CN105957029A - Magnetic resonance image reconstruction method based on tensor dictionary learning - Google Patents

Abstract

The invention relates to a magnetic resonance image reconstruction method based on tensor dictionary learning. The magnetic resonance image reconstruction method is characterized in that (1) original k space data is acquired by adopting a variable density random undersampling way, and inverse Fourier transform of sampling data is carried out to acquire an initial reconstruction image; (2) a compressed sensing reconstruction model is established based on the tensor dictionary learning; (3) a part of three-dimensional sub-image blocks are extracted from a reconstructed image for the tensor dictionary learning, and then a tensor dictionary used for sparse expression is acquired; (4) the sparse expression of the tensor dictionary is used for all of the sub-image blocks by adopting a hard domain method; (5) the reconstructed image is updated by adopting a least square method; (6) the step (3) to the step (5) are repeated until convergence is realized, and the final reconstructed image is acquired. The magnetic resonance image reconstruction method based on the tensor dictionary learning is advantageous in that the reconstructed image quality is improved, and the calculation is simple.

Description

MR image reconstruction method based on tensor dictionary learning

Technical field

The present invention relates to mr imaging technique field, be specifically related under a kind of compressive sensing theory based on tensor dictionary The MR image reconstruction method of study.

Background technology

On the international top magazines such as Nature, relevant natural image sparse coding is delivered from Olshausen in 1996 etc. After initiative paper, the concern of dictionary learning is got more and more by people.Olshausen etc. are derived with l₁Norm is as coefficient Sparsity metric, the most this with openness for criterion carry out study obtain dictionary each of which atom form with In visual cortex, the impression of V1 district simple cell is also similar to, and their achievement in research has established the neuro physiology base of sparse coding Plinth.

In recent years, solve image indirect problem with the openness priori of signal and cause the extensive concern of scholars, especially Compressed sensing field.The correlation theory proposed according to Donoho and Candes etc., signal expression coefficient under dictionary is the most sparse Then reconstruction quality is the highest, and therefore the selection of dictionary is particularly significant, and which determine image indirect problem solves quality.Traditional based on The building method of matrix dictionary is generally divided into two kinds: analytic method and learning method.Analytic method is by good certain of predefined Plant mathematic(al) manipulation or harmonic analysis method constructs, such as discrete cosine transform, wavelet transformation, bi-input bi-output system conversion, profile Wave conversion, Shearlet, Grouplet and parametrization dictionary etc..Traditional dictionary design and respective algorithms thereof are all based on square Formation dictionary, along with the development of science and technology, in fields such as image procossing, computer vision, data mining, brain science, blind source separating The data produced are a high dimensional data (i.e. tensors) in essence.If continuation transmission method processes, it is necessary to by tensor data Change into matrix data, the most likely can cause the loss of details, it is also difficult to utilize the structural information of initial data.

Therefore, not enough for prior art, it is provided that a kind of MR image reconstruction method based on tensor dictionary learning with Overcome prior art deficiency the most necessary.

Summary of the invention

It is an object of the invention to the deficiency for existing MR image reconstruction method, it is provided that a kind of based on tensor dictionary The MR image reconstruction method of study, to improve reconstructed image quality.

The above-mentioned purpose of the present invention is realized by following technological means:

A kind of MR image reconstruction method based on tensor dictionary learning is provided, comprises the steps:

(1) use variable density random lack sampling mode to obtain raw k-space data, sampled data is carried out Fourier's inversion Get initial reconstructed image in return；

(2) compressed sensing reconstruction model based on tensor dictionary learning is set up；

(3) described reconstruction image is extracted partial 3-D subimage block at random and carry out tensor dictionary learning, obtain a use Tensor dictionary in rarefaction representation；

(4) with hard threshold value method all subimage blocks are carried out the rarefaction representation under described tensor dictionary；

(5) reconstruction image is updated with method of least square；

(6) repeat step (3)-(5) until convergence, finally rebuild image.

