CN107330950A - A kind of MRI image reconstructing method based on non local singular value decomposition with estimation - Google Patents
A kind of MRI image reconstructing method based on non local singular value decomposition with estimation Download PDFInfo
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T11/00—2D [Two Dimensional] image generation
- G06T11/003—Reconstruction from projections, e.g. tomography
- G06T11/008—Specific post-processing after tomographic reconstruction, e.g. voxelisation, metal artifact correction
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- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T2207/00—Indexing scheme for image analysis or image enhancement
- G06T2207/10—Image acquisition modality
- G06T2207/10072—Tomographic images
- G06T2207/10088—Magnetic resonance imaging [MRI]
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- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T2207/00—Indexing scheme for image analysis or image enhancement
- G06T2207/20—Special algorithmic details
- G06T2207/20021—Dividing image into blocks, subimages or windows
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T2207/00—Indexing scheme for image analysis or image enhancement
- G06T2207/20—Special algorithmic details
- G06T2207/20048—Transform domain processing
Abstract
The invention discloses a kind of MRI image reconstructing method based on non local singular value decomposition with estimation.Belong to technical field of medical image processing.It is a kind of based on the local sparse image reconstructing method being combined with non local self-similarity.First look for the corresponding similar image set of blocks of each target image block, and corresponding unusual value coefficient is obtained to similar image set of blocks progress singular value decomposition, it is then based on the estimation that linear MMSE criterion realizes singular value, and the similar image set of blocks noise variance needed for the criterion is estimated, to improve the accuracy of estimation characteristic value；The present invention is carried out singular value decomposition to similar image set of blocks and obtains unusual value coefficient and estimated using linear minimum mean-squared error, the detailed information of image can preferably be estimated, therefore the image after reconstructing is showed closer to true picture in whole structure and details, available for the reconstruction quality and visual effect for improving nuclear magnetic resonance image.
Description
Technical field
The invention belongs to technical field of medical image processing, it is more particularly to based on non local singular value decomposition and estimation
MRI image reconstructing method, quality and visual effect for improving reconstruct medical image.
Background technology
Magnetic resonance imaging (MRI) with its observe human dissection or physical arrangement fine definition and it is non-invasive and in medical science
Boundary is applied more and more widely.Traditional MRI image needs to adopt initial data K spaces according to Nyquist's theorem
Sample, then, because required sampled data is very huge, causes the sampling time longer its Fourier inversion into MRI image.
MRI imagings (CS-MRI) based on compressed sensing then can be down-sampled to the progress of initial data K spaces, and the data volume of sampling is far small
According to the data volume needed for nyquist sampling theorem, so as to greatly shorten the sampling time.Should with CS-MRI
With the high MRI image of definition how is preferably reconstructed from down-sampled data turns into study hotspot in recent years.
Existing some CS-MRI image reconstructing methods are to reconstruct MRI image using the openness of image, are typically used
Anchoring base (such as DCT dictionaries, DWT dictionaries, profile dictionary) to carry out rarefaction representation to image, so as to obtain last reconstruct
As a result.Because such method lacks adaptability, therefore some are employed using the method for adaptive learning dictionary (such as KSVD)
To on MRI image reconstruct, but the dictionary of KSVD training is difficult to effectively represent all local details of image.In addition, by right
Sparse coefficient, which enters row constraint, can effectively improve the quality of reconstructed image, but many MRI image reconstructing methods only considered at present
Image block sparse coefficient itself it is openness, do not use the non local similitude on image this body structure, therefore resulting
Reconstruction result still have worth improvements.
