CN109146805B - Image restoration method based on double-layer block extraction framework - Google Patents

Image restoration method based on double-layer block extraction framework Download PDF

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CN109146805B
CN109146805B CN201810836102.5A CN201810836102A CN109146805B CN 109146805 B CN109146805 B CN 109146805B CN 201810836102 A CN201810836102 A CN 201810836102A CN 109146805 B CN109146805 B CN 109146805B
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常丽萍
鲁欣
姜倩茹
徐红
李胜
何熊熊
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Zhejiang University of Technology ZJUT
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Abstract

The double-layer block extraction framework firstly carries out first block decomposition on a current damaged image, then carries out second block decomposition on each single block, each single block after the first decomposition is taken as a restoration object, then independently restores each single block by utilizing parallel operation, and finally integrates all the restored single blocks to finish the final image restoration. And the improved dictionary updating frame is used for updating the dictionary obtained by training again by using a Closed-form solution aiming at the dictionary updating stage of the K-SVD image restoration algorithm. The double-layer block extraction framework and the improved K-SVD dictionary updating algorithm can improve the repairing effect of the damaged image, the repaired image is clearer in detail, and meanwhile, the repairing efficiency of the image is improved due to parallel operation. The invention is not limited to the field of image restoration, and the double-layer block extraction framework can be applied to any other image processing field and has very wide application prospect.

Description

Image restoration method based on double-layer block extraction framework
The technical field is as follows:
the invention relates to a computer image restoration method.
Background art:
the main idea of digital image restoration is to fill and repair the damaged area by using the known information in the image, so that the restored image meets the visual requirements of human beings. Digital image restoration techniques are now used in many areas, in the medical field, to restore missing or blurred medical images to assist physicians in diagnosing medical conditions. It can also be used in video processing, such as assisting police in catching criminals.
How to utilize the known information of the damaged image is the core of solving the image restoration problem. Three types of algorithms which are representative in comparison are an image restoration model based on Partial Differential Equations (PDE), an image restoration model based on texture synthesis, and an image restoration model based on sparse representation. The core of the sparse representation-based image restoration model is mainly divided into 2 processes, one is dictionary generation and selection, and the other is how to solve the rarest solution. And the learning dictionary is based on a large number of learning samples, through the characteristics of the learning object signals, the rarest solution aiming at the current signals is solved, the dictionary is further updated, and the finally optimized dictionary is obtained through cyclic iteration. The learning dictionary breaks through the adaptability limitation of the fixed dictionary and can achieve better repairing effect, but the dictionary training needs a large amount of time as cost. Currently, the commonly used learning dictionary training algorithms include an MOD dictionary training algorithm, a K-SVD dictionary training algorithm, an online dictionary training algorithm and the like.
In the image restoration model based on sparse representation, if the whole image is taken as input, the dictionary dimension of the design is large, thereby increasing the complexity and the calculation amount of the restoration algorithm. Therefore, the image is generally subjected to a blocking operation, and the whole image is subjected to blocking processing according to a block template with a certain size. The traditional block fetching method is to use a block fetching template to fetch blocks of a picture in a non-overlapping extraction mode, but the non-overlapping fetching of blocks can cause a block boundary effect of a repaired image. Then, overlapping extraction of image blocks is proposed, and complete overlapping extraction is commonly used at present. The same repeated information exists between the adjacent image blocks, the overlapped part is only required to be placed back into the corresponding area of the original image after all the image blocks are repaired and divided by the weight value for average operation, the repairing performance of the image can be further improved by completely overlapping extraction operation, and the blocking effect phenomenon is effectively avoided. However, when the whole image is subjected to full-overlap extraction, the obtained image data is a matrix with a very large number of columns, such as a 256 × 256 image, and the obtained data matrix after performing 8 × 8 full-overlap operation is 64 × 62001. If the whole matrix is used as the input of the image restoration model, the calculation amount of the model is increased.
The invention content is as follows:
in order to overcome the defects in the prior art, the invention provides an image restoration method based on a double-layer block extraction framework.
