CN113628114A - Image super-resolution reconstruction method of two-channel sparse coding - Google Patents

Image super-resolution reconstruction method of two-channel sparse coding Download PDF

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CN113628114A
CN113628114A CN202110942771.2A CN202110942771A CN113628114A CN 113628114 A CN113628114 A CN 113628114A CN 202110942771 A CN202110942771 A CN 202110942771A CN 113628114 A CN113628114 A CN 113628114A
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骆霖
杨欣
李恒锐
朱义天
周大可
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Nanjing University of Aeronautics and Astronautics
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Abstract

The invention discloses a double-channel sparse coding image super-resolution reconstruction method, which comprises the steps of firstly preprocessing an LR image by using bicubic interpolation and bilinear interpolation algorithms, and training a dictionary by using a dictionary training method based on non-local self-similarity for a preprocessed image block; then, an improved sparse representation-based reconstruction model is provided, self-adaptive double channels are established, two self-adaptive coefficients are designed to control respective proportions of the two channels, and sparse representation coefficients are calculated according to the model; and finally, reconstructing an HR image block according to the sparse representation coefficient, and fusing all the HR image blocks to obtain a final HR image. The method improves and optimizes the model, improves the robustness of the reconstruction process to a greater extent, improves the quality of the HR image, and has better reconstruction effect in both qualitative and quantitative aspects.

Description

Image super-resolution reconstruction method of two-channel sparse coding
Technical Field
The invention relates to a double-channel sparse coding image super-resolution reconstruction method, and belongs to the technical field of image reconstruction.
Background
The image super-resolution reconstruction is a very classical application in the field of machine vision, and means that a low-resolution target image is reconstructed into a high-resolution image through a corresponding software or hardware method, namely the resolution of the high-resolution target image is improved through the technology. Image super-resolution reconstruction can be divided into two categories: the first category is known as super-resolution reconstruction of a single image. Only the current low resolution target image needs to be referenced and the super resolution of the other related images is not taken into account. The second category is multi-frame video (multi-image) super-resolution reconstruction techniques that require super-resolution reconstruction involving multiple related target images or multiple video frames. Here we focus on super-resolution reconstruction of a single picture.
In real life, the application field of image super-resolution reconstruction is very wide, and the method has extremely important application value in the fields of security monitoring equipment, medical image analysis, biological information identification, microscopic imaging, video restoration and the like.
At present, the following two common image super-resolution reconstruction algorithms are available: conventional reconstruction methods and learning-based reconstruction methods. An image super-resolution reconstruction method based on interpolation and an image super-resolution reconstruction method based on reconstruction belong to the traditional reconstruction methods. The most widely used interpolation methods include nearest neighbor interpolation, bilinear interpolation, and bicubic interpolation. The resolution of the low-resolution image can be improved to a large extent through interpolation, but the edge of the reconstructed image is blurred due to the defect of interpolation. Conventional image reconstruction techniques also include frequency domain based methods and spatial domain based methods. The SR algorithm based on the space domain, including MAP, POCS, IBP, etc., can overcome the disadvantages of the frequency domain method. Therefore, it is widely used.
The image super-resolution reconstruction method based on interpolation is that the value of a certain point can be calculated according to a certain formula by the values of a plurality of known points around the point and the position relation between the surrounding points and the point, and the method is the interpolation method. Regarding how to place points of the original image in the new image and determine specific coordinates; when calculating unknown points, how many surrounding points need to be involved, how the formula is calculated, and different options, the interpolation algorithm involved has certain differences. The super-resolution reconstruction by using the interpolation algorithms is limited in the improvement degree of image details, so that the super-resolution reconstruction is used less. Generally, reconstruction by interpolation between multiple images is also a means.
