CN113643399B - Color image self-adaptive reconstruction method based on tensor chain rank - Google Patents
Color image self-adaptive reconstruction method based on tensor chain rank Download PDFInfo
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Abstract
The invention relates to a color image self-adaptive reconstruction method based on tensor chain rank, which comprises the steps of processing an image to be reconstructed to generate a reference image and a high-order tensor to be complemented; step two, adding different offsets to a first-order tensor chain rank of an initialized tensor chain rank of a high-order tensor to be complemented to generate m candidate tensor chain ranks; thirdly, carrying out minimization treatment on each candidate tensor chain rank to obtain m reconstructed tensors; converting the reconstructed tensor into a reconstructed image; fourthly, selecting a candidate tensor chain rank corresponding to the reconstructed image with the highest structural similarity as a first-order tensor chain rank according to the structural similarity between the reconstructed image and the reference image; and fifthly, repeatedly executing the second to fourth steps until the structural similarity between the reconstructed image and the reference image is greater than 0.95, and obtaining the optimal reconstructed image. The method can reconstruct the missing image without resorting to the original data structure.
Description
Technical Field
The invention belongs to the technical field of image processing, and particularly relates to a color image self-adaptive reconstruction method based on tensor chain rank.
Background
As digital image processing is widely used in the fields of communication, medicine, aerospace and the like, as an important research field of digital image processing, image restoration gradually becomes a research hotspot. Since color images are natural tensor forms, the reconstruction problem for color images can be considered as a tensor complement problem.
The Tensor chain (TT) decomposition model solves the problem that the efficiency of capturing Tensor global information by a rank minimization scheme is low due to unbalanced matrix size of the traditional Tensor decomposition model expansion matrix by means of a more balanced matrixing mode, and becomes a research hot spot in recent years. The tensor chain decomposition model can fully capture the correlation between data with different dimensions, has successful application in digital signal processing, image processing and the like, converts the image data into a high-order tensor by means of a tensor enhancement technology, and realizes high-quality reconstruction of color images by means of an image complement method based on tensor chains.
At present, the color image reconstruction based on the TT method needs to acquire the rank information of the complete image data in advance, and parameters need to be continuously adjusted according to an experimental result compared with an original image so as to achieve the optimal reconstruction effect. In practical problems, the data of the image to be reconstructed is incomplete, and the rank information of the complete image data cannot be obtained, so that the current TT-based method is difficult to apply to the practical problems. In addition, the existing TT-based method regards the reconstruction quality of the known data as the reconstruction quality of the whole data with an initial rank obtained randomly, which can cause artifacts to seriously affect the reconstruction quality of the known data, and when the image data deletion rate is too high, the reconstruction quality of the known data cannot represent the reconstruction quality of the whole image.
In summary, the application provides a color image self-adaptive reconstruction method based on tensor chain rank, which is applicable to all types of data-missing images.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide a color image self-adaptive reconstruction method based on tensor chain rank.
The technical scheme adopted by the invention for solving the technical problems is as follows:
the color image self-adaptive reconstruction method based on tensor chain rank is characterized by comprising the following steps:
the method comprises the steps of firstly, processing an image to be reconstructed to generate a reference image and a high-order tensor to be complemented;
a second step of adding different offsets to a first-order tensor chain rank of an initialized tensor chain rank of a high-order tensor to be complemented to generate m candidate tensor chain ranks, wherein the m candidate tensor chain ranks form a first-order candidate tensor chain rank list;
thirdly, carrying out minimization treatment on each candidate tensor chain rank in the first-order candidate tensor chain rank list, and reconstructing the high-order tensor to be complemented to obtain m reconstructed tensors; converting each reconstructed tensor into an image with the same size as the original data of the image to be reconstructed to obtain m reconstructed images;
a fourth step of respectively calculating the structural similarity between each reconstructed image and the reference image, selecting a candidate tensor chain rank corresponding to the reconstructed image with the highest structural similarity as a first-order tensor chain rank, and finishing the selection of the first-order tensor chain rank and the updating of the initialized tensor chain rank of the high-order tensor to be complemented;
and fifthly, repeatedly executing the operations of the second step to the fourth step on each order of tensor chain rank of the initialized tensor chain rank of the high-order tensor to be complemented obtained in the fourth step, and stopping the selection of the tensor chain rank until the structural similarity between the reconstructed image and the reference image is greater than 0.95, and stopping iteration of the image to be reconstructed to obtain the optimal reconstructed image.
Supplementing the image to be reconstructed by adopting a Delaunay triangulation interpolation method to obtain a reference image; and generating a high-order tensor to be complemented by using a tensor enhancement method.
And thirdly, respectively carrying out the inverse operation of the tensor enhancement method in the first step on the m reconstructed tensors, and converting the reconstructed tensors into images with the same size as the original data of the images to be reconstructed.
Initializing tensor chain rank r of high-order tensor to be complemented 1 =r 2 =…=r N-1 =1, n represents the total order of the high-order tensor to be complemented.