In above-mentioned steps (2), set up based on compressed sensing reconstruction model:

$\begin{array}{cc}\underset{X,G,D}{\min }& \underset{i=1}{\overset{L}{\Σ}}\left|\right|G_i|{|}_0+v||{\mathrm{\Φ}}_M\left(X\right)-Y|{|}_F^2\\ s.t.& X_i=G_i\×{D_1}_1\×{D_2}_2\×{D_3}_3,i=1,2,L,L;\end{array}\mathrm{......}\left(I\right);$

Wherein, | | | |₀Represent zero norm, define by calculating nonzero element number, | | | |_FRepresent Frobenius Norm, Y represents the three-dimensional k-space data of lack sampling, and X is image to be reconstructed, Φ_MFor part K space encoding operator, D₁、D₂、D₃ For the factor matrix of self adaptation tensor dictionary, D=₁D₁×₂D₂×₃D₃For tensor dictionary, ν is regularization parameter, and G is by all systems Number G_iThe tetradic of composition, G is by all image block X_iExpression coefficient G under D_iThe tetradic of composition, wherein i=1, 2, L, L, L are the image block sums extracted by sliding window method.

Above-mentioned random extraction partial 3-D subimage block carries out the step of tensor dictionary learning, including:

X and G is regarded as known constant, formula (I) is become following formula II:

$\begin{array}{cc}\underset{D}{\min }& \underset{i}{\Σ}\left|\right|X_i-G_i\×{D_1}_1\×{D_2}_2\×{D_3}_3|{|}_F^2\\ s.t.& {D_j}^H{D}_j=I_{n_j},D_j\∈C^{n_j\×n_j},j=1,2,3\end{array}\mathrm{......}\left(II\right);$

Wherein ()^HRepresent conjugate transposition operation, n_j(j=1,2,3) image block extracted it is respectively two space sides To with the dimension size on a time orientation, I representation unit matrix；

Utilize Higher-order Singular value decomposition method to solve formula II, obtain the tensor dictionary after renewal, specifically:

D₁=U₁V₁ ^H, D₂=U₂V₂ ^H, D₃=U₃V₃ ^H

Wherein, U_jAnd V_j(j=1,2,3) it is respectively Left singular vector and right singular vector composition matrix, wherein R_(j)For all image blocks The p-mode expansion of the tetradic of composition, G_(j)For the j-mode expansion of the tetradic that all coefficient of correspondence form, symbol The Kroncker product of representing matrix.

The step of the above-mentioned rarefaction representation with hard threshold value method, all subimage blocks carried out under described tensor dictionary, including:

X and D is regarded as known constant, formula (I) is become following formula III:

$\begin{array}{cc}\underset{G}{\min }& \underset{i=1}{\overset{L}{\Σ}}\left|\right|G_i|{|}_0+\mathrm{\λ}||X_i-G_i\×{D_1}_1\×{D_2}_2\×{D_3}_3|{|}_F^2\end{array}\mathrm{......}\left(III\right);$

Utilize hard threshold value method to solve formula III, obtain the rarefaction representation of image block: WhereinFor hard domains Value Operations operator, act on tensor X pixel-by-pixel_i×₁D₁×₂D₂×₃D₃, z is Any plural.

Above-mentioned method of least square updates the step rebuilding image, including:

G and D is regarded as known constant, formula (I) is become following formula IV:

$\begin{array}{cc}\underset{X}{\min }& \underset{i}{\Σ}\left|\right|X_i-G_i\×{D_1}_1\×{D_2}_2\×{D_3}_3|{|}_2^2+v||{\mathrm{\Φ}}_{M}X-Y|{|}_F^2\end{array}\mathrm{......}\left(IV\right);$

Formula IV is a typical least square problem, solves with method of least square, makes X_i=R_iX, wherein R_iRepresent and extract The linear operator of subimage block operation, then the reconstruction graphical representation updated is:

$X={(\underset{i}{\Σ}{R_i}^T{R}_i+{{\mathrm{v\Φ}}_M}^H{\mathrm{\Φ}}_M)}^{-1}\left(\underset{i}{\Σ}{R_i}^T\right(G_i{\×}_1{D}_1{\×}_2{D}_2{\×}_3{D}_3)+{{\mathrm{v\Φ}}_M}^{H}y).$

A kind of MR image reconstruction method based on tensor dictionary learning of the present invention, comprises the steps: that (1) uses and becomes Density random lack sampling mode obtains raw k-space data, sampled data is carried out inverse Fourier transform and obtains original reconstruction figure Picture；(2) compressed sensing reconstruction model based on tensor dictionary learning is set up；(3) described reconstruction image is extracted part three at random Dimension subimage block carries out tensor dictionary learning, obtains a tensor dictionary for rarefaction representation；(4) with hard threshold value method to all Subimage block carries out the rarefaction representation under described tensor dictionary；(5) reconstruction image is updated with method of least square；(6) step is repeated (3)-(5), until convergence, are finally rebuild image.It is somebody's turn to do MR image reconstruction method based on tensor dictionary learning, it is possible to Improve reconstructed image quality, and calculate simple.

Accompanying drawing explanation

The present invention is further illustrated to utilize accompanying drawing, but the content in accompanying drawing does not constitute any limit to the present invention System.

Cine cardiac imaging data used by Fig. 1 emulation experiment of the present invention and experimental result contrast schematic diagram.In FIG, Method involved in the present invention is called for short TenDLMRI method, and (a) is original image (as a example by the 1st frame)；B () Descartes samples square Battle array；C () is the PSNR result figure under the different lack sampling factors；D () is the SSIM result figure under the different lack sampling factors.

The time graph experimental result comparison diagram of the area-of-interest that Fig. 2 chooses.In fig. 2, (a) is original image, The dotted line wherein marked represents area-of-interest；B () is fully sampled reconstructed results；C () is the time plot of DLTG method； D () is the time plot that the inventive method obtains.

Heart perfusion imaging data used by Fig. 3 emulation experiment of the present invention and experimental result contrast schematic diagram.In figure 3, Display the 1st, 15,30,45 frame reconstructed results, show fully sampled reconstructed results, zero padding weight the most successively the most successively Build result, the reconstructed results of DLTG method and the reconstructed results of the inventive method.

Detailed description of the invention

Below in conjunction with following example, the invention will be further described.

Embodiment 1.

A kind of MR image reconstruction method based on tensor dictionary learning, comprises the steps:

(1) use variable density random lack sampling mode to obtain raw k-space data, sampled data is carried out Fourier's inversion Get initial reconstructed image in return；

(2) compressed sensing reconstruction model based on tensor dictionary learning is set up；

(3) described reconstruction image is extracted partial 3-D subimage block at random and carry out tensor dictionary learning, obtain a use Tensor dictionary in rarefaction representation；

(4) with hard threshold value method all subimage blocks are carried out the rarefaction representation under described tensor dictionary；

(5) reconstruction image is updated with method of least square；

(6) repeat step (3)-(5) until convergence, finally rebuild image.

In above-mentioned steps (2), set up based on compressed sensing reconstruction model:

$\begin{array}{cc}\underset{X,G,D}{\min }& \underset{i=1}{\overset{L}{\Σ}}\left|\right|G_i|{|}_0+v||{\mathrm{\Φ}}_M\left(X\right)-Y|{|}_F^2\\ s.t.& X_i=G_i\×{D_1}_1\×{D_2}_2\×{D_3}_3,i=1,2,L,L;\end{array}\mathrm{......}\left(I\right);$

Wherein, | | | |₀Represent zero norm, define by calculating nonzero element number, | | | |_FRepresent Frobenius Norm, Y represents the three-dimensional k-space data of lack sampling, and X is image to be reconstructed, Φ_MFor part K space encoding operator, D₁、D₂、D₃ For the factor matrix of self adaptation tensor dictionary, D=₁D₁×₂D₂×₃D₃For tensor dictionary, ν is regularization parameter, and G is by all systems Number G_iThe tetradic of composition, G is by all image block X_iExpression coefficient G under D_iThe tetradic of composition, wherein i=1, 2, L, L, L are the image block sums extracted by sliding window method.