In order to solve the defects of the traditional reconstruction method, the generated image has blurred edges and lost high-frequency detail information, the image and a complex structure cannot be processed, and researchers apply image super-resolution reconstruction of deep learning. Because the experimental result is satisfactory, the image super-resolution reconstruction based on the deep learning is gradually the mainstream method at present. From the super-resolution SRCNN method proposed at the earliest, researchers began to find out the shortcomings of the algorithm and gradually improved, and the methods structures of FSRCNN, ESPCN, VDSR, RCAN, etc. were designed and used. The method is obtained by research after looking up more documents, and the image super-resolution reconstruction of the currently used deep convolutional network, the image super-resolution reconstruction of the multi-level fusion network and the like are endless. Because the thinking of deep learning is very flexible, researchers can design various more satisfactory structural algorithms through continuous deep research, and the image super-resolution reconstruction method based on deep learning is a widely used method at present and has better development potential in the future.
Meanwhile, the development of the Compressed Sensing (CS) theory provides a new idea for the SR technology. According to the CS theory, under a proper condition, an LR image generated by an HR image is reconstructed into the HR image by adopting a high-probability down-sampling operation. In 2009, Sen et al applied CS theory to SR image restoration. The method utilizes the prior knowledge of sparse coding of the face image under the wavelet base. Then, the correlation between the down-sampling matrix and the wavelet base is reduced by adding a fuzzy filter. However, since the details of the natural image are rich and have a complex structure, the wavelet base cannot provide the optimal sparse coding for the natural image.
Under a particular dictionary pair, the LR image patch has the same sparse coefficients as the reconstructed HR image patch. Therefore, researchers can reconstruct the HR image by using the prior constraint, and a better effect is achieved. The traditional information retrieval method based on sparse representation adopts a unified human resource dictionary and a human resource dictionary, and the performance of information retrieval results is limited. Therefore, Liu et al introduced a K-nearest neighbor (KNN) based dictionary in each LRpatch to reconstruct the HR image.
Fang et al propose a shape adaptive SR reconstruction method that better reflects the complex structure of multispectral images. Li et al synchronously consider the edge and texture features of the image and learn the over-complete sparse dictionaries of the HR and LR image blocks by using a Fast Sparse Coding (FSC) algorithm based on feature classification.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the method for reconstructing the super-resolution image of the two-channel sparse coding has the advantages that the robustness of the reconstruction process is improved to a large extent through the improvement and optimization of the model, and the quality of the HR image is improved.
The invention adopts the following technical scheme for solving the technical problems:
a double-channel sparse coding image super-resolution reconstruction method comprises the following steps:
step 1, preprocessing an original LR image to obtain a training set consisting of a plurality of image blocks;
step 2, training a training set by using a dictionary training method based on non-local self-similarity, and constructing by using a K-SVD algorithm to obtain a dictionary;
step 3, constructing an image SR reconstruction model based on the two-channel sparse representation based on the dictionary obtained in the step 2, and solving the model by adopting a steepest descent method to obtain a sparse representation coefficient;
and 4, reconstructing each image block by utilizing the dictionary and the sparse representation coefficient to obtain an HR image block, and fusing all the HR image blocks to obtain a final HR image.
As a preferred embodiment of the present invention, the specific process of step 1 is as follows:
the original LR images are interpolated separately using bicubic and bilinear interpolation algorithms,obtaining training images X corresponding to each algorithm1And X2From training images X1And X2Extracting image blocks to form a training set Qh。
As a preferred embodiment of the present invention, the specific process of step 3 is as follows:
based on the dictionary obtained in the step 2, an image SR reconstruction model based on the two-channel sparse representation is constructed as follows:
Figure BDA0003215733890000031
where α represents a sparse representation coefficient, c1、c2Representing adaptive channel coefficients, Y representing the sparse processed HR image block, H representing a degradation matrix, DhIs a dictionary, λ is a normal number, β is a constant, w is a constant, τiFor locally adaptive coefficients, xi(u, v) is represented by DhA and
Figure BDA0003215733890000032
the ith element of the different matrix in between,
Figure BDA0003215733890000033
the norm of L1 is shown,
Figure BDA0003215733890000034
representing the norm L2, M × N representing the size of the HR image block;
solving the model by adopting a steepest descent method, obtaining a sparse representation coefficient through iterative calculation, and calculating the adaptive channel coefficient of the nth iteration according to the following formula
Figure BDA0003215733890000035
And
Figure BDA0003215733890000036
Figure BDA0003215733890000037
Figure BDA0003215733890000041
wherein, T(n)Is the intermediate variable for the nth iteration,
Figure BDA0003215733890000042
is the adaptive channel coefficient of the (n-1) th iteration, h is the amplification coefficient, U is the adaptive channel threshold, R(n)Is the residual index for the nth iteration,
Figure BDA0003215733890000043
representing the average value of the previous K iteration results before the (n-1) th iteration, wherein K is a constant;
when the iteration termination condition is met, outputting a sparse representation coefficient of the nth iteration as follows:
α(n+1)＝α(n)-r(n)R(n)
wherein alpha is(n)Sparse representation coefficient for nth iteration, r(n)For the learning rate of the nth iteration,
Figure BDA0003215733890000044
Figure BDA0003215733890000045
Figure BDA0003215733890000046
wherein,
Figure BDA0003215733890000047
representing a shift matrix that shifts the image horizontally by u pixels,
Figure BDA0003215733890000048
representing a shift matrix that vertically shifts the image by v pixels.