The double-layer block extraction framework provided by the invention can reduce the data volume of dictionary training each time and accelerate the training speed. Meanwhile, an improved dictionary updating framework is provided, the dictionary obtained by training is updated again by using a dictionary optimization Closed-form solution, and then the two frameworks are combined to improve the K-SVD image restoration algorithm. Under the framework of double-layer block extraction, compared with the existing algorithm, the improved K-SVD image restoration algorithm has the advantages that the performance is greatly improved, the restoration result is clearer in detail, and the image restoration speed is accelerated due to the adoption of parallel operation. The technical scheme of the invention is as follows:
an improved K-SVD image restoration method based on a double-layer block extraction framework comprises the following steps:
(1) two-layer partitioning extraction and consolidation framework
(a) A first stage of double-layer block extraction: let broken image P be E.RL×LSelecting a block template with the size of NXN for first blocking, and setting the interval between blocks as Delta when the blocks are taken1(△1Less than or equal to N). The block taking sequence is that the block taking module is moved by one column or one row. For picture P ∈ RL×LThe image blocks formed after the first stage of block taking are combined into a whole
Figure GDA0002696926350000031
(b) And a second stage: for a set of image blocks
Figure GDA0002696926350000032
Each block p thereinkThe selected block-fetching template size is n × n, and the interval between blocks in block fetching is Δ2(△2N) the same order of block fetching as in the first stage can be adopted.
(c) Will be in each image block pkAll sample blocks taken are stitched, wherein each sample block forms n2The X1 column vector, resulting in the composition matrix X. And the matrix is used as an operation object based on the improved K-SVD image restoration algorithm, and waits for all the image blocks pkAnd finishing repairing of the corresponding matrix X, returning according to the reverse operation sequence of the block taking, averaging the overlapped parts, and integrating to obtain a complete repaired image.
(2) Improved K-SVD image restoration algorithm
Firstly, learning and training a damaged image P by using a traditional K-SVD dictionary learning algorithm to obtain a dictionary DKSVDThen, a dictionary updated analytic (Closed-form) formula is deduced, and the obtained dictionary D is subjected toKSVDPerforming dictionary updating again to obtain optimized dictionary DoptAnd the dictionary is used as the dictionary when the image is repaired.
In a word, the invention provides a double-layer block extraction framework, namely, the damaged image is subjected to secondary block division, a single block obtained after the first block division is taken as an object to be repaired each time, and then the second block division is carried out, so that the data volume of dictionary training each time can be reduced, and the training speed is accelerated. Meanwhile, each image block is independently repaired, so that the image repairing speed is increased by utilizing parallel operation. And simultaneously, an improved dictionary updating framework is provided, the dictionary obtained by training is updated again by using a dictionary optimization Closed-form solution, and then the two frameworks are combined to improve the K-SVD image restoration algorithm. Experimental simulation results show that compared with the existing algorithm, the improved K-SVD image restoration algorithm based on double-layer block extraction provided by the invention has the advantages that the performance is greatly improved, the restoration result is clearer in details, and meanwhile, due to the introduction of parallel computing, the restoration speed is accelerated.
The invention provides a double-layer block extraction framework and an improved dictionary updating framework based on image restoration algorithm research of sparse representation, is used for image restoration, and can be used for cultural relic protection, video processing, medical imaging and the like.
The invention is not limited to the field of image restoration, and the double-layer block extraction framework can be applied to any other image processing field and has very wide application prospect. The invention has the advantages that: the repair result is clearer in detail, and the repair speed is increased.
Description of the drawings:
FIG. 1 is a flow chart of an image inpainting algorithm of the present invention
FIG. 2 is a diagram of a two-layer chunking extraction framework
FIG. 3 is an improved dictionary update framework
Fig. 4a to 4d are repairing effects of 25% missing pixels in an image, showing that the repairing effects of the invention and a DCT dictionary repairing algorithm and a K-SVD dictionary repairing algorithm are compared with each other, where: figure 4a is a missing 25% pixel Barbara image; fig. 4b is a DCT repair image, PSNR 28.2866dB (SSIM 0.9095); fig. 4c is a K-SVD repair image, PSNR 31.8112dB (SSIM 0.9502); fig. 4d shows a repair image of the proposed algorithm, PSNR 34.3248dB (SSIM 0.9613).