Above-mentioned random extraction partial 3-D subimage block carries out the step of tensor dictionary learning, including:

X and G is regarded as known constant, formula (I) is become following formula II:

$\begin{array}{cc}\underset{D}{\min }& \underset{i}{\Σ}\left|\right|X_i-G_i\×{D_1}_1\×{D_2}_2\×{D_3}_3|{|}_F^2\\ s.t.& {D_j}^H{D}_j=I_{n_j},D_j\∈C^{n_j\×n_j},j=1,2,3\end{array}\mathrm{......}\left(II\right);$

Wherein ()^HRepresent conjugate transposition operation, n_i(i=1,2,3) image block extracted it is respectively two space sides To with the dimension size on a time orientation, I representation unit matrix；

Utilize Higher-order Singular value decomposition method to solve formula II, obtain the tensor dictionary after renewal, specifically:

D₁=U₁V₁ ^H, D₂=U₂V₂ ^H, D₃=U₃V₃ ^H

Wherein, U_jAnd V_j(j=1,2,3) it is respectively Left singular vector and right singular vector composition matrix, wherein R_(j)For all image blocks The j-mode expansion of the tetradic of composition, G_(j)For the j-mode expansion of the tetradic that all coefficient of correspondence form, symbol The Kroncker product of representing matrix.

The step of the above-mentioned rarefaction representation with hard threshold value method, all subimage blocks carried out under described tensor dictionary, including:

X and D is regarded as known constant, formula (I) is become following formula III:

$\begin{array}{cc}\underset{G}{\min }& \underset{i=1}{\overset{L}{\Σ}}\left|\right|G_i|{|}_0+\mathrm{\λ}||X_i-G_i\×{D_1}_1\×{D_2}_2\×{D_3}_3|{|}_F^2\end{array}\mathrm{......}\left(III\right);$

Utilize hard threshold value method to solve formula III, obtain the rarefaction representation of image block: WhereinFor hard domains Value Operations operator, act on tensor X pixel-by-pixel_i×₁D₁×₂D₂×₃D₃, z is Any plural.

Above-mentioned method of least square updates the step rebuilding image, including:

G and D is regarded as known constant, formula (I) is become following formula IV:

$\begin{array}{cc}\underset{X}{\min }& \underset{i}{\Σ}\left|\right|X_i-G_i\×{D_1}_1\×{D_2}_2\×{D_3}_3|{|}_2^2+v||{\mathrm{\Φ}}_{M}X-Y|{|}_F^2\end{array}\mathrm{......}\left(IV\right);$

Formula IV is a typical least square problem, solves with method of least square, makes X_i=R_iX, wherein R_iRepresent and extract The linear operator of subimage block operation, then the reconstruction graphical representation updated is:

Implement available operator R_iAnd Φ_MFeature, be simple computing pixel-by-pixel by its approximate representation.

Present invention MR image reconstruction based on tensor dictionary learning method, has image reconstruction quality high, algorithm letter Single is specific.

Embodiment 2.

With heart computer data instance, as shown in Figure 1 and Figure 2, for heart computer data in the different lack sampling factors Under, use the MR image reconstruction method based on tensor dictionary learning of the present invention to carry out, specifically include following steps:

(1) obtain fully sampled raw k-space data by magnetic resonance imaging, according to given different lack sampling because of Son, carries out retrospective lack sampling to k-space data, obtains lack sampling k-space data Y；Described k-space data Y is carried out zero padding Fourier rebuilds, and obtains rebuilding the initial value of image X, and the initial value with G in season is null matrix.