Compared with the prior art, the invention has the beneficial effects that:
firstly, the image to be reconstructed is complemented by using a Delaunay triangulation interpolation method, so that most structural information of the image to be reconstructed is effectively recovered, the interpolated image is used as a reference image for calculating structural similarity, the structural information of the interpolated image is used for guiding a reconstruction direction of minimizing a tensor chain rank of a high-order tensor to be complemented, the missing image can be reconstructed without the aid of an original data structure of the image to be reconstructed, and the method is suitable for images with all types of data missing.
Secondly, under the condition that original complete data of an image to be reconstructed is unknown, a backtracking method is adopted for each order of tensor chain rank to generate candidate tensor chain ranks, the candidate tensor chain rank corresponding to the reconstructed image with the highest structural similarity of the reference image is selected as the tensor chain rank of each order, the image to be reconstructed is iterated successively to obtain an optimal reconstructed image, and the problem that the conventional tensor chain-based completion method is difficult to practically apply is solved.
Drawings
FIG. 1 is an overall flow chart of the present invention;
FIG. 2 is a comparison of structural similarity between a reconstructed image and an original image to be reconstructed using the present invention and the prior art method;
FIG. 3 is a graph showing peak SNR contrast of a reconstructed image and an original image to be reconstructed using the present invention and the prior art method.
Detailed Description
The following describes the technical scheme of the present invention in detail with reference to specific drawings and examples, but is not used for limiting the protection scope of the present application.
The invention relates to a color image self-adaptive reconstruction method (method for short) based on tensor chain rank, which comprises the following steps:
the method comprises the steps of firstly, generating a reference image and a high-order tensor to be complemented;
the image to be reconstructed is the image with partial data missing, and is recorded asThe real number domain, p is a positive integer; image to be reconstructed +.>Acting on standard color image for random deletion operator Ω>Obtained above and marked as->The position of the known data in the image to be reconstructed is an index position, and gray values of the rest positions except the index position in the image to be reconstructed are all 0; the image to be reconstructed is complemented by using the Delaunay triangulation interpolation method so as to effectively recover the structure of the image to be reconstructedInformation, get reference image->Delta () represents an interpolation operator based on delaunay triangulation;
image to be reconstructed using tensor enhancement methodIs rearranged without changing the data structure, and the image to be reconstructed is converted into the higher-order tensor to be complemented +.>The order n=p+1; the specific process of tensor enhancement is as follows: firstly, constructing an initial data block, and rearranging data of an image to be reconstructed into a plurality of initial data blocks; the pixel position of the initial data block is denoted as i 1 The initial data block is represented as:
in the formula (1), c i1j The pixel value representing each point corresponding to color j,representing pixel position i 1 Corresponding orthogonal basis, e 1 =(1,0,0,0),e 2 =(0,1,0,0),e 3 =(0,0,1,0),e 4 =(0,0,0,1);u j Representing the orthonormal corresponding to color j, u 1 =(1,0,0),u 2 =(0,1,0),u 3 =(0,0,1);/>Representing a tensor product;
expanding an initial data block into a second data block containing 4×4 pixelsRearranging data of an image to be reconstructed into a plurality of data blocks II; data block two->Expressed as:
in the formula (2), i 2 Representing the pixel location of data block two,pixel value representing each initial data block corresponding to color j +.>Representing pixel position i 2 A corresponding orthogonal basis;
similarly, data blocks containing more pixels are sequentially constructed, and the image to be reconstructed is obtained by continuously expanding the addressing and rearrangement processRearranged as higher order tensors to be complemented +.>The higher order tensor to be complemented is represented as:
in the formula (3), i p Representing a high-order tensor to be complementedIs>Pixel value representing each data block corresponding to color j +.>Representing pixel position i p A corresponding orthogonal basis;
second step, high order tensor to be complementedFirst order tensor chain rank r of the initialized tensor chain rank of (a) 1 Adding different offsets to generate m candidate tensor chain ranks, wherein the m candidate tensor chain ranks form a first-order candidate tensor chain rank list; high order tensor to be complemented +.>The initialization tensor chain rank is denoted as l= (r 1 ,r 2 ,...,r k ,...,r N-1 ),r 1 =r 2 =…=r N-1 =1; k=1, 2,..n-1, N represents the higher order tensor to be complemented +.>Is a total order of (2); the rank list of the first order candidate tensor chain is The d candidate tensor chain rank, delta, representing the first order tensor chain rank d =2 d Representing offset list δ= [2 ] 1 ,2 2 ,...2 d ...,2 m ]The d-th offset in (a);
thirdly, minimizing each candidate tensor chain rank in the first-order candidate tensor chain rank list by using the formula (4), and treating the high-order tensor to be complementedReconstructing to obtain m reconstructed tensors;
wherein I F Representing the Frobenius norm operator,representing a higher order tensor to be complemented +.>Matrixing a kth order tensor chain; />Respectively is matrix C [k] Is a decomposition matrix of (2); />Representing a higher order tensor to be complemented +.>The d candidate tensor chain rank of the k-th order tensor chain rank; n represents the number of matrix columns; alpha k Is a weighting coefficient, is a constant, representing the higher order tensor to be complemented after the effect of the random deletion operator Ω>
Respectively carrying out the inverse operation of the tensor enhancement method in the first step on the m reconstructed tensors, and converting each reconstructed tensor into an image with the same size as the original data of the image to be reconstructed to obtain m reconstructed images;
fourth, calculating each reconstructed image and reference image respectivelyStructural similarity R between the d-th reconstructed image +.>And reference image->The structural similarity between them is->d=1, 2,. -%, m; selecting a candidate tensor chain rank corresponding to the reconstructed image with highest structural similarity as a first-order tensor chain rank, completing the selection of the first-order tensor chain rank, and carrying out high-order tensor +.>Updating the initialized tensor chain rank of the image to be reconstructed at the moment to finish the first reconstruction iteration;
fifth step, high order tensor to be complementedAnd (3) repeatedly executing the second to fourth steps of operations on each order of tensor chain rank of the tensor chain rank, wherein each order of tensor chain rank is selected, the image to be reconstructed is completed by one reconstruction iteration when each order of tensor chain rank is selected, and the selection of the tensor chain rank is stopped until the structural similarity between the reconstructed image and the reference image is greater than 0.95, and the image to be reconstructed is stopped from iteration, so that the optimal reconstructed image is finally obtained.