Fig. 5a to 5d are repairing effects of 50% missing pixels in an image, showing that the repairing effects of the invention and a DCT dictionary repairing algorithm and a K-SVD dictionary repairing algorithm are compared with each other, wherein: figure 5a is a Barbara image with 50% pixels missing; fig. 5b is a DCT repair image, PSNR 27.3560dB (SSIM 0.8916); fig. 5c is a K-SVD repair image, PSNR 29.0650dB (SSIM 0.9251); fig. 5d shows a repair image of the proposed algorithm, PSNR 32.8734dB (SSIM 0.9511).
Fig. 6a to 6d are image restoration effects when 75% of pixels are missing in an image, showing the comparison of the image restoration effects of the present invention with the DCT dictionary restoration algorithm and the K-SVD dictionary restoration algorithm, wherein: figure 6a is a 75% missing pixel Barbara image; fig. 6b is a DCT repair image, PSNR 23.1367dB (SSIM 0.7690); fig. 6c is a K-SVD repair image, PSNR 24.3595dB (SSIM 0.8010); fig. 6d shows a repair image of the proposed algorithm, PSNR 28.3609dB (SSIM 0.9131).
The specific implementation mode is as follows:
the invention will be further described with reference to specific examples, but the scope of the invention is not limited thereto.
The invention discloses an image restoration method based on a double-layer block extraction framework, which specifically comprises the following steps:
(1) extracting double-layer blocks and integrating frames;
(a) a first stage of double-layer block extraction: let broken image P be E.RL×LSelecting a block template with the size of NXN for first blocking, and setting the interval between blocks as Delta when the blocks are taken1(△1Less than or equal to N). The block taking sequence is that the block taking module is moved by one column or one row. For picture P ∈ RL×LThe image blocks formed after the first stage of block taking are combined into a whole
Figure GDA0002696926350000061
(b) And a second stage: for a set of image blocks
Figure GDA0002696926350000062
Each block p thereinkThe selected block-fetching template size is n × n, and the interval between blocks in block fetching is Δ2(△2N) the same order of block fetching as in the first stage can be adopted.
(c) Will be in each image block pkAll sample blocks taken are stitched, wherein each sample block forms n2The X1 column vector, resulting in the composition matrix X. And the matrix is used as an operation object based on the improved K-SVD image restoration algorithm, and waits for all the image blocks pkAnd finishing repairing of the corresponding matrix X, returning according to the reverse operation sequence of the block taking, averaging the overlapped parts, and integrating to obtain a complete repaired image.
(2) Improving a learning algorithm of a K-SVD dictionary;
training damaged images by utilizing K-SVD dictionary learning algorithm to obtain dictionary DKSVDThen, the obtained data is used as the input of the updated Closed-form dictionary, and the sparse coefficient of the image sample is firstly obtained by using the OMP algorithm
Figure GDA0002696926350000063
Then fixed
Figure GDA0002696926350000064
And updating the dictionary. The specific optimization problem can be described as follows:
Figure GDA0002696926350000065
wherein
Figure GDA0002696926350000066
Is corresponding to image block ykThe local mask matrix of (A), D is a sparse dictionary, alphakAs a sparse coefficient, Y represents the restored image, RkDenotes a block fetch operation, yk＝RkY, the number of the image blocks is T, namely k is more than or equal to 1 and less than or equal to T. The updating of the Closed-form dictionary is mainly divided into the following two steps:
the first step is as follows:
the optimization problem can be converted into:
Figure GDA0002696926350000071
wherein
Figure GDA0002696926350000072
And a sparse coefficient matrix
Figure GDA0002696926350000073
The specific solving process is as follows, firstly, SVD decomposition is carried out on the sparse coefficient matrix A to obtain
Figure GDA0002696926350000074
Wherein
Figure GDA0002696926350000075
We then split Ψ and χ into two parts, i.e., using the dimension of Σ A
Figure GDA0002696926350000076
Then:
Figure GDA0002696926350000077
then equation (2) can be converted to:
Figure GDA0002696926350000078
to minimize the above equation, take
Figure GDA0002696926350000079
At this time Ψ may be updated by the following equation,
Figure GDA00026969263500000710
the second step is that:
the goal is to solve for D from ΨoptFirst, Ψ may be divided into Ψ ═ Ψ1,Ψ2,…ΨT]Wherein each dictionary Ψk∈RS×QThen, solving the problem can be converted into:
Figure GDA0002696926350000081
order to
Figure GDA0002696926350000082
Then equation (6) is equivalent to
Figure GDA0002696926350000083
Similar to the first step solution process, M is first subjected to SVD decomposition, i.e.