(2) compressed sensing reconstruction model based on tensor dictionary learning is set up:

$\begin{array}{cc}\underset{X,G,D}{\min }& \underset{i=1}{\overset{L}{\Σ}}\left|\right|G_i|{|}_0+v||{\mathrm{\Φ}}_M\left(X\right)-Y|{|}_F^2\\ s.t.& X_i=G_i\×{D_1}_1\×{D_2}_2\×{D_3}_3,i=1,2,L,L;\end{array}\mathrm{......}\left(I\right);$

Wherein, | | | |₀Represent zero norm, define by calculating nonzero element number, | | | |_FRepresent Frobenius Norm, Y represents the three-dimensional k-space data of lack sampling, and X is image to be reconstructed, Φ_MFor part K space encoding operator, D₁、D₂、D₃ For the factor matrix of self adaptation tensor dictionary, D=₁D₁×₂D₂×₃D₃For tensor dictionary, ν is regularization parameter, and G is by all systems Number G_iThe tetradic of composition, G is by all image block X_iExpression coefficient G under D_iThe tetradic of composition, wherein i=1, 2, L, L, L are the image block sums extracted by sliding window method.

(3) X and G is regarded as known constant, formula (I) is become following optimization problem:

X and G is regarded as known constant, formula (I) is become following formula II:

$\begin{array}{cc}\underset{D}{\min }& \underset{i}{\Σ}\left|\right|X_i-G_i\×{D_1}_1\×{D_2}_2\×{D_3}_3|{|}_F^2\\ s.t.& {D_j}^H{D}_j=I_{n_j},D_j\∈C^{n_j\×n_j},j=1,2,3\end{array}\mathrm{......}\left(II\right);$

Wherein ()^HRepresent conjugate transposition operation, n_i(i=1,2,3) image block extracted it is respectively two space sides To with the dimension size on a time orientation, I representation unit matrix；

Utilize Higher-order Singular value decomposition method to solve formula II, obtain the tensor dictionary after renewal, specifically:

D₁=U₁V₁ ^H, D₂=U₂V₂ ^H, D₃=U₃V₃ ^H

Wherein, U_jAnd V_j(j=1,2,3) it is respectively Left singular vector and right singular vector composition matrix, wherein R_(j)For all image blocks The j-mode expansion of the tetradic of composition, G_(j)For the j-mode expansion of the tetradic that all coefficient of correspondence form, symbol The Kroncker product of representing matrix.

(4) X and D is regarded as known constant, formula (I) is become following problem:

$\begin{array}{cc}\underset{G}{\min }& \underset{i=1}{\overset{L}{\Σ}}\left|\right|G_i|{|}_0+\mathrm{\λ}||X_i-G_i\×{D_1}_1\×{D_2}_2\×{D_3}_3|{|}_F^2\end{array}\mathrm{......}\left(III\right);$

Utilize hard threshold value method to solve formula III, obtain the rarefaction representation of image block: WhereinFor hard domains Value Operations operator, act on tensor X pixel-by-pixel_i×₁D₁×₂D₂×₃D₃, z is Any plural.

(5) G and D is regarded as known constant, formula (1) is become following problem:

$\begin{array}{cc}\underset{X}{\min }& \underset{i}{\Σ}\left|\right|X_i-G_i\×{D_1}_1\×{D_2}_2\×{D_3}_3|{|}_2^2+v||{\mathrm{\Φ}}_{M}X-Y|{|}_F^2\end{array}$

Above formula is a typical least square problem, and available method of least square solves above-mentioned optimization problem, makes X_i=R_iX, Wherein R_iRepresent the linear operator extracting subimage block operation, then the reconstruction image updated can be expressed as:

(6) λ=λ is made₀·δ^kAnd ν=ν₀·δ^k, wherein λ₀=0.5 and ν₀=100 is a previously given initial value, δ Taking 0.9, k represents current iteration step number, repeats (3)-(5), until algorithmic statement.

(5) image is finally rebuild in output, and calculates PSNR and SSIM.

