition image consists of (K)z/α)2A KY×KYImage block composition;
in the step 2, adding a certain intensity of gaussian noise to the preprocessed training data set is as follows:
to (K)z/α)2*4*KaAdding Gaussian noise with certain intensity into a training data set after preprocessing of the Zhang HD image blocks to obtain a noise-containing training data set:
Figure FDA0003116790530000032
c∈[1，(Kz/α)2*4]
wherein the content of the first and second substances,
Figure FDA0003116790530000033
for corresponding noisy images, PcFor high-definition images, [ sigma ]pFor noise variance, randn (size (P)c) Is generated with P)cRandom matrices of the same size;
in the step 2, adding a certain intensity of Gaussian noise to the test data set is as follows:
adding Gaussian noise with certain intensity to the test data set in the step 1 to obtain a noise-containing training data set:
Figure FDA0003116790530000034
wherein the content of the first and second substances,
Figure FDA0003116790530000035
for corresponding noisy images, PbFor high-definition images, [ sigma ]pFor noise variance, randn (size (P)b) Is generated and
Figure FDA0003116790530000036
random matrices of the same size.
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