As a preferred embodiment of the present invention, the residual index is defined as follows:
Figure BDA0003215733890000049
Figure BDA00032157338900000410
is defined as follows:
Figure BDA00032157338900000411
wherein, R represents a residual index,
Figure BDA00032157338900000412
represents the mean value, R, of the results of the previous K iterations before the nth iteration(n+1-i)Representing the residual index, alpha, of the (n + 1) -i) th iteration(n+1-i)Sparse representation coefficients representing the (n + 1) -i) th iteration.
As a preferred aspect of the present invention, the HR image block in step 4 is represented as follows:
Y＝HDhα+N
wherein D ishThe method is a dictionary, alpha represents a sparse representation coefficient, H represents a degradation matrix, N represents Gaussian white noise, and Y represents an HR image block subjected to sparse processing.
Compared with the prior art, the invention adopting the technical scheme has the following technical effects:
the invention designs a training method based on non-local self-similarity to train a dictionary, and the method makes full use of the redundancy characteristic of images. A sparse representation-based reconstruction model is improved and comprises a fidelity term and a regular term. In the aspect of fidelity, a self-adaptive dual-channel optimization model is established, so that good robustness is ensured, and high-quality reconstruction is obtained. Two adaptive coefficients are designed to control the respective proportions of the two channels. In addition, an adaptive regularization term is constructed based on the image spatial features to sharpen edges and suppress noise. Simulation results show that the method has better reconstruction effect in qualitative and quantitative aspects.
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FIG. 1 is an overall architecture diagram of the image super-resolution reconstruction method of the two-channel sparse coding of the present invention.
Fig. 2 is a model schematic based on sparse representation.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.
In order to ensure that the network model has good robustness, the reconstructed image can well solve the problems of edge sharpening, noise suppression and the like. The invention provides a double-channel sparse coding image super-resolution reconstruction method, which comprises the following specific steps as shown in figure 1:
step 1, carrying out interpolation on an original LR image by adopting a bicubic interpolation algorithm and a bilinear interpolation algorithm to obtain a training set.
Respectively interpolating the original LR image by using bicubic interpolation and bilinear interpolation algorithms to obtain a training set image X1And training set image X2. By X1And X2Form a training set Qh＝[x1,x2,…,xq]，xiRepresenting the vector form of the ith image block.
Step 2, training the training set by adopting a dictionary training method based on non-local self-similarity, and constructing by using a K-SVD algorithm to obtain a dictionary DhThe redundancy characteristic of the image is fully utilized.
And 3, establishing an image SR reconstruction model based on dual-channel sparse representation, simultaneously using an L1 norm and an L2 norm in the model, introducing self-adaptive parameters, and solving the model to obtain a sparse representation coefficient.
The two-channel model is as follows:
Figure BDA0003215733890000061
wherein, c1And c2Adaptive Channel Coefficients (ACCs). ACCs are used to control the ratio of the L1 norm channel and the L2 norm channel.
