CN111105364A - Image restoration method based on rank-one decomposition and neural network - Google Patents

Image restoration method based on rank-one decomposition and neural network Download PDF

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CN111105364A
CN111105364A CN201911221840.XA CN201911221840A CN111105364A CN 111105364 A CN111105364 A CN 111105364A CN 201911221840 A CN201911221840 A CN 201911221840A CN 111105364 A CN111105364 A CN 111105364A
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庄吓海
高尚奇
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Abstract

The invention relates to an image restoration method based on rank-one decomposition and a neural network, which comprises the following steps: (1) acquiring paired original images and degraded images to generate a training sample; (2) constructing a rank-one projection unit through a neural network based on a rank-one approximation principle to obtain rank-one approximation of the image; (3) constructing a circulating rank decomposition network through a rank-one projection unit based on a matrix low-rank decomposition principle, wherein the circulating rank decomposition network is used for extracting low-rank components and residual errors of a degraded image; (4) constructing a rank-one reconstruction network by using a residual error network, and recovering an original image from low-rank components and residual errors of a degraded image; (5) training a rank-one decomposition network and a rank-one reconstruction network by using an optimizer; (6) and connecting the trained rank-one decomposition network and the rank-one reconstruction network in series to form a rank-one network for image restoration. Compared with the prior art, the method has the advantages of high robustness, strong generalization capability, short calculation time and convenient realization.