The content of the invention
It is an object of the invention to the deficiency for estimating sparse coefficient to exist in reconstructing for existing MRI image, one is proposed
Plant the MRI image reconstructing method based on non local singular value decomposition with estimation.This method has been taken into full account between MRI image block
Non local similitude, obtains unusual value coefficient, and use non-linear least mean squares error by similar image set of blocks singular value decomposition
Method of estimation is estimated unusual value coefficient, while optimizing estimation to the variance in estimation procedure, makes what is estimated
Unusual value coefficient is closer to actual value, and therefore, the method can reconstruct the MRI image closer to true picture.Including with
Lower step：
Step 1: non local singular value decomposition and Image Reconstruction
In order to using the non local analog information between image block, first, image block extraction, and profit be carried out to target image
Abstract image block x is calculated with formula (1)jWith target image block xiDistance：
Then find out and xiL-1 minimum similar image block of distance, and constitute similar image block collection with target image block
Close Xi=[x1,x2,…,xL], then to XiCarry out singular value decomposition：
[D,γi, Φ] and=SVD (Xi) formula (2)
Wherein D and Φ are respectively the left and right orthogonal transform matrix after SVD is decomposed, γiFor unusual value coefficient, therefore combine non-
The total model of Image Reconstruction of local message is：
WhereinFor the unusual value coefficient after estimation,Matrix, F are extracted for image block setUFor Fourier's sampling transformation
Matrix, Υ () represents sparse constraint, and the model can be analyzed to coefficient estimation model again：
With Image Reconstruction model：
To two mold cycle iteratives, to the total model solution of image；
Step 2: unusual value coefficient estimation
In order to be solved to step one Chinese style (4) coefficient estimation model, the similar diagram to being inputted in each iteration first
As set of blocks WiSingular value decomposition obtains corresponding singular value coefficient gammaW, while in order to preferably estimate true picture singular value system
Number, additive noise noise reduction model is converted to by iconic model：
Wherein v is equivalent noise, F and FHFor Fourier transformation and its reverse transform matrix, U and UHRepresent to adopt under frequency spectrum respectively
Sample and zero padding operator, therefore the unusual value coefficient of input picture is represented by iteration every time：
γW=γX+γVFormula (7)
Wherein γXFor the unusual value coefficient of true picture, γVFor equivalent noise signal singularity value coefficient, then using linearly most
Small mean-square error criteria is estimated the unusual value coefficient of true picture：
Wherein E [] represents expectation, and Cov () represents covariance, it is assumed that Cov (γX) and Cov (γV) be diagonal matrix, then
In k-th of coefficient be：
WhereinFor the variance of the unusual value coefficient of equivalent noise,For the variance of the unusual value coefficient of actual signal.
Step 3: variance evaluation and Image Reconstruction in unusual value coefficient
For the equivalent noise needed for estimator (9) respectively and the singular value parameter variance corresponding to true pictureWithCan be byIt is converted into：
Wherein σ2It is variance of the equivalent noise in spatial domain, according still further to the renewal of formula (11) iteration：
WhereinFor equivalent noise spatial domain initial variance, after being estimatedAfterwards, it can be estimated according to formula (12)
Meter
Wherein γkFor γWIn k-th of nonzero element, m be its nonzero element number, estimating true picture singular value
After coefficient, you can according to formula (13) reconstructed image：
After the reconstructed image estimated, formula (4) unusual value coefficient of formula (5) iterative and reconstruct estimation figure are recycled
Picture, the final estimation image until being met requirement.
The innovative point of the present invention is to be combined the openness of image with statistical in image reconstruction procedure；By image
Non local similitude is converted to the expression of the unusual value coefficient of similar image set of blocks；And estimated using linear MMSE criterion
The unusual value coefficient of true picture is counted, to improve the estimated accuracy of the unusual value coefficient of true picture, and this method is used for MRI image
Reconstruct.
Beneficial effects of the present invention：By the openness estimation for being combined with statistical, improving unusual value coefficient of image
Precision；Singular value decomposition is carried out to similar image set of blocks, has obtained being more suitable for expression similar image set of blocks row and column just
Transformation matrix is handed over, and includes the unusual value coefficient of ranks relevant information simultaneously；Using the side of Linear Minimum Mean-Square Error Estimation
The corresponding unusual value coefficient of method estimation true picture, preferably protects image texture details while larger coefficient is accurately estimated
Not only whole structure, closer to true picture, also retains the abundant line of image to image after corresponding small coefficient, therefore reconstruct
Manage details.
The main method for using emulation experiment of the invention is verified that all steps, conclusion are verified all on MATLAB8.0
Correctly.
Brief description of the drawings
Fig. 1 is the workflow block diagram of the present invention；
Fig. 2 is the zero padding sampled images used in this experiment simulation；
Fig. 3 is the image result reconstructed using SIDWT methods；
Fig. 4 is the image result reconstructed using PANO methods；
Fig. 5 is the image result reconstructed using NLR-CS methods；
Fig. 6 is the image result reconstructed using the inventive method.