To determine the ACCs, SR reconstruction is made more adaptive. According to the above expression, the introduced residual index is:
Figure BDA0003215733890000062
r is a residual index, and when R is relatively large, the robustness of the algorithm needs to be enhanced.
Introduction of
Figure BDA0003215733890000063
The average value of the results of K iterations before the current iteration is shown and is given
Figure BDA0003215733890000064
Is defined as follows:
Figure BDA0003215733890000065
wherein K is a constant.
Finally, the ACCs for the nth iteration can be calculated.
In the following, a brief description of the sparse representation is given, and fig. 2 is a model illustration based on the sparse representation.
In a general image degradation model, the HR image Z is represented by a degradation matrix H and noise N as:
Y＝HZ+N
z represents the original HR image, Y represents the LR image, H represents the degradation matrix, and N represents white Gaussian noise.
The solution to the image degradation equation is a highly uncertain problem, the solution of which is not unique. CS theory of laborNote that Z can be in an overcomplete dictionary DhThe sparse coding is represented as:
Z＝Dhα
then, one can obtain:
Y＝HDhα+N
under the framework of the maximum posterior probability theory, the image SR reconstruction problem is modeled as a sparse regularization optimization problem:
Figure BDA0003215733890000071
α is a sparse representation coefficient of the image block x. | alpha | non-conducting phosphor1Is the L1 norm of α, representing the sum of the absolute values of all elements in α, and λ is a positive constant.
To further improve the reconstruction effect, a new spatial domain constraint term is added, which is expressed as follows:
Figure BDA0003215733890000072
v (X) represents the reconstruction of the spatial constraint term and β is a constant that balances the proportions of the terms. V (X) is a very important parameter, which determines whether the performance of the network model can be further improved.
The bilateral tv (btv) regularization term is proposed as a feature transform on T1, denoted as:
Figure BDA0003215733890000073
Figure BDA0003215733890000074
is a shift matrix that can shift the image X by u and v pixels horizontally and vertically, w is a constant whose value is set to 3, and τ is a constant, determined experimentally.
By combining and modifying the above formula, one can obtain:
Figure BDA0003215733890000075
some action then needs to be taken to sharpen the edge. It can be seen that the larger τ, the sharper the edges of the reconstructed HR image, but the more noisy. Conversely, a smaller τ may smooth the image, reducing noise, but blurring the edges.
An adaptive regularization term is given below:
Figure BDA0003215733890000076
τiin order to be a local adaptive coefficient,
Figure BDA0003215733890000077
based on the above analysis, the image reconstruction problem is transformed into the following model optimization problem:
Figure BDA0003215733890000078
there is no closed form solution to the minimization problem of the above equation. The iterative solution framework is:
α(n+1)＝α(n)-r(n)R(n)
α(n)is the sparseness coefficient, r, in n iterations(n)Is the learning rate calculated for the nth iteration.
Calculating adaptive channel coefficients according to a formula
Figure BDA0003215733890000081
And
Figure BDA0003215733890000082
Figure BDA0003215733890000083
Figure BDA0003215733890000084
Figure BDA0003215733890000085
by setting up
Figure BDA0003215733890000086
To determine the learning rate:
Figure BDA0003215733890000087
Figure BDA0003215733890000088
and 4, reconstructing the image blocks in the training set by using the sparse representation coefficient to obtain HR image blocks, and fusing all the HR image blocks to obtain a final HR image.
Example (b):
the method comprises the following steps: yang91 was selected as the training Set, and Set5 and Set14 were selected as the test Set.
Step two: for a more convenient and intuitive comparison experiment, all images were cut uniformly to the same size, i.e., 256 × 256. To blur the original image, an LR image thereof is obtained. The image blocks are set to a size of 10 x 10 with an overlap of 2 pixels.
Step three: gaussian noise is added and a down-sampling operation is performed. The gaussian kernel size is 7 × 7, and the down-sampling factors are set to × 2, × 3, × 4 according to different reconstruction experiments.
Step four: and loading a training set and starting to train the network model.
The above embodiments are only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited thereby, and any modifications made on the basis of the technical scheme according to the technical idea of the present invention fall within the protection scope of the present invention.

Claims (5)

1. A double-channel sparse coding image super-resolution reconstruction method is characterized by comprising the following steps:
step 1, preprocessing an original LR image to obtain a training set consisting of a plurality of image blocks;
step 2, training a training set by using a dictionary training method based on non-local self-similarity, and constructing by using a K-SVD algorithm to obtain a dictionary;
step 3, constructing an image SR reconstruction model based on the two-channel sparse representation based on the dictionary obtained in the step 2, and solving the model by adopting a steepest descent method to obtain a sparse representation coefficient;
and 4, reconstructing each image block by utilizing the dictionary and the sparse representation coefficient to obtain an HR image block, and fusing all the HR image blocks to obtain a final HR image.
2. The two-channel sparse coding image super-resolution reconstruction method according to claim 1, wherein the specific process of the step 1 is as follows:
respectively interpolating the original LR image by using bicubic interpolation and bilinear interpolation algorithms to obtain a training image X corresponding to each algorithm1And X2From training images X1And X2Extracting image blocks to form a training set Qh。
3. The two-channel sparse coding image super-resolution reconstruction method according to claim 1, wherein the specific process of the step 3 is as follows:
based on the dictionary obtained in the step 2, an image SR reconstruction model based on the two-channel sparse representation is constructed as follows:
Figure FDA0003215733880000011
where α represents a sparse representation coefficient, c1、c2Representing adaptive channel coefficients, Y representing the sparse processed HR image block, H representing a degradation matrix, DhIs a dictionary, λ is a normal number, β is a constant, w is a constant, τiFor locally adaptive coefficients, xi(u, v) is represented by DhA and
Figure FDA0003215733880000012
the ith element of the different matrix in between,
Figure FDA0003215733880000013
the norm of L1 is shown,
Figure FDA0003215733880000014
representing the norm L2, M × N representing the size of the HR image block;
solving the model by adopting a steepest descent method, obtaining a sparse representation coefficient through iterative calculation, and calculating the adaptive channel coefficient of the nth iteration according to the following formula
Figure FDA0003215733880000015
And
Figure FDA0003215733880000016
Figure FDA0003215733880000017
Figure FDA0003215733880000021
wherein, T(n)Is the intermediate variable for the nth iteration,
Figure FDA0003215733880000022
is the adaptive channel coefficient of the (n-1) th iteration, h is the amplification coefficient, U is the adaptive channel threshold, R(n)Is the residual index for the nth iteration,
Figure FDA0003215733880000023
representing the average value of the previous K iteration results before the (n-1) th iteration, wherein K is a constant;
when the iteration termination condition is met, outputting a sparse representation coefficient of the nth iteration as follows:
α(n+1)＝α(n)-r(n)R(n)
wherein alpha is(n)Sparse representation coefficient for nth iteration, r(n)For the learning rate of the nth iteration,
Figure FDA0003215733880000024
Figure FDA0003215733880000025
Figure FDA0003215733880000026
wherein,
Figure FDA0003215733880000027
representing a shift matrix that shifts the image horizontally by u pixels,
Figure FDA0003215733880000028
representing a shift matrix that vertically shifts the image by v pixels.
4. The dual-channel sparse-coding image super-resolution reconstruction method of claim 3, wherein the residual index is defined as follows:
Figure FDA0003215733880000029
Figure FDA00032157338800000210
is defined as follows:
Figure FDA00032157338800000211
wherein, R represents a residual index,
Figure FDA00032157338800000212
represents the mean value, R, of the results of the previous K iterations before the nth iteration(n+1-i)Representing the residual index, alpha, of the (n + 1) -i) th iteration(n+1-i)Sparse representation coefficients representing the (n + 1) -i) th iteration.
5. The dual-channel sparsely encoded image super-resolution reconstruction method of claim 1, wherein the HR image block of step 4 is represented as follows:
Y＝HDhα+N
wherein D ishThe method is a dictionary, alpha represents a sparse representation coefficient, H represents a degradation matrix, N represents Gaussian white noise, and Y represents an HR image block subjected to sparse processing.
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