CN108346167A - It is a kind of based on orthogonal dictionary similarly hereinafter when sparse coding MRI image reconstructing method - Google Patents

It is a kind of based on orthogonal dictionary similarly hereinafter when sparse coding MRI image reconstructing method Download PDF

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CN108346167A
CN108346167A CN201711463209.1A CN201711463209A CN108346167A CN 108346167 A CN108346167 A CN 108346167A CN 201711463209 A CN201711463209 A CN 201711463209A CN 108346167 A CN108346167 A CN 108346167A
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structure group
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sparse coding
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CN108346167B (en
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刘书君
沈晓东
曹建鑫
张新征
李勇明
张奎
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Shenzhen Zhongwu Photon Technology Co ltd
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Chongqing University
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    • G06F18/28—Determining representative reference patterns, e.g. by averaging or distorting; Generating dictionaries
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    • G06V—IMAGE OR VIDEO RECOGNITION OR UNDERSTANDING
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    • G06V10/40—Extraction of image or video features
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06V—IMAGE OR VIDEO RECOGNITION OR UNDERSTANDING
    • G06V10/00—Arrangements for image or video recognition or understanding
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Abstract

The MRI image reconstructing method of sparse coding when the invention discloses a kind of based on orthogonal dictionary similarly hereinafter.Belong to digital image processing techniques field.It is a kind of MRI image reconstructing method using orthogonal dictionary to image progress rarefaction representation and to sparse coefficient sparse coding optimization simultaneously.The similar image set of blocks i.e. structure group of target image block is found first, the image reconstruction model that sparse coding is established while structure group is then based under orthogonal dictionary finally solves the sparse coefficient and reconstructed image of structure group in the model with broad sense Soft thresholding；The present invention carries out rarefaction representation by orthogonal dictionary to structure group, it can optimize to structure group rarefaction representation performance, and sparse coefficient is constrained and solved using sparse coding and broad sense Soft thresholding simultaneously, more efficient it can accurately estimate sparse coefficient, the MRI image reconstructed through the invention is integrally more clear, and detailed information is more rich, the accuracy higher of reconstruct, therefore can be used for the reconstruct of medical image.