In embodiment 1, the method for the present invention is rebuild with the most typical compressed sensing based on matrix dictionary learning Method DLTG (Caballero J., Price A.N., Rueckert D.et al.Dictionary learning and time sparsity for dynamic MR data reconstruction.IEEE Transactions on Medical Imaging.2014；33 (4): 979-994.) comparing, by comparing discovery, no matter method proposed by the invention exists Qualitative aspect or quantitatively aspect will be better than DLTG method.

Embodiment 3.

As it is shown on figure 3, in embodiment 3, for and Perfusion Imaging data under the given lack sampling factor, it is provided that MR image reconstruction method based on tensor dictionary learning, the method comprises the steps:

(1) the fully sampled k-space data to emulation, according to the given lack sampling factor, is carried out back described k-space data Gu property lack sampling, obtains lack sampling k-space data Y；Described k-space data Y is carried out zero padding Fourier's reconstruction, obtains reconstruction figure As the initial value of X, the initial value with Γ in season is null matrix.

(2) compressed sensing reconstruction model based on tensor dictionary learning is set up, such as (I) formula；

(3) X and G is regarded as known constant, formula (I) is become following optimization problem:

X and G is regarded as known constant, formula (I) is become following formula II:

$\begin{array}{cc}\underset{D}{\min }& \underset{i}{\Σ}\left|\right|X_i-G_i\×{D_1}_1\×{D_2}_2\×{D_3}_3|{|}_F^2\\ s.t.& {D_j}^H{D}_j=I_{n_j},D_j\∈C^{n_j\×n_j},j=1,2,3\end{array}\mathrm{......}\left(II\right);$

Wherein ()^HRepresent conjugate transposition operation, n_i(i=1,2,3) image block extracted it is respectively two space sides To with the dimension size on a time orientation, I representation unit matrix；

Utilize Higher-order Singular value decomposition method to solve formula II, obtain the tensor dictionary after renewal, specifically:

D₁=U₁V₁ ^H, D₂=U₂V₂ ^H, D₃=U₃V₃ ^H

Wherein, U_jAnd V_j(j=1,2,3) it is respectively Left singular vector and right singular vector composition matrix, wherein R_(j)For all image blocks The j-mode expansion of the tetradic of composition, G_(j)For the j-mode expansion of the tetradic that all coefficient of correspondence form, symbol The Kroncker product of representing matrix.

(4) X and D is regarded as known constant, formula (I) is become following problem:

$\begin{array}{cc}\underset{G}{\min }& \underset{i=1}{\overset{L}{\Σ}}\left|\right|G_i|{|}_0+\mathrm{\λ}||X_i-G_i\×{D_1}_1\×{D_2}_2\×{D_3}_3|{|}_2^2\end{array}\mathrm{......}\left(III\right);$

Utilize hard threshold value method to solve formula III, obtain the rarefaction representation of image block: WhereinFor hard domains Value Operations operator, act on tensor X pixel-by-pixel_i×₁D₁×₂D₂×₃D₃, z is Any plural.

(5) G and D is regarded as known constant, formula (1) is become following problem:

$\begin{array}{cc}\underset{X}{\min }& \underset{i}{\Σ}\left|\right|X_i-G_i\×{D_1}_1\×{D_2}_2\×{D_3}_3|{|}_2^2+v||{\mathrm{\Φ}}_{M}X-Y|{{|}_F}^2\end{array}$

Above formula is a typical least square problem, and available method of least square solves above-mentioned optimization problem, makes X_i=R_iX, Wherein R_iRepresent the linear operator extracting subimage block operation, then the reconstruction image updated can be expressed as:

(6) λ=λ is made₀·δ^kAnd ν=ν₀·δ^k, wherein λ₀=0.5 and ν₀=100 is a previously given initial value, δ Taking 0.9, k represents current iteration step number, repeats (3)-(5), until algorithmic statement.

(7) image is finally rebuild in output, and draws the image of designated frame.