Embodiment
Reference picture 1, the present invention is the MRI image reconstructing method based on non local singular value decomposition with estimation, specific steps
Including as follows：
Step 1: non local singular value decomposition and Image Reconstruction
First, image block extraction is carried out to lower target image, and found and target image block x using formula (1)iAway from
From searching out and xiAfter L-1 minimum similar image block of distance, extracted using formula (14) and constitute similar diagram therewith
As set of blocks Xi=[x1,x2,…,xL]：
Then to XiAs formula (2) carries out singular value decomposition, γiFor the openness and non-office of part for containing image block set
The unusual value coefficient of portion's similitude, then sets up the Image Reconstruction model of formula (3), by by total model decomposition be formula (4) and
(5) two submodels of formula are solved respectively, you can obtain final reconstructed image.
Step 2: non local unusual value coefficient estimation
In order to solve the total model of Image Reconstruction, iconic model is being converted to by additive noise noise reduction model by formula (6)
Afterwards, singular value coefficient gammaWThe form that true unusual value coefficient is added with equivalent noise figure can be converted to such as formula (7), then
Then estimation coefficient, which can pass through formula, is estimated to the unusual value coefficient of true picture using linear MMSE criterion
(8) calculate, if true unusual value coefficient is uncorrelated to equivalent noise figure, formula (8) can be converted into：
ForEach unusual value coefficient, its solve as shown in formula (9), if trying to achieve true singular value parameter varianceWith equivalent noise figure varianceUnusual value coefficient and according to this reconstructed image can be estimated.
Step 3: variance evaluation and Image Reconstruction in unusual value coefficient
To try to achieve unusual value coefficient, by formula (10) formula (11) formula (12) to singular value parameter varianceWith
, need to be to the initial equivalent noise variance in spatial domain before being estimatedEstimated.Make similar image set of blocks WiCovariance
Matrix is：
Cov(Wi)=Wi TWi/ n formulas (16) make the order of the unusual value coefficient of true picture set of blocks be r, then should be less than containing
Make an uproar the order L of similar image set of blocks, and L-r singular values meet the distribution of formula (17) in the matrix of formula (16)：
Wherein
Again：
I.e.For the expectation of L-r singular values thereafter, the unusual of equivalent noise and true picture thus can be finally estimated
The variance of value coefficientWithAnd the reconstructed image of estimation is solved using formula (13), then model and figure are estimated to coefficient
As reconstruction model is iterated solution, final reconstruction result can be obtained until meeting iteration ends requirement.
The effect of the present invention can be further illustrated by following emulation experiment：
First, experiment condition and content
Experiment condition：It is Fig. 2 to test the input picture used, and pixel size is 256 × 256, and sample rate is 0.1, noise
Standard deviation δ=0.02.Each reconstructing method is all realized using MATLAB Programming with Pascal Language in experiment.
Experiment content：Under these experimental conditions, using SIDWT methods, PANO methods and NLR-CS methods and the present invention
Method is contrasted.The objective evaluation result for reconstructing reducing power is weighed with Y-PSNR PSNR.
Experiment 1：Fig. 2 is carried out respectively with the inventive method and existing SIDWT methods, PANO methods and NLR-CS methods
Reconstruct.Wherein SIDWT methods are a kind of typical MRI image reconstructing methods based on sparse transformation, and its reconstruction result is Fig. 3；
PANO methods are that rarefaction representation ability and image are improved based on similar image set of blocks and using the non local similitude of image
The 3D rarefaction representation MRI image reconstructing methods of the protective capability of grain details, its reconstruction result is Fig. 4；And NLR-CS methods are sharp
With the singular value decomposition of similar image set of blocks come rarefaction representation, and sparse coefficient is constrained using logdet, threshold value, which is shunk, to be solved
True sparse coefficient is so as to reconstruct MRI image, and its reconstruction result is Fig. 5.The inventive method sets tile size in experimentThe image block number L that similar image set of blocks is included, image block extracts sliding distance s and is respectively set to：L=
25, s=5；Final reconstruction result is Fig. 6.