Description

It is a kind of based on orthogonal dictionary similarly hereinafter when sparse coding MRI image reconstructing method
Technical field
The invention belongs to digital image processing techniques fields, it more particularly to carries out structure group using orthogonal dictionary sparse The MRI image reconstructing method with the restricted coefficients of equation of sparse coding progress simultaneously is indicated, for the high quality resume to medical image.
Background technology
Magnetic resonance imaging (MRI) is a kind of electromagnetic wave reality for utilizing nuclear magnetic resonance principle, being emitted by additional gradient magnetic The method for now drawing interior of articles image, and be commonly used in the fields such as medical treatment, archaeology, petrochemical industry.Compare previous doctor For learning imaging technique, magnetic resonance imaging has to soft tissue resolution higher, to human body without ionization radiation injury and imaging spirit One of the advantages such as active higher imaging parameters are more, therefore have become most important medical imaging technology at present.However, magnetic resonance Imaging technique is there is also some urgent problems to be solved, and as image taking speed is slower, and obtained image is often accompanied by artifact phenomenon, right Diagnostic message produces great interference, and therefore, the main improvement for magnetic resonance imaging aims to solve the problem that the two main problems.
MRI image taking speeds are improved other than improving the performance of hardware device and the scanning technique in the spaces K, with compressed sensing Theoretical proposition, the theory can break through the limitation of conventional Nyquist sampling thheorem, i.e., using the K spacing waves of lack sampling come weight Structure goes out MRI image, to larger reduction sweep time.Therefore, how preferably to restore image from sampled signal just becomes The emphasis of one research.Traditional MRI image reconstructing method based on compressed sensing generally utilizes the fixed transformation such as small echo to figure As carrying out rarefaction representation, and yield good result.In recent years, the similar characteristic inside image is gradually taken seriously, also by The fields such as image noise reduction are applied to, and are greatly improved the picture quality finally obtained.
Invention content
It is insufficient existing for existing MRI image reconstructing method it is an object of the invention to be directed to, it proposes a kind of based on orthotropic word Under allusion quotation simultaneously sparse coding MRI image reconstructing method.This method fully consider image transform domain sparsity and image block Between non local similitude, the structure group that similar image set of blocks is obtained carries out rarefaction representation using orthogonal dictionary, and using same When sparse coding and broad sense Soft thresholding estimation optimized to sparse coefficient, improve estimated accuracy.Specifically include following steps：
Step 1: the acquisition of structure group
In order to realize the promotion of degree of rarefication using sparse coding simultaneously, optimization similar image set of blocks, that is, structure group is orthogonal Sparse coefficient under dictionary needs to build the corresponding structure group of target image block, the image x first after initial reconstitution(0)Middle pumping Take out target image block xi, then using the method that Euclidean distance compares with target image block xiCentered on search range seek Look for corresponding similar image block, and by similar image block and target image block xiIt is configured to structure group Xi；
Step 2: the foundation of sparse coding restricted model simultaneously
Obtain structure group XiAfterwards, at the same time during sparse coding, using non-convex norm to structure group XiIn orthogonal dictionary D Under sparse coefficient collection AiCarry out sparse constraint：
Wherein 0 ＜ p ＜ 1, αkIndicate coefficient matrices AiIn row k, on this basis, establish about image and sparse system Several restricted models：
Wherein M is structure group number, FuFor down-sampling Fourier transform matrix,Matrix is extracted for structure group；
Step 3: the solution of sparse coefficient and the reconstruct of MRI image
Restricted model is solved using alternating direction iterative algorithm, it can be respectively with sparse coefficient AiEstimate with needs Reconstructed image x is that optimization object is solved, wherein the subproblem about sparse coefficient is represented by：
Wherein β is regularization parameter, can will be in the subproblem in order to be solved to the subproblem It is converted：
WhereinThe W that changes commanders is become by inequality againiAnd AiThe form for being converted to diagonal matrix, further should Subproblem is converted into：
Wherein ΛiAnd ΣiIt is diagonal matrix, and the size of each diagonal entry is respectively equal to WiAnd AiIn per a line system Two several norms, then estimate Σ using broad sense Soft thresholdingiIn each diagonal entry size, to what is estimated Sparse coefficient Ai, and substituted into the subproblem about reconstructed image x：
The least square problem can be solved with conjugate gradient method, to reconstruct final image.
The innovative point of the present invention is to use orthogonal dictionary to structure group using image local sparsity and non local similitude Rarefaction representation is carried out to structure group；Optimize the constraint to sparse coefficient using sparse coding simultaneously, further increases sparse coefficient Estimated accuracy；Sparse coefficient is estimated using broad sense Soft thresholding, and this method is applied to magnetic resonance image (MRI) Reconstruct.
Beneficial effects of the present invention：Rarefaction representation is carried out to structure group using orthogonal dictionary, is optimized to the dilute of structure group It dredges and indicates performance；Sparse coefficient is constrained using sparse coding simultaneously, and coefficient is estimated using broad sense Soft thresholding Meter, not only whole visual effect is good for the image for improving the estimated accuracy of coefficient, therefore finally estimating, and also retains image Internal a large amount of details, make entire estimated result closer to actual value.
The present invention mainly uses the method for emulation experiment to verify, and all steps, conclusion are all verified on MATLAB8.0 Correctly.
Description of the drawings
Fig. 1 is the workflow block diagram of the present invention；
Fig. 2 is the MRI cardiac image artworks used in present invention emulation；
Fig. 3 is the reconstruction result for the MRI cardiac images for being 30% to sample rate with RecPF methods；
Fig. 4 is the reconstruction result for the MRI cardiac images for being 30% to sample rate with PBDW methods；
Fig. 5 is the reconstruction result with the MRI cardiac images for being 30% to sample rate with PANO methods；
Fig. 6 is the reconstruction result for the MRI cardiac images for being 30% to sample rate with the method for the present invention.
Specific implementation mode
Referring to Fig.1, the present invention be based on orthogonal dictionary similarly hereinafter when sparse coding MRI image reconstructing method, specific steps Including as follows：
Step 1: the acquisition of structure group
The raw k-space data y of input is subjected to initial reconstitution using total variation method, obtains initial reconstructed image x(0), so Image x after reconstitution afterwards(0)In extract target image block xi, then with target image block xiFor search center, model is being searched for Enclose interior movement images block one by one and target image block xiEuclidean distance, Euclidean distance is smaller then more similar, by this similar Image Block- matching finds target image block xiSimilar image block, and using structure group extract matrixObtain target image block pair The structure group answered
Step 2: the foundation of sparse coding restricted model simultaneously
Obtain structure group XiAfterwards, sparse coefficient is constrained using the non-convex norm of formula (1), then in conjunction with the weight of image The restricted model of vertical (2) about image and sparse coefficient is built, which is further rewritten into no constraint expression formula：
Wherein λ and β is regularization parameter；
Step 3: the solution of sparse coefficient and the reconstruct of MRI image
The restricted model of image and sparse coefficient is solved using alternating direction iterative algorithm, is first divided into model Two sub-problems about sparse coefficient and image reconstruction are solved, wherein such as formula of the subproblem about sparse coefficient (3) institute Show, it, can will be in formula (3) in order to be solved to the subproblemItem carries out equivalent transformation according to formula (4), so It is further obtained afterwards according to Cauchy-Schwarz inequality：
Then the subproblem of formula (3) can be converted into formula (5), due to ΣiIn each coefficient it is mutually orthogonal, ΛiFor known quantity, Therefore can continue to be converted into scalar form：
Then estimate each coefficient using broad sense Soft thresholding：
The expression formula of wherein threshold value is：
After obtaining sparse coefficient by broad sense Soft thresholding, shown in the subproblem such as formula (6) about image reconstruction, by this Least square problem can be solved to obtain with conjugate gradient method：
The image reconstructed, then by entire restructuring procedure iteration until variation is less than iteration between adjacent reconstruction result twice When terminating thresholding, you can the MRI image finally reconstructed.
The effect of the present invention can be further illustrated by following emulation experiment：
One, experiment condition and content
Experiment condition：Experiment uses Descartes's sampling model；Experimental image uses true heart MRI image, such as Fig. 2 institutes Show；Experimental result evaluation index is using Y-PSNR PSNR come objective evaluation reconstruction result, the higher expression reconstruct knot of PSNR values Fruit is more preferable, closer to true picture.
Experiment content：Under these experimental conditions, reconstruction result uses representative in MRI image reconstruction field at present RecPF methods, PBDW methods and PANO methods and the method for the present invention compared.
Experiment 1：Image after being sampled respectively to Fig. 2 with the method for the present invention and RecPF methods, PBDW methods and PANO methods It is reconstructed.Wherein RecPF methods traditional carry out l using wavelet transformation and total variation to be a kind of to whole image1Norm The method of sparse constraint, reconstruction result Fig. 3；PBDW methods first look for the optimal direction wavelet transformation of image block, and adopt Use l1Norm carries out restricted coefficients of equation to realize MRI image reconstruct, reconstruction result Fig. 4；PANO methods are a kind of typical right Structure group carries out 3 D wavelet transformation and uses l1The reconstructing method of norm constraint sparse coefficient, reconstruction result Fig. 5.In experiment Tile size is arranged in the method for the present inventionImage block number m=32 in structure group, maximum iteration T= 100, iteration ends thresholding η=5 × 10-8；Final reconstruction result is Fig. 6.
Comparison RecPF is can be seen that from the reconstruction result and regional area enlarged drawing of Fig. 3, Fig. 4, Fig. 5 and Fig. 6 each method Method, PBDW methods, PANO methods can be seen that the method for the present invention with the method for the present invention and be higher than in the detail section of reconstruction result Other control methods.
The PSNR indexs of the different reconstructing methods of table 1
Image RecPF methods PBDW methods PANO methods The method of the present invention
MRI human brain figures 34.11 34.40 34.61 35.36
Table 1 gives the PSNR index situations of each method reconstruction result, and the wherein higher expression quality reconstruction of PSNR values is better； It can be seen that the method for the present invention comparison other methods PSNR values improve a lot, illustrate this method reconstruction result closer to really Image, this result match with quality reconstruction figure.
Above-mentioned experiment shows reconstructing method of the present invention, and not only reduction effect is apparent, but also reconstructed image is abundant in content, together When objective evaluation index it is higher, it can be seen that the present invention to medical image reconstruct be effective.