In example 2, the present invention compares with described DLTG method, by comparing discovery, proposed by the invention Method have obvious advantage in terms of clear-cut margin keeping.

It is last it should be noted that, the present invention is only protected by above example in order to technical scheme to be described The restriction of scope, although being explained in detail the present invention with reference to preferred embodiment, those of ordinary skill in the art should manage Solve, technical scheme can be modified or equivalent, without deviating from technical solution of the present invention essence and Scope.

Claims (6)

1. a MR image reconstruction method based on tensor dictionary learning, it is characterised in that comprise the steps:

(1) use variable density random lack sampling mode to obtain raw k-space data, sampled data is carried out inverse Fourier transform and obtains To initial reconstructed image；

(2) compressed sensing reconstruction model based on tensor dictionary learning is set up；

(3) described reconstruction image is extracted partial 3-D subimage block at random and carry out tensor dictionary learning, obtain one for dilute The tensor dictionary that relieving the exterior syndrome shows；

(4) with hard threshold value method all subimage blocks are carried out the rarefaction representation under described tensor dictionary；

(5) reconstruction image is updated with method of least square；

(6) repeat step (3)-(5) until convergence, finally rebuild image.

MR image reconstruction method based on tensor dictionary learning the most according to claim 1, it is characterised in that described In step (2), set up based on compressed sensing reconstruction model:

Wherein, | | | |₀Represent zero norm, define by calculating nonzero element number, | | | |_FRepresent Frobenius model Number,Represent the three-dimensional k-space data of lack sampling,For image to be reconstructed, Φ_MFor part K space encoding operator, D₁、D₂、D₃ For the factor matrix of self adaptation tensor dictionary, D=₁D₁×₂D₂×₃D₃For tensor dictionary, v is regularization parameter,It is by owning CoefficientThe tetradic of composition,It is by all image blocksExpression coefficient under DThe tetradic of composition, wherein i= 1,2 ..., L, L are the image block sums extracted by sliding window method.

MR image reconstruction method based on tensor dictionary learning the most according to claim 1, it is characterised in that described The random partial 3-D subimage block that extracts carries out the step of tensor dictionary learning, including:

?WithRegard known constant as, formula (I) become such as following formula (II):

Wherein ()^HRepresent conjugate transposition operation, n_j(j=1,2,3) is respectively the image block extracted at two direction in spaces With the dimension size on a time orientation, I representation unit matrix；

Higher-order Singular value decomposition method is utilized to solve formula II, the tensor dictionary after being updated.

MR image reconstruction method based on tensor dictionary learning the most according to claim 3, it is characterised in that utilize Higher-order Singular value decomposition method solves formula II, obtains the tensor dictionary after renewal, specifically:

D₁=U₁V₁ ^H, D₂=U₂V₂ ^H, D₃=U₃V₃ ^H

Wherein, U_jAnd V_j(j=1,2,3) it is respectively Left singular vector and right singular vector composition matrix, wherein R_(j)For all image blocks The j-mode expansion of the tetradic of composition, G_(j)For the j-mode expansion of the tetradic that all coefficient of correspondence form, symbol The Kroncker product of representing matrix.

MR image reconstruction method based on tensor dictionary learning the most according to claim 1, it is characterised in that described With hard threshold value method all subimage blocks are carried out the step of rarefaction representation under described tensor dictionary, including:

?Regard known constant as with D, formula (I) become following formula III:

Utilize hard threshold value method to solve formula III, obtain the rarefaction representation of image block:Its InFor hard domains Value Operations operator, act on tensor pixel-by-pixelZ is Any plural.

MR image reconstruction method based on tensor dictionary learning the most according to claim 1, it is characterised in that described The step rebuilding image is updated with method of least square, including:

?Regard known constant as with D, formula (I) become following formula IV:

Formula IV is a typical least square problem, solves with method of least square, orderWherein R_iRepresent and extract son The linear operator of image block operation, then the reconstruction graphical representation updated is: