CN104111431A - Method and device for reconstruction in dynamic magnetic resonance imaging - Google Patents

Abstract

The invention provides a method and a device for reconstruction in dynamic magnetic resonance imaging. The method comprises the following steps: a magnetic resonance signal obtained through sparse collection is received; estimation is performed according to a partially separable function to obtain a time basis function; the partially separable function and a total variation constraint are jointly adopted to obtain a spatial basis function of the magnetic resonance signal; and the obtained time basis function and the obtained spatial basis function are substituted into a low-rank partially separable function model to obtain a dynamic magnetic resonance image of the recovered magnetic resonance signal. The device comprises a signal receiving module, an estimation module, a spatial basis operation module, and an image generation module. By adopting the method and the device of the invention, a high-resolution dynamic magnetic resonance image can be quickly obtained.

Description

Method for reconstructing in dynamic magnetic resonance imaging and device

Technical field

The present invention relates to magnetic resonance fast imaging technology, particularly relate to method for reconstructing and device in a kind of dynamic magnetic resonance imaging.

Background technology

The many merits radiationless, multi-faceted and multiparameter imaging of magnetic resonance makes magnetic resonance imaging become one of important means of clinical medicine inspection, for clinical medicine provides very valuable diagnostic message.Magnetic resonance is very responsive to the inspection of software organization, the shape information that not only can show human anatomic structure, but also can reflect some Physiology and biochemistry information of tissue, if can be applied