Fig. 2 and fig. 3 are quality comparisons of reconstructing an image Lena by using the method of the present invention and the existing method, and the reconstruction quality of the image is measured by using the structural similarity and the peak signal-to-noise ratio, respectively, and the higher the numerical value is, the better the reconstruction effect is. As can be seen from the figure, the reconstruction using the delaunay triangle interpolation method directly has the worst effect, since there is not enough known data for the interpolation reconstruction when the deletion rate of the image to be reconstructed is high or when the partial blocking region is missing. It is worth noting that, although the existing TT-based method is relatively close to the reconstruction effect of the present invention, the existing TT-based method requires complete tensor chain rank information of the image to be reconstructed, and parameters are required to be continuously adjusted according to the experimental result to achieve the optimal reconstruction effect, but in practice the complete tensor chain rank information of the image to be reconstructed cannot be obtained, so that the existing TT-based method is difficult to be practically applied. The method has the advantages that the situation of missing data structures of the image to be reconstructed is not limited, good reconstruction effects can be obtained under the condition of unknown data, the reconstruction effects are integrally superior to those of the existing method under different sampling rates, the problem that the existing method cannot be applied under the actual condition is solved, and the method has important practical application value.
The invention is applicable to the prior art where it is not described.
Claims (4)
1. The color image self-adaptive reconstruction method based on tensor chain rank is characterized by comprising the following steps:
the method comprises the steps of firstly, processing an image to be reconstructed to generate a reference image and a high-order tensor to be complemented;
a second step of adding different offsets to a first-order tensor chain rank of an initialized tensor chain rank of a high-order tensor to be complemented to generate m candidate tensor chain ranks, wherein the m candidate tensor chain ranks form a first-order candidate tensor chain rank list;
thirdly, carrying out minimization treatment on each candidate tensor chain rank in the first-order candidate tensor chain rank list, and reconstructing the high-order tensor to be complemented to obtain m reconstructed tensors; converting each reconstructed tensor into an image with the same size as the original data of the image to be reconstructed to obtain m reconstructed images;
a fourth step of respectively calculating the structural similarity between each reconstructed image and the reference image, selecting a candidate tensor chain rank corresponding to the reconstructed image with the highest structural similarity as a first-order tensor chain rank, and finishing the selection of the first-order tensor chain rank and the updating of the initialized tensor chain rank of the high-order tensor to be complemented;
and fifthly, repeatedly executing the operations of the second step to the fourth step on each order of tensor chain rank of the initialized tensor chain rank of the high-order tensor to be complemented obtained in the fourth step, and stopping the selection of the tensor chain rank until the structural similarity between the reconstructed image and the reference image is greater than 0.95, and stopping iteration of the image to be reconstructed to obtain the optimal reconstructed image.
2. The adaptive reconstruction method of color images based on tensor chain rank according to claim 1, wherein the image to be reconstructed is complemented by using delaunay triangulation interpolation method to obtain a reference image; and generating a high-order tensor to be complemented by using a tensor enhancement method.
3. The method according to claim 2, wherein in the third step, the inverse operation of the tensor enhancement method in the first step is performed on the m reconstructed tensors, respectively, so as to convert the reconstructed tensors into an image with the same size as the original data of the image to be reconstructed.
4. A tensor chain rank-based color image adaptive reconstruction method according to any one of claims 1-3, characterized by an initialized tensor chain rank r of the higher order tensor to be complemented 1 =r 2 =…=r N-1 =1, n represents the total order of the high-order tensor to be complemented.
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