CN109712205A - A kind of compression of images perception method for reconstructing based on non local self similarity model - Google Patents
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Abstract
本发明请求保护一种基于非局部自相似模型的图像压缩感知重建方法，属于信号与图像处理领域。具体地，为了提高传统图像压缩感知重建的质量，本发明利用图像的先验信息，构建了图像的非局部自相似模型，通过计算图像块的权值矩阵，进而利用图像块的非局部自相似先验信息构造了一个图像的自适应非局部正则项，提出了图像压缩感知重建的数学模型，并利用高效的Split Bregman Iteration(SBI)算法交替迭代更新，进而改进了图像压缩感知的重建性能。同时在字典的学习的过程中，通过当前近似估计图像d，提取训练样本，利用K‑SVD算法交替更新得到自适应学习字典。本发明提出的非局部自相似模型的自适应图像压缩感知重建方法，在实际中具有普遍意义。有效的提高了图像压缩感知重建的质量，减小了图像的块效应，保持图像的纹理和细节不丢失，更好的刻画了图像的纹理和细节。
The present invention claims to protect an image compressive sensing reconstruction method based on a non-local self-similar model, which belongs to the field of signal and image processing. Specifically, in order to improve the quality of traditional image compressed sensing reconstruction, the present invention uses the prior information of the image to construct a non-local self-similar model of the image, and then uses the non-local self-similarity of the image block by calculating the weight matrix of the image block. A priori information constructs an adaptive non-local regular term for an image, and a mathematical model for image compressive sensing reconstruction is proposed, and the efficient Split Bregman Iteration (SBI) algorithm is used to alternate iteratively update, thereby improving the reconstruction performance of image compressive sensing. At the same time, in the process of dictionary learning, the training samples are extracted through the current approximate estimation image d, and the adaptive learning dictionary is obtained by alternately updating the K-SVD algorithm. The adaptive image compressed sensing reconstruction method of the non-local self-similar model proposed by the present invention has universal significance in practice. It effectively improves the quality of image compression sensing reconstruction, reduces the block effect of the image, keeps the texture and details of the image from being lost, and better describes the texture and details of the image.
Description
Technical field
The invention belongs to signal and field of image processing, specifically a kind of compression of images based on non local self similarity model
Perceive method for reconstructing.
Background technique
With being constantly progressive for society, information and its acquisition modes become indispensable composition portion in people's daily life
Point, image information content abundant becomes the chief source of information that the mankind obtain information.However the figure Jing Guo digitized processing
Picture data volume is very huge, sizable difficulty is brought to actual storage, transmission and understanding, simultaneously because the limitation of hardware
With to the cost consideration for improving efficiency of transmission, makes to be indicated by important information of seldom data to target and transmit, store up again
It is saved as key to solve these problems.Image sparse indicates that the foundation of model is the basis that image processing application is carried out how
Design is not only succinct but also efficient image table representation model, reduces huge image data amount bring pressure in practical application, is figure
As a highly important project in treatment theory and practical studies.
Nyquist (Nyquist) sampling thheorem traditional simultaneously requires the sample rate of signal must not be lower than signal bandwidth
2 times, this undoubtedly gives corresponding hardware acquisition data equipment to bring bigger challenge.Traditional signal compression frame is in two steps
It walks: first sampling recompression.Coding side first samples signal, then to sampled value carry out orthogonal transformation (such as wavelet transformation, it is discrete
Cosine transform etc.) and encode the amplitude of wherein significant coefficient and position, encoded radio is finally subjected to storage or transmission, is solved
Code end is decompressed to received signal, and be restored signal after inverse transformation.However there are two for this traditional compression method
Defect: 1) due to being limited by Nyquist sampling thheorem, the sampling rate of signal is higher than 2 times of signal bandwidth, this just makes
It obtains hardware sampling system and is faced with very big pressure；2) in compression encoding process, the small coefficient of amplitude is lost in a large amount of transform domains
It abandons, causes the waste of data calculating and memory source.Compressed sensing (Compressed Sensing, CS) technology has been broken only
Have and be higher than twice of signal bandwidth or more the processing frame that could restore signal completely in sample rate, can it is pointed out Exact recovery letter
It number is determined by the structure and content of signal.By compressive sensing theory it is found that when image is under some excessively complete dictionary
In sparse or compressible situation, so that it may reconstruct original image by the observation of image.As shown in Figure 1, a width X ∈ RN×N
Image use observing matrix Φ ∈ Rm×n, m < n progress accidental projection, image block xi∈RnSight at random observation matrix Φ
Measured value is yi=Φ xi, Ψ is dictionary, then specific step is as follows for compressed sensing restructing algorithm:
(1) sparse coefficient is solved using sparse coding optimization algorithm
(2) image block restores,
(3) image block is rearranged to obtain reconstructed image
It solves optimization problem represented by above formula and belongs to non-convex optimization problem, can be by some greedy algorithms, it can also be with
Solution can also be passed throughThe optimization problem of Norm minimum solves:
Pass through observation yiIt can rebuild to obtain image x with great probability.The theory of CS shows if a signal energy
It is enough that there is sparse characteristic in some domain, then the signal can be decoded with the measured value less than Nyquist sampling thheorem
Come.Therefore, a key in CS Problems of Reconstruction is how that the domain that can carry out signal rarefaction representation, signal need to be found
Showed in this domain more sparse, CS reconstructing restored result is better.
Because there is currently compressed sensing reconstruction algorithm in mostly using fixed basic function, that is, in determining domain
In signal is decomposed, such as: DCT domain, wavelet field and gradient field, but these domains all have ignored natural sign non-stationary it is special
Property, lack adaptive ability, from being unable to picture breakdown enough to sparse, also allows for the poor effect of CS reconstruction, limit
Application of the CS in terms of image is made.Simultaneously in the learning process of sparse coding and dictionary, each block is independent consideration,
The correlation between block and block is had ignored, it is not accurate enough so as to cause sparse coding.
Summary of the invention
The present invention aiming at the problem that there are the characteristics that and image itself above, using the non local similar characteristic of image,
It is proposed a kind of adapting to image compressed sensing restructing algorithm of non local regularization.In the algorithm, image is non local from phase
It is dissolved into regular terms like model, while a kind of efficient adaptive dictionary learning algorithm features image well and is based on block
Local sparse characteristic, to further improve the quality of reconstruction image.
The technical solution key step of invention are as follows:
1. the non local self similarity model of image is constructed first with the non local self similarity prior information of image,
Least square method is utilized by square of minimum error, solves weight matrix B, non local regular terms has been constructed, by it
It is dissolved into compression of images perception algorithm for reconstructing.
2. having constructed the mathematical model of the compression of images perception algorithm for reconstructing based on non local self similarity model.In the number
It learns in model, is to merge non local regular terms by the expression-form that the prior information of the non local self similarity of image passes through mathematics
The compressed sensing for having arrived image is reruned in method.
3. being solved using a kind of efficient Split Bregman Iteration (SBI) algorithm.By separating variables,
It decomposes for multiple and different subproblem solution procedurees, alternately updates reconstructed image and sparse coding coefficient, reconstruct image is obtained with this
Picture.
4. constructing a kind of efficient adaptive dictionary learning algorithm, the approximation obtained after being updated using iteration each time is original
Training sample is extracted in the estimation of image, by K-SVD algorithm sparse come alternating iteration renewal learning dictionary and sparse coding, obtains
To study dictionary.
Detailed description of the invention
The observation process of Fig. 1 compression of images perception
The non local self similarity model of Fig. 2 image
Flow chart is rebuild in the perception of Fig. 3 compression of images
Specific embodiment
1. constructing the non local self similarity model regular terms of image.In the field of image procossing, natural image signal shows
A most important characteristic be non-local self-similarity, i.e. an image block image other positions there are many similar block,
The structural information of image has redundancy, and the texture and details of better picture engraving are capable of using this property, and then improves
The quality reconstruction of image.It include the natural image prior model that repetitive structure pattern feature is established based on image itself
It is as shown in Figure 2: in image block x0Neighborhood in there is similar blocks:Therefore image block x0
Can be weighted with the similar block in neighborhood indicates:
WhereinFor weight, therefore for whole image block:
Wherein j indicates the number of similar block, enables the weight matrix of the block of single image are as follows:Similar image block matrix:Then single image block
Weight matrix, which calculates, utilizes least square method, and the quadratic sum by minimizing error finds the best match of data:
Above formula is a stringent quadratic function minimization problem, and enabling the gradient of function is zero, the envelope of available formula
Solution is closed, is expressed as follows:
Particularly, matrix (XTX+γI)-1For symmetric positive definite matrix, above formula can be solved with Conjugate gradient descent algorithm.Cause
This has weight matrix B for whole image:
ThereforeE is error term, so the mathematical model of the non local self similarity of image are as follows:
2. rarefaction representation image block based
The basic unit of the rarefaction representation of image is image block (patch) in the method, and mathematicization is expressed as, and is enabled
x∈RNWithIts size isOriginal picture block and size beImage block, wherein sharing
N image fritter, i.e. k=1,2 ..., n.There is following formula:
xk=Akx (9)
WhereinIndicate the matrix manipulation operator that k-th of image block is extracted from original image x.This patent
In the image block used be overlapping one another, therefore this rarefaction representation based on overlapping image block is with highly redundant
, but this overlapping image block all can greatly reduce the blocking artifact of image in rarefaction representation, to improve the reconstruction of image
Quality.According to formula (9), restoring original image using overlapped image block is following formula:
For giving a dictionary, that is, sparse basisEach piece of xkSparse coding at sparse basis D is αk, i.e.,
αkMiddle most elements are zero or are close to zero, so that xk≈Dαk.Original image x can be by one group of rarefaction representation coefficient { αkCome
It is approximate to indicate.Same formula (10) equally, passes through rarefaction representation coefficient { αkLai Huifu original image x can indicate are as follows:
Wherein α indicates all αkSet, i.e.,It is image block based dilute to represent original image x
Dredge coding.
3. the adapting to image compressed sensing reconstruction framework of non local regularization.In compressed sensing reconstruction algorithm, tradition
Compressed sensing reconstruction algorithm be utilized the sparse representation model of image, but image prior information and be underutilized, with
It is bad as image reconstruction effect details and grain effect.Non local regular terms is incorporated in compressed sensing algorithm, is obtained as follows
Mathematical model:
Wherein x=D α, D are dictionary, are solved to formula (12) using efficient SBI algorithm, SBI algorithm is as follows:
Objective function are as follows:
It is presented below and how using SBI algorithm frame to be solved (12):
DefinitionWithWhereinEven w=x, x=D α, by the analysis to SBI algorithm, in conjunction with this paper objective function by formula (12)
The alternating iteration for being converted to following five target formulas updates optimization problem.
b(t+1)=b(t)-(x(t+1)-w(t+1)) (16)
c(t+1)=c(t)-(x(t+1)-Dα(t+1)) (17)
To sum up to analyze, the adapting to image compressed sensing of non local regularization rebuilds derivation algorithm, and it is converted to and solves x,
The solution procedure of three subproblems of w, α.
4., for the subproblem that formula (13) solve, formula (13) is one tight when given α sparse coding coefficient and w
The quadratic function of lattice, minimization problem derivation algorithm are.To formula (13) derivation.Have:
D=HTy-HTHx+μ1(x-w-b)+μ2(x-Dα-c) (18)
It enables (18) of formula to be equal to zero just to obtain:
For compression of images perception is rebuild, using accidental projection H, not any special construction, in order to keep away
Exempt from the inverse of solution matrix, the higher computation complexity of bring, therefore use steepest descent algorithm solution formula (19):
Wherein d is the gradient direction of formula (18), and γ is step-length, therefore compressed sensing multigraph pictureIt is asked by iteration following formula
Solution:
5., using formula (14), the subproblem for solving w can state for given for given x are as follows:
Derivation is carried out to above formula (22) are as follows:
D=(η (I-B)T(I-B)-μ1I)w-(x-b) (23)
Its derivative is enabled to be equal to zero:
Conjugate gradient descent algorithm rapid solving can be used to above formula.
6., using formula (15), the subproblem for solving α can state for given x are as follows:
Due to the definition for α, it is difficult directly to utilize equations α, enables r=D α, therefore formula can transform to d=x-c:
The sparse coding of formula (26) is sparse in order to obtain, it is assumed that d is an approximate image of original image r, wherein scheming
Picture error is e=r-d, it is therefore assumed that it is δ that each of e element, which all obeys method,2, mean value be 0 independent same distribution.At this
Under one of sample assumes, using probability theory law of great number, have to draw a conclusion: sparse coding image block based, it can be by following
Formula (27) obtains
WhereinTherefore sparse coding Solve problems image block based can switch to following formula (28):
For formula (28), can by orthogonal matching pursuit algorithm (Orthogonal Matching Pursuit,
OMP) algorithm solves.
Wherein δ is control errors, is overlapped image block by batch processing, finally obtains the rarefaction representation system of whole image
Number.
7. adaptive learning dictionary
In order to make image have a preferable rarefaction representation, the solution of sparse basis or dictionary becomes particularly important.Such as
What, which can find an optimal domain, makes image have an optimal rarefaction representation.Many algorithms are proposed from given one
In group training sample, a study dictionary haveing excellent performance is obtained.Pass through optimization following formula:
In order to obtain dictionary D, formula (25) is a large-scale optimization problem, in order to obtain feasible solution, algorithm
MOD, K-SVD, which are proposed, comes alternative optimization dictionary D and sparse coding coefficient A.
Usually during dictionary learning, in order to obtain the dictionary of an adaptive study, usual training sample comes
From in the original image of current image to be processed.But in compression of images perception, it is unable to get original image.In this feelings
Under condition, can use in the approximate original image obtained after iteration each time updates and extract training sample, alternately more newly arrive or
Obtain image x and study dictionary D.In formula (21), just d is regarded as a good approximate evaluation of original image r.Therefore
Training sample image block can be extracted in approximate image d and carrys out training dictionary, using K-SVD algorithm come adaptive in this method
Renewal learning dictionary.
Claims (4)
1. a kind of compression of images based on non local self similarity model perceives method for reconstructing, it is characterised in that include the following steps:
First with the non local self similarity prior information of image, the non local self similarity model of image is constructed, is utilized
Least square method is solved weight matrix B, has been constructed non local regular terms, be dissolved by square of minimum error
Compression of images perceives in algorithm for reconstructing.
2. according to claim 1, having constructed the compression of images perception algorithm for reconstructing based on non local self similarity model
Mathematical model, it is characterised in that in the mathematical model, table that the prior information of the non local self similarity of image is passed through into mathematics
Existing form is that adaptive non local regular terms has been fused in the compressed sensing reconstruction of image.Expression is as follows:
3. it is solved according to claim 1 with 2 using a kind of efficient Split Bregman Iteration (SBI) algorithm,
It is characterized in that decompose for the solution of multiple subproblems by separating variables, alternately update reconstructed image and sparse coding coefficient,
The algorithm makes the number of iterations and convergence rate be superior to traditional optimization algorithm, to obtain preferable quality reconstruction.
4. constructing a kind of efficient adaptive dictionary learning calculation in the dictionary On The Choice that claim 3 solves subproblem
Method, it is characterised in that extract training sample in the approximate original image obtained after updating using iteration each time, calculated by K-SVD
Method updates dictionary and sparse coding is sparse to replace, to feature the block-based local sparse characteristic of image, thus further
Improve the quality of reconstruction image.
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