Figure GDA0002696926350000084
Wherein
Figure GDA0002696926350000085
Then dividing D and psi into parts
Figure GDA0002696926350000086
While
Figure GDA0002696926350000087
Can obtain
Figure GDA0002696926350000088
Equation (7) can be converted to:
Figure GDA0002696926350000089
to minimize the above equation, let
Figure GDA00026969263500000810
Can deduce
Figure GDA00026969263500000811
DoptNamely, the dictionary optimization analysis (Closed-form) formula.
Fig. 1 shows a flow chart of an image algorithm based on two-layer block extraction, wherein the method of the invention is implemented, the two-layer block extraction framework is shown in fig. 2, and the improved K-SVD image restoration algorithm is shown in fig. 3. In the experimental simulation, the performance is measured by using two indexes of PSNR and SSIM. The test pictures used in the experiment are all from commonly used test pictures, such as Peppers, Lena, House, etc., and the size of each picture is 128x 128. To verify the validity of the two-layer block extraction framework, a simulation experiment was performed on the full overlap extraction and the two-layer block extraction under the same K-SVD algorithm, and parameters of the block size were discussed, i.e., N ═ 16, 32, 64, where the initial dictionary was a DCT dictionary, the dictionary size was 64x256, and the dictionary size was 64x256The number of iterations is 15, and the other parameters m is 8, δ1＝N/2,δ21. In the case of text pollution and curve breakage of the image, the simulation results are shown in tables 1 and 2, and it can be seen that the repair performance is improved to a certain extent by using the double-layer block extraction framework provided by the present invention compared with the conventional full overlap mode, and when N is 16, the PSNR can be improved by about 3 dB.
TABLE 1 repair results under text contamination at different N values
Figure GDA0002696926350000091
TABLE 2 repair results under curve failure at different N values
Figure GDA0002696926350000092
Fig. 4, 5 and 6 are schematic diagrams of the improved K-SVD restoration (i.e. the optimized dictionary obtained based on the dual-layer block extraction framework and the improved image restoration algorithm) and the restoration effect of the DCT dictionary and the conventional K-SVD dictionary on the image when the barbarbara image loses 25%, 50% and 75% of pixels, and tables 3, 4 and 5 are schematic diagrams of the restoration effect of different restoration algorithms on different images: boat, Peppers, Barbara, Lena, House, 25%, 50%, and 75% missing image pixels. As can be seen from the graph, the improved K-SVD restoration provided by the invention has a great improvement on restoration effect compared with DCT dictionary restoration and K-SVD restoration, the restored image is clearer in detail, and a better restoration result can be obtained under the condition that 75% of pixels are lost. Meanwhile, each block is independently processed and then overlapped, so that parallel calculation can be adopted, the image restoration time is saved, and the image restoration efficiency is accelerated.
Table 3 repair results of different repair algorithms for different images at 25% pixel dropout
Figure GDA0002696926350000101
Table 4 repair results of different repair algorithms for different images with 50% missing pixels
Figure GDA0002696926350000102
Figure GDA0002696926350000111
Table 5 repair results of different repair algorithms for different images with 75% pixel missing
Figure GDA0002696926350000112
Therefore, the method can improve the image restoration effect and efficiency, has great significance to the image restoration field, and particularly provides a new image block extraction mode by the proposed double-layer block extraction framework, is not limited to the image restoration field, and can be applied to any image processing field related to image blocks.
