CN109840888B - Image super-resolution reconstruction method based on joint constraint - Google Patents
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Abstract
The invention discloses an image super-resolution reconstruction method based on joint constraint, which comprises the steps of firstly extracting image blocks from a natural image, carrying out dictionary training learning by using a K-SVD algorithm under the condition of being based on low-order constraint, and updating atoms in a dictionary one by one in the dictionary training process; secondly, obtaining a graph block set similar to the image blocks in the same scale and multiple scales through searching, carrying out weighted estimation on the real codes by using the sparse codes of the similar image blocks, and introducing the difference between the real codes and the obtained sparse codes into an objective function as a constraint term; and finally, multiplying and estimating the image block to be reconstructed by utilizing atoms in the dictionary and the sparse coefficient to obtain the high-resolution image block. The invention reduces noise influence by introducing constraint terms, and simultaneously enhances the reconstruction result to obtain more image details.
Description
Technical Field
The invention relates to an image super-resolution reconstruction method based on joint constraint, and belongs to the technical field of image processing.
Background
In recent years, image super-resolution reconstruction attracts attention of researchers, and has been widely used in various fields of reality such as medical image, video transmission, and the like. However, there are many problems to be solved in practical applications, such as: noise effects, image edge effects, ringing effects, etc., and removing noise effects is a more urgent problem to be alleviated.
The reconstruction algorithm of the super-resolution image mainly comprises an interpolation-based method, a reconstruction-based method and a learning-based method. The learning-based method comprises the following steps: a neighborhood embedding method, a sparse representation method and a deep learning method. Most of the algorithms are considered from the learning-based angle and are realized step by step, so that sparse-based algorithm comparison is popular to students, but the algorithm with the best effect is considered from the deep learning aspect, but the deep learning requires a large amount of data and time, so that each thinking direction has respective advantages and disadvantages, and the basic idea of the sparse representation super-resolution image reconstruction algorithm is as follows: training HR image blocks and LR image blocks obtained by degradation as data sets to obtain a dictionary, and solving an optimization problemAnd obtaining a sparse representation coefficient, and finally, linearly combining atoms in the dictionary by using the sparse representation coefficient. Literature (Shang L.Denoising natural images based on a modified sparse coding algorithm [ J)].Applied Mathematics&Calculation, 2008,205 (2): 883-889) uses maximum kurtosis as the maximum sparsity metric criterion, uses a fixed variance term of the sparse coefficients to generate a fixed information capacity, and uses a determined basis function obtained by a fast non-fixed point independent component analysis algorithm as an initialization feature basis function of the sparse coding algorithm in order to increase the convergence speed of the algorithm. Literature (Nath A G, nair M S, rajan J.Single Image Super Resolution from Compressive Samples Using Two Level Sparsity Based Reconstruction [ J)]Procedia Computer Science,2015, 46:1643-1652) a two-level sparsity-based reconstruction method is proposed, which is implemented by patch-based image interpolation and dictionary learning. Literature (Peleg T, elad M.A Statistical Prediction Model Based on Sparse Representations for Single Image Super-Resolution [ J ]]IEEE Transactions on Image Processing A Publication of the IEEE Signal Processing Society,2014,23 (6): 2569-82) uses statistical predictive models based on sparse representations of LR and HR image blocks to process super-resolution of individual images. Prediction of the HR image block is obtained through MMSE estimation, and a plurality of basic algorithms are clustered and cascaded by using data, so that the method is superior to the existing method in terms of calculation complexity, numerical standard and the like aiming at a training model of the obtained network. Literature (Xie C, zeng W, jiang S, et al multiscale Self-similarity and Sparse Representation Based Single Image Super-Resolution [ J ]]Neurostarting, 2017,260) from l using multi-scale self-similarity construction 1 The norms define regularization compensation pairs to suppress sparse noise, resulting in a more reliable reconstruction effect.
However, the above methods have no good noise suppression capability, so that the image reconstruction effect is poor.
Disclosure of Invention
The technical problems to be solved by the invention are as follows: the method for reconstructing the image super-resolution based on the joint constraint is provided, the influence of noise is reduced by introducing constraint terms, the reconstruction result is enhanced, and more image details are obtained.
The invention adopts the following technical scheme for solving the technical problems:
a super-resolution reconstruction method of an image based on joint constraint comprises the following steps:
step 1, dividing a high-resolution image into image blocks with the same size, taking a set of image blocks formed by all the image blocks as a training sample, training a dictionary by using a K-SVD algorithm under the condition of being based on low-order constraint to obtain a trained dictionary, and obtaining sparse codes according to the trained dictionary;
step 2, for a low-resolution image to be reconstructed, dividing the low-resolution image into image blocks with the same size, for a certain image block to be reconstructed, searching for image blocks similar to the image block in the same scale and similar to the image block in multiple scales, carrying out weighted estimation on a real code by using sparse codes of the image blocks similar to the image block in the same scale and similar to the image block in multiple scales to obtain an estimated real code, introducing a difference value between the estimated real code and the sparse code obtained in the step 1 as a constraint term into an objective function, and solving the objective function to obtain a sparse coefficient;
and 3, multiplying atoms in the dictionary trained in the step 1 and the sparse coefficient obtained in the step 2 to obtain a high-resolution image for the low-resolution image to be reconstructed.
As a preferable scheme of the invention, the specific process of the step 1 is as follows:
(a) Dictionary learning constraint optimization problems are:
wherein D is a dictionary, D opt For a trained dictionary, Λ is sparse coding, ε represents a sparsity constraint, Z is a set of high resolution image blocks for dictionary training, t s For the selected tile spatial dimension, t n R is the time point in the data lowrank Is a low rank matrix (t s ×t n ) P represents a matrix;
(b) Fixing Λ, and updating the dictionary:
the updating of atoms in the dictionary is:
s.t.P(d i ,t s ,t n )∈R lowrank
wherein E (i) is a residual matrix, d i 、Λ i Respectively representing the ith column in D and Λ, delta (i) being the matrix, Λ i,m respectively->Column m, & gt>Represent trained d i 。
As a preferable scheme of the invention, the specific process of the step 2 is as follows:
(a) Searching and image block x j Image blocks with the same-scale similarity and the multiple-scale similarity are obtained to obtain a same-scale similarity set ψ j And multiscale similarity set O j Using ψ j And O (outer circle) j Sparse coding of middle image blocksWeight average estimation:
wherein omega j,k Representation and image block x j Image block x of similar scale j,k Weights, ω j,q Representation and image block x j Multiscale similar image block x j,q Weight, Λ of (2) j,k 、Λ j,q Respectively is psi j 、Ο j Middle image block x j,k And x j,q W is a normalization factor, respectively lambda type j 、Λ j,k 、Λ j,q Λ (Λ)) (Λ j Represents the j-th column in sparse coding lambda, D is dictionary, h is control constant, ρ j 、τ j Sparse coding values of the same-scale similarity and multi-scale similarity estimation are respectively obtained;
(b) Introducing a difference value between the estimated real code and the obtained sparse code as a constraint term into an objective function, wherein the objective function model is as follows:
wherein the superscript (l) represents the first iteration, Λ y Representing sparse coding to be solved, y representing a low resolution image, η 1 、η 2 Are all constants;
(c) And D, fixing the D, and updating the lambda to obtain the sparse coefficient.
As a preferred embodiment of the present invention, the constant η 1 ＝0.8,η 2 ＝0.15。
As a preferred embodiment of the present invention, the reconstruction formula of the high resolution image in step 3 is:
wherein X represents a high resolution image, D is a dictionary, Λ y For the obtained sparsity coefficient, R j To extract image block x from an image j J is the number of low-resolution image blocks, Λ y,j For image block x j Is a sparse representation of coefficients.
Compared with the prior art, the technical scheme provided by the invention has the following technical effects:
according to the invention, the constraint item is introduced to improve the noise suppression capability of the reconstruction method, so that a better reconstruction effect of the image is realized.
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FIG. 1 is a basic flow chart of an image super-resolution reconstruction method based on joint constraint.
Detailed Description
Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings. The embodiments described below by referring to the drawings are exemplary only for explaining the present invention and are not to be construed as limiting the present invention.
As shown in fig. 1, an image super-resolution reconstruction method based on joint constraint includes the following steps:
step 1: under the condition based on low-order constraint, carrying out dictionary training learning by utilizing a K-SVD algorithm, and updating atoms in a dictionary one by one in the dictionary training process;
(1) Dictionary learning constraint optimization problem:
wherein D is a dictionary, D opt For optimizing the best dictionary after finishing, Λ is a sparse representation coefficient, epsilon is used for guaranteeing sparsity, Z is a high-resolution image for dictionary training, and t s For choosingImage block space dimension, t n R is the time point in the data lowrank Is a low rank matrix (t s ×t n )。
(2) And fixing lambda and updating the dictionary. The residual matrix is E (i), since:
thus, the update of dictionary atoms is:
wherein, the liquid crystal display device comprises a liquid crystal display device,sum lambda i,m Respectively->And->One of which is->Definition mu i To use d i Reconstruction { x } j Index set, μ at } time i ＝{h|1≤h≤H,Λ i (h) Not equal to 0}, H is the total number of rows of the sparse coefficients, Λ i (h) Is lambda type i In column h, delta (i) is J×|mu i Matrix of the magnitude, in (μ i (h) The values at h) are all 1, the values at the rest are all 0, J is the image block { x } j Number of }.
Step 2: the method comprises the steps of carrying out weighted estimation on real codes by using sparse codes of similar image blocks, introducing a difference value between the real codes and the obtained sparse codes into an objective function as a constraint term, and weakening the influence of noise by using the constraint term, wherein the specific process is as follows:
(1) The difference between the true code and the found Λ is delta α ＝Λ y -Λ x Wherein, lambda x Is true coding.
(2) Searching and image block x using redundancy between image blocks j Image block set ψ similar to same-scale and multi-scale j And O (outer circle) j Using ψ j And O (outer circle) j Λ weighted average estimation of middle image block:
wherein, lambda j,k Sum lambda j,q Respectively is psi j And O (outer circle) j Middle pattern block x j,k And x j,q Sparse code, omega j,k And omega j,q Weights of the same scale and different scales respectively,w is a normalization factor, h is a control constant, ρ j And τ j The sparse estimates are co-scale and multi-scale, respectively.
(3) The final objective function model is:
(4) And D is fixed, and Λ is updated.
In the present embodiment, η 1 ＝0.8,η 2 ＝0.15。
Step 3: by means ofReconstructing an image block.
Wherein R is j An operator for extracting image blocks from an image.
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 thereto, and any modification made on the basis of the technical scheme according to the technical idea of the present invention falls within the protection scope of the present invention.
Claims (4)
1. The image super-resolution reconstruction method based on the joint constraint is characterized by comprising the following steps of:
step 1, dividing a high-resolution image into image blocks with the same size, taking a set of image blocks formed by all the image blocks as a training sample, training a dictionary by using a K-SVD algorithm under the condition of being based on low-order constraint to obtain a trained dictionary, and obtaining sparse codes according to the trained dictionary; the specific process is as follows:
(a) Dictionary learning constraint optimization problems are:
wherein D is a dictionary, D opt For a trained dictionary, Λ is sparse coding, ε represents a sparsity constraint, Z is a set of high resolution image blocks for dictionary training, t s For the selected tile spatial dimension, t n R is the time point in the data lowrank Is a low rank matrix (t s ×t n ) P represents a matrix;
(b) Fixing Λ, and updating the dictionary:
the updating of atoms in the dictionary is:
wherein E (i) is a residual matrix, d i 、Λ i Respectively representing the ith column in D and Λ, delta (i) being the matrix,Λ i,m respectively->Column m, & gt>Represent trained d i ；
Step 2, for a low-resolution image to be reconstructed, dividing the low-resolution image into image blocks with the same size, for a certain image block to be reconstructed, searching for image blocks similar to the image block in the same scale and similar to the image block in multiple scales, carrying out weighted estimation on a real code by using sparse codes of the image blocks similar to the image block in the same scale and similar to the image block in multiple scales to obtain an estimated real code, introducing a difference value between the estimated real code and the sparse code obtained in the step 1 as a constraint term into an objective function, and solving the objective function to obtain a sparse coefficient;
and 3, multiplying atoms in the dictionary trained in the step 1 and the sparse coefficient obtained in the step 2 to obtain a high-resolution image for the low-resolution image to be reconstructed.
2. The method for reconstructing the super-resolution image based on the joint constraint according to claim 1, wherein the specific process of the step 2 is as follows:
(a) Searching and image block x j Image blocks with the same-scale similarity and the multiple-scale similarity are obtained to obtain a same-scale similarity set ψ j And multiscale similarity set O j Using ψ j And O (outer circle) j Sparse coding weighted average estimation of middle image block:
wherein omega j,k Representation and image block x j Image block x of similar scale j,k Weights, ω j,q Representation and image block x j Multiscale similar image block x j,q Weight, Λ of (2) j,k 、Λ j,q Respectively is psi j 、Ο j Middle image block x j,k And x j,q W is a normalization factor, respectively lambda type j 、Λ j,k 、Λ j,q Λ (Λ)) (Λ j Represents the j-th column in sparse coding Λ, h is a control constant, ρ j 、τ j Sparse coding values of the same-scale similarity and multi-scale similarity estimation are respectively obtained;
(b) Introducing a difference value between the estimated real code and the obtained sparse code as a constraint term into an objective function, wherein the objective function model is as follows:
wherein, superscript (l) Representing the first iteration, Λ y Representing sparse coding to be solved, y representing a low resolution image, η 1 、η 2 Are all constants;
(c) And D, fixing the D, and updating the lambda to obtain the sparse coefficient.
3. The method for reconstructing an image super-resolution based on joint constraint according to claim 2, wherein said constant η 1 ＝0.8,η 2 ＝0.15。
4. The method for reconstructing an image super-resolution based on joint constraint according to claim 1, wherein the reconstruction formula of the high-resolution image in step 3 is:
wherein X represents a high resolution image, Λ y For the obtained sparsity coefficient, R j To extract image block x from an image j J is the number of low-resolution image blocks, Λ y,j For image block x j Is a sparse representation of coefficients.
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