Description

Image restoration method based on rank-one decomposition and neural network
Technical Field
The invention relates to an image restoration method, in particular to an image restoration method based on rank-one decomposition and a neural network.
Background
With the development of deep learning, the image restoration quality and the calculation efficiency are greatly improved, so that the application of the image restoration technology to mobile equipment and real-time image restoration becomes possible. Specifically, the image restoration task can be divided into image denoising, image deblurring and image super-resolution according to the image degradation process in the imaging system. Under natural conditions, the imaging system is subject to interference from a variety of factors, both intrinsic and extrinsic, and thus the image degradation process results in a combination of degradation scenarios. In addition, the images themselves have strong non-local similarity, so that the local similarity between the images can be learned through additional samples, and the non-local similarity of the images themselves can be fully developed through a model. The traditional non-learning method utilizes prior knowledge and an optimization method to restore an image through a degradation process of a modeling image. However, these methods require manual setting of parameters for different tasks, which can result in expensive labor costs in the application due to their non-fully automatic drawbacks. In addition, the learning method is generally realized through an iterative framework, so that the image restoration time is longer during testing. The new learning-based approach simulates the image restoration process by building a network and trains the network with a large number of training samples. The learning-based method has a very objective effect on the task of image restoration, and one is that the learning-based method can learn the local similarity characteristics of the image through a large number of samples, so that the image restoration quality can be greatly improved; and secondly, the method based on learning can be realized in parallel through a deep learning framework, so that the image restoration time can be greatly shortened in the test process. However, in practical tests, the learning-based image restoration method still has the following two challenges:
(1) the restoration results obtained by the learning method are very different for different samples in the same image restoration task, because the condition distributions of different pixels in the same image are different, and thus the robustness of the learning method is insufficient.
(2) For different image restoration tasks, the learning-based method lacks flexibility to adapt to different tasks because the degraded image pixel distribution under different tasks is very different, and thus the generalization ability of the learning method is not sufficient.
The investigation of the existing literature finds that the robustness of the image restoration method can be improved to a great extent by fully developing the non-local similarity of the image. In addition, an effective network structure is designed, and the generalization capability of the learning method can be improved. However, how to improve the robustness and generalization ability of the learning method still remains an open challenge.
Disclosure of Invention
The present invention is directed to overcome the above-mentioned drawbacks of the prior art, and to provide an image restoration method based on rank-one decomposition and neural network.
The purpose of the invention can be realized by the following technical scheme:
an image restoration method based on rank-one decomposition and neural network, the method comprising the steps of:
(1) acquiring paired original images and degraded images to generate a training sample;
(2) constructing a rank-one projection unit through a neural network based on a rank-one approximation principle to obtain a rank-one image of a degraded image;
(3) constructing a circulating rank decomposition network through a rank-one projection unit based on a matrix low-rank decomposition principle, wherein the circulating rank decomposition network is used for extracting low-rank components and residual errors of a degraded image;
(4) constructing a rank-one reconstruction network by using a residual error network, and recovering an original image from low-rank components and residual errors of a degraded image;
(5) training a rank-one decomposition network and a rank-one reconstruction network by using an optimizer;
(6) and connecting the trained rank-one decomposition network and the rank-one reconstruction network in series to form a rank-one network for image restoration.
And (2) constructing a rank-one projection unit through a convolutional neural network.
Finding the optimal rank-one approximation by optimizing a convolutional neural network in the process of constructing the rank-one projection unit, wherein an objective function in the optimization process is as follows:
Figure BDA0002301062220000021
wherein, X is a degraded image,
Figure BDA0002301062220000022
in order to be a rank-one projection,
Figure BDA0002301062220000023
for a rank-one image of the degraded image X,
Figure BDA0002301062220000024
for degraded image X and rank-one image
Figure BDA0002301062220000025
The Euclidean distance of (a) is,
Figure BDA0002301062220000026
to represent
Figure BDA0002301062220000027
The minimum corresponding rank-one projection is taken.
Optimizing a rank-decomposition network in step (3) based on the following objective function:
Figure BDA0002301062220000031
wherein, X is a degraded image,
Figure BDA0002301062220000032
a rank-resolved network is represented, with the rank,
Figure BDA0002301062220000033
a degraded image is mapped to a set of L rank-one images,
Figure BDA0002301062220000034
representing an ith rank-one image of a set of rank-one images,
Figure BDA0002301062220000035
representing a rank-one summed image resulting from summing the L rank-one images,
Figure BDA0002301062220000036
representing degraded image X and L rank-sum images
Figure BDA0002301062220000037
The Euclidean distance of (a) is,
Figure BDA0002301062220000038
to represent
Figure BDA0002301062220000039
And taking the minimum corresponding rank-decomposition network.
The rank-one reconstruction network of step (4) includes three residual error networks:
a first residual network: recovering low-rank components of the original image from the low-rank components of the degraded image;
a second residual network: recovering a residual error of the original image from a residual error of the degraded image;
a third residual network: and restoring the original image by using the low-rank components and the residual error of the restored original image.
The residual error network is a convolution neural network.
Optimizing the rank-one reconstruction network by using the following objective function in the process of constructing the rank-one reconstruction network:
Figure BDA00023010622200000310
wherein ,
Figure BDA00023010622200000311
representing a rank-one reconstruction network, (I)1,I2,…,IL) Represents a low rank component, ELWhich is indicative of the residual error,
Figure BDA00023010622200000312
representing the images recovered by the rank-one reconstruction network, T representing the original image,
Figure BDA00023010622200000313
representing the euclidean distance of the images restored by the rank-one reconstruction network from the original images,
Figure BDA00023010622200000314
to represent
Figure BDA00023010622200000315
And taking the minimum corresponding rank-one to reconstruct the network.