The embodiments described in this specification are merely illustrative of implementations of the inventive concept and the scope of the present invention should not be considered limited to the specific forms set forth in the embodiments but rather by the equivalents thereof as may occur to those skilled in the art upon consideration of the present inventive concept.

Claims (1)

1. The image restoration method based on the double-layer block extraction framework specifically comprises the following steps:
(1) extracting double-layer blocks and integrating frames;
(a) a first stage of double-layer block extraction: let broken image P be E.RL×LSelecting a block template with the size of NXN for first blocking, and setting the interval between blocks as Delta when the blocks are taken1，△1N is less than or equal to N; the block taking sequence is a column-column moving block taking module or a row-line moving block taking moduleA plate; for picture P ∈ RL×LThe image blocks formed after the first stage of block taking are combined into a whole
Figure FDA0002696926340000011
(b) And a second stage: for a set of image blocks
Figure FDA0002696926340000012
Each block p thereinkThe selected block-fetching template size is n × n, and the interval between blocks in block fetching is Δ2，△2N is less than or equal to n, the same block taking sequence as the first stage can be adopted;
(c) will be in each image block pkAll sample blocks taken are stitched, wherein each sample block forms n2A column vector of X1 to obtain a composition matrix X; and the matrix is used as an operation object based on the improved K-SVD image restoration algorithm, and waits for all the image blocks pkAfter the corresponding matrix X is repaired, putting back the matrix X according to the reverse operation sequence of the block taking, averaging the overlapped parts and integrating to obtain a complete repaired image;
(2) improving a learning algorithm of a K-SVD dictionary;
training damaged images by utilizing K-SVD dictionary learning algorithm to obtain dictionary DKSVDThen, the obtained data is used as the input of the updated Closed-form dictionary, and the sparse coefficient of the image sample is firstly obtained by using the OMP algorithm
Figure FDA0002696926340000013
Then fixed
Figure FDA0002696926340000014
Updating the dictionary; the specific optimization problem can be described as follows:
Figure FDA0002696926340000015
wherein
Figure FDA0002696926340000016
Is corresponding to image block ykThe local mask matrix of (A), D is a sparse dictionary, alphakAs a sparse coefficient, Y represents the restored image, RkDenotes a block fetch operation, yk＝RkY, the number of the image blocks is T, namely k is more than or equal to 1 and less than or equal to T; the updating of the Closed-form dictionary is divided into the following two steps:
the first step is as follows:
the optimization problem can be converted into:
Figure FDA0002696926340000021
wherein
Figure FDA0002696926340000022
And a sparse coefficient matrix
Figure FDA0002696926340000023
The specific solving process is as follows, firstly, SVD decomposition is carried out on the sparse coefficient matrix A to obtain
Figure FDA0002696926340000024
Wherein
Figure FDA0002696926340000025
Psi and χ are then split into two parts, i.e., using the dimension of Σ a
Figure FDA0002696926340000026
Then:
Figure FDA0002696926340000027
then equation (2) can be converted to:
Figure FDA0002696926340000028
to minimize the above equation, take
Figure FDA0002696926340000029
At this time Ψ is updated by the following equation,
Figure FDA00026969263400000210
the second step is that:
the goal is to solve for D from ΨoptFirst, Ψ may be divided into Ψ ═ Ψ1,Ψ2,…ΨT]Wherein each dictionary Ψk∈RS×QThen, solving the problem can be converted into:
Figure FDA0002696926340000031
order to
Figure FDA0002696926340000032
Then equation (6) is equivalent to
Figure FDA0002696926340000033
Similar to the first step solution process, M is first subjected to SVD decomposition, i.e.
Figure FDA0002696926340000034
Wherein
Figure FDA0002696926340000035
Then dividing D and psi into parts
Figure FDA0002696926340000036
While
Figure FDA0002696926340000037
Figure FDA0002696926340000038
Can obtain
Figure FDA0002696926340000039
Equation (7) translates to:
Figure FDA00026969263400000310
to minimize the above equation, let
Figure FDA00026969263400000311
Deducing
Figure FDA00026969263400000312
DoptThe analysis formula is the dictionary optimization analysis formula.
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