Contrast SIDWT methods, PANO methods and the inventive method can be seen that both approaches reconstruction result and contain substantially
Aliasing artefacts；It can be seen that its detailed information and whole structure are better than SIDWT methods by PANO method reconstruction results, it is basic herein
Upper existing no small raising, but still it is not ideal；The result of NLR-CS methods is compared first two and improved a lot, whole structure compared with
Good, artifact has also obtained preferably suppressing, but the local such as edge details of details still have much room for improvement；The inventive method schemes MRI
The part of picture is sparse to be combined with non local similitude, is more agreed with the singular value system of image block set with singular value decomposition
Number, and unusual value coefficient is accurately estimated using with reference to the linear minimum mean error approach of equivalent noise variance evaluation so that weight
Not only overall visual effect is good for the image of structure, and detailed information preferably retains.
The PSNR indexs of the different restorative procedures of table 1
| Image | SIDWT methods | PANO methods | NLR-CS methods | The inventive method |
| MRI | 21.54 | 24.86 | 27.94 | 28.55 |
Table 1 gives the PSNR index situations for each method that Fig. 2 is reconstructed, and wherein PSNR values are higher represents reconstruct effect
Fruit is better.It can be seen that the inventive method contrast other method improves a lot, this result matches with quality reconstruction figure.
Above-mentioned experiment shows that not only quality reconstruction is notable for reconstructing method of the present invention, and reconstructed image detailed information is more
Plus it is abundant, while visual effect and objective evaluation index are all preferable, it can be seen that the present invention is effective to MRI image reconstruct.
Claims (1)
1. a kind of MRI image reconstructing method based on non local singular value decomposition with estimation, it is characterised in that comprise the following steps that：
Step 1: non local singular value decomposition and Image Reconstruction
Using the non local similitude between image block, to extract target image from entire image first, Euclidean is recycled
Distance is found and target image block xiL-1 minimum similar image block of distance, and by target image block and similar image block one
Play composition similar image set of blocks Xi=[x1,x2,…,xL], then to XiCarry out singular value decomposition：
[D,γi, Φ] and=SVD (Xi)
Wherein D and Φ represent the left and right orthogonal transform matrix after singular value decomposition, γ respectivelyiFor unusual value coefficient, therefore based on non-
Singular Value Decomposition and the MRI image reconstruction model of estimation are：
WhereinFor the unusual value coefficient after estimation,Matrix, F are extracted for image block setUFor Fourier's sampling transformation matrices,
Υ () represents singular value restricted coefficients of equation, and the model can be analyzed to unusual value coefficient estimation model again：
With Image Reconstruction model：
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Respectively two model alternating iterations are solved to realize the reconstruct to MRI image again；
Step 2: unusual value coefficient estimation
To obtain final reconstructed image, it is necessary first to estimate model solution to the unusual value coefficient in step one, be from each
Similar image set of blocks W in iterationiCorresponding singular value coefficient gammaWIn estimate the coefficient of true picture, can will be down-sampled
The unusual value coefficient of image is regarded as being made up of the unusual value coefficient of true picture and the unusual value coefficient of equivalent noise respectively：
γW=γX+γV
Wherein γXFor the unusual value coefficient of true picture, γVFor the unusual value coefficient of equivalent noise, then using it is linear it is minimum
Singular value coefficient gamma of the square error criterion to true pictureXEstimated：
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Step 3: variance evaluation and Image Reconstruction in unusual value coefficient
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After the reconstructed image estimated, then model and Image Reconstruction model, which are iterated solution, Zhi Daoman, to be estimated to coefficient
Sufficient iteration ends requirement can obtain final reconstruction result.
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| CN106780399A (en) * | 2017-01-10 | 2017-05-31 | 南开大学 | Based on multiple dimensioned group of sparse compressed sensing image reconstructing method |
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| CN105427264A (en) * | 2015-12-23 | 2016-03-23 | 重庆大学 | Image reconstruction method based on group sparsity coefficient estimation |
| CN106780399A (en) * | 2017-01-10 | 2017-05-31 | 南开大学 | Based on multiple dimensioned group of sparse compressed sensing image reconstructing method |
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