And (5) respectively training a rank-one decomposition network and a rank-one reconstruction network by using the training samples, inputting the rank-one decomposition network into a degraded image, outputting the degraded image into a low-rank component and a residual error of the degraded image, inputting the rank-one reconstruction network into the low-rank component and the residual error of the degraded image output by the rank-one decomposition network, and outputting the degraded image into a restored original image.
Compared with the prior art, the invention has the following advantages:
(1) the method combines the neural network and the rank decomposition to extract the self-similarity characteristic of the image, and has high robustness and strong generalization capability;
(2) the invention has the advantages of full automation, short calculation time, convenient realization and the like.
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FIG. 1 is a block diagram of a flow chart of an image restoration method based on rank-one decomposition and a neural network according to the present invention.
Detailed Description
The invention is described in detail below with reference to the figures and specific embodiments. Note that the following description of the embodiments is merely a substantial example, and the present invention is not intended to be limited to the application or the use thereof, and is not limited to the following embodiments.
Examples
As shown in fig. 1, an image restoration method based on rank-one decomposition and neural network includes the following steps:
step 1, acquiring an original image and a degraded image which are paired to generate a training sample, specifically, generating the degraded image by the original image through degradation operation, and combining the degraded image and the corresponding original image to form a pair of training samples; the training image is inverted and rotated using a data augmentation technique to generate a plurality of training samples. These prepared samples will be used for the network training of the fifth step.
Step 2, because the rank of the degraded image is not one in general, an image with rank one needs to be sought to approximate the degraded image, so based on the principle of rank-one approximation, a rank-one projection unit is constructed through a neural network, and a rank-one image of the degraded image is obtained, specifically: constructing a rank-one projection unit through a convolutional neural network, and searching an optimal rank-one approximation through an optimized convolutional neural network in the process of constructing the rank-one projection unit, wherein an objective function in the optimization process is as follows:
Figure BDA0002301062220000041
wherein, X is a degraded image,
Figure BDA0002301062220000042
in order to be a rank-one projection,
Figure BDA0002301062220000043
the images can be mapped to rank-one images,
Figure BDA0002301062220000044
for a rank-one image of the degraded image X,
Figure BDA0002301062220000045
for degraded image X and rank-one image
Figure BDA0002301062220000046
The Euclidean distance of (a) is,
Figure BDA0002301062220000047
to represent
Figure BDA0002301062220000048
The minimum corresponding rank-one projection is taken.
Different rank-one projections
Figure BDA0002301062220000049
Degraded images can be mapped to different rank-one images, and the goal of the invention is to findFinding a rank-one image closest to the degraded image, and finding an optimal rank-one projection by minimizing the Euclidean distance between the degraded image and the rank-one image, wherein the rank-one projection is parameterized, a convolutional neural network is used for simulation, and the optimal rank-one projection is found by training.
And 3, constructing a circulating rank-decomposition network through a rank-one projection unit based on the matrix low-rank decomposition principle, and extracting low-rank components and residual errors of the degraded image. Specifically, a rank-decomposition network is optimized based on the following objective function:
Figure BDA00023010622200000410
wherein, X is a degraded image,
Figure BDA00023010622200000411
a rank-resolved network is represented, with the rank,
Figure BDA00023010622200000412
mapping a degraded image into L
Figure BDA00023010622200000413
Corresponding rank-resolved network.
By using a rank-decomposition network, two components with high self-similarity can be separated from the degraded image, and the two components can be used as the input of the next network to restore the original image.
And 4, constructing a rank-one reconstruction network by using the residual error network, wherein the rank-one reconstruction network is used for recovering the original image from the low-rank components and the residual errors of the degraded image, and the rank-one reconstruction network in the step 4 comprises three residual error networks:
a first residual network: recovering low-rank components of the original image from the low-rank components of the degraded image;
a second residual network: recovering a residual error of the original image from a residual error of the degraded image;
a third residual network: and restoring the original image by using the low-rank components and the residual error of the restored original image.
The residual error network is a convolutional neural network.
Optimizing the rank-one reconstruction network by using the following objective function in the process of constructing the rank-one reconstruction network:
Figure BDA0002301062220000051
wherein ,
Figure BDA0002301062220000052
representing a rank-one reconstruction network, (I)1,I2,…,IL) Represents a low rank component, ELWhich is indicative of the residual error,
Figure BDA0002301062220000053
representing the images recovered by the rank-one reconstruction network, T representing the original image,
Figure BDA0002301062220000054
representing the euclidean distance of the images restored by the rank-one reconstruction network from the original images,
Figure BDA0002301062220000055
to represent
Figure BDA0002301062220000056
And taking the minimum corresponding rank-one to reconstruct the network.
And 5, training a rank-one decomposition network and a rank-one reconstruction network by using an optimizer, specifically, respectively training the rank-one decomposition network and the rank-one reconstruction network by using training samples, inputting the rank-one decomposition network into a degraded image, outputting a low-rank component and a residual error of the degraded image, inputting the rank-one reconstruction network into a low-rank component and a residual error of the degraded image output by the rank-one decomposition network, and outputting the low-rank component and the residual error of the degraded image into a restored original image.
And 6, connecting the trained rank-one decomposition network and the rank-one reconstruction network in series to form a rank-one network for image restoration, wherein the input of the rank-one network is a degraded image, and the output of the rank-one network is a restored image. In the application process, a user can obtain a restoration result only by inputting the degraded image, and manual operation is not needed in the middle. The encapsulated rank-one network is fully automatic and flexible to use.
The above embodiments are merely examples and do not limit the scope of the present invention. These embodiments may be implemented in other various manners, and various omissions, substitutions, and changes may be made without departing from the technical spirit of the present invention.

Claims (8)

1. An image restoration method based on rank-one decomposition and neural network, characterized by comprising the steps of:
(1) acquiring paired original images and degraded images to generate a training sample;
(2) constructing a rank-one projection unit through a neural network based on a rank-one approximation principle to obtain a rank-one image of a degraded image;
(3) constructing a circulating rank decomposition network through a rank-one projection unit based on a matrix low-rank decomposition principle, wherein the circulating rank decomposition network is used for extracting low-rank components and residual errors of a degraded image;
(4) constructing a rank-one reconstruction network by using a residual error network, and recovering an original image from low-rank components and residual errors of a degraded image;
(5) training a rank-one decomposition network and a rank-one reconstruction network by using an optimizer;
(6) and connecting the trained rank-one decomposition network and the rank-one reconstruction network in series to form a rank-one network for image restoration.
2. The method for image restoration based on rank-one decomposition and neural network as claimed in claim 1, wherein step (2) constructs rank-one projection unit by convolution neural network.
3. The method for image restoration based on rank-one decomposition and neural network as claimed in claim 1, wherein the step (2) finds the optimal rank-one approximation by optimizing the convolutional neural network in the process of constructing the rank-one projection unit, and the objective function in the optimization process is:
Figure FDA0002301062210000011
wherein, X is a degraded image,
Figure FDA0002301062210000012
in order to be a rank-one projection,
Figure FDA0002301062210000013
for a rank-one image of the degraded image X,
Figure FDA0002301062210000014
for degraded image X and rank-one image
Figure FDA0002301062210000015
The Euclidean distance of (a) is,
Figure FDA0002301062210000016
to represent
Figure FDA0002301062210000017
The minimum corresponding rank-one projection is taken.
4. The method for image restoration based on rank-one decomposition and neural network as claimed in claim 1, wherein in step (3), the rank-one decomposition network is optimized based on the following objective function:
Figure FDA0002301062210000018
wherein, X is a degraded image,
Figure FDA0002301062210000019
a rank-resolved network is represented, with the rank,
Figure FDA00023010622100000110
a degraded image is mapped to a set of L rank-one images,
Figure FDA00023010622100000111
representing an ith rank-one image of a set of rank-one images,
Figure FDA00023010622100000112
representing a rank-one summed image resulting from summing the L rank-one images,
Figure FDA00023010622100000113
representing degraded image X and L rank-sum images
Figure FDA0002301062210000021
The Euclidean distance of (a) is,
Figure FDA0002301062210000022
to represent
Figure FDA0002301062210000023
And taking the minimum corresponding rank-decomposition network.
5. The method for image restoration based on rank-one decomposition and neural network as claimed in claim 1, wherein the rank-one reconstruction network of step (4) comprises three residual networks:
a first residual network: recovering low-rank components of the original image from the low-rank components of the degraded image;
a second residual network: recovering a residual error of the original image from a residual error of the degraded image;
a third residual network: and restoring the original image by using the low-rank components and the residual error of the restored original image.
6. The method of claim 5, wherein the residual network is a convolutional neural network.
7. The method for image restoration based on rank-one decomposition and neural network as claimed in claim 1, wherein the rank-one reconstruction network is optimized by using the following objective function in the process of constructing the rank-one reconstruction network:
Figure FDA0002301062210000024
wherein ,
Figure FDA0002301062210000025
representing a rank-one reconstruction network, (I)1,I2,…,IL) Represents a low rank component, ELWhich is indicative of the residual error,
Figure FDA0002301062210000026
representing the images recovered by the rank-one reconstruction network, T representing the original image,
Figure FDA0002301062210000027
representing the euclidean distance of the images restored by the rank-one reconstruction network from the original images,
Figure FDA0002301062210000028
to represent
Figure FDA0002301062210000029
And taking the minimum corresponding rank-one to reconstruct the network.
8. The method for image restoration based on rank-one decomposition and neural network as claimed in claim 1, wherein step (5) trains rank-one decomposition network and rank-one reconstruction network respectively by using training samples, the rank-one decomposition network inputs degraded images and outputs low rank components and residual errors of the degraded images, and the rank-one reconstruction network inputs low rank components and residual errors of the degraded images output by the rank-one decomposition network and outputs restored original images.
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