Claims (1)

1. it is a kind of based on orthogonal dictionary similarly hereinafter when sparse coding MRI image reconstructing method, it is characterised in that include the following steps：
Step 1: the acquisition of structure group
In order to realize the promotion of degree of rarefication using sparse coding simultaneously, optimization similar image set of blocks, that is, structure group is in orthogonal dictionary Under sparse coefficient, need to build the corresponding structure group of target image block, the image x first after initial reconstitution(0)In extract Target image block xi, then using the method that Euclidean distance compares with target image block xiCentered on search range find pair The similar image block answered, and by similar image block and target image block xiIt is configured to structure group Xi；
Step 2: the foundation of sparse coding restricted model simultaneously
Obtain structure group XiAfterwards, at the same time during sparse coding, using non-convex norm to structure group XiAt orthogonal dictionary D Sparse coefficient collection AiCarry out sparse constraint：
Wherein 0 ＜ p ＜ 1, αkIndicate coefficient matrices AiIn row k establish on this basis about image and sparse coefficient Restricted model：
Wherein M is structure group number, FuFor down-sampling Fourier transform matrix,Matrix is extracted for structure group；
Step 3: the solution of sparse coefficient and the reconstruct of MRI image
Restricted model is solved using alternating direction iterative algorithm, it can be respectively with sparse coefficient AiThe reconstruct estimated with needs Image x is that optimization object is solved, wherein the subproblem about sparse coefficient is represented by：
Wherein β is regularization parameter, can will be in the subproblem in order to be solved to the subproblemIt carries out Transformation：
WhereinThe W that changes commanders is become by inequality againiAnd AiThe form of diagonal matrix is converted to, further asks the son Topic is converted into：
Wherein ΛiAnd ΣiIt is diagonal matrix, and the size of each diagonal entry is respectively equal to WiAnd AiIn each row coefficient two Then norm estimates Σ using broad sense Soft thresholdingiIn each diagonal entry size, the sparse system to be estimated Number Ai, and substituted into the subproblem about reconstructed image x：
The least square problem can be solved with conjugate gradient method, to reconstruct final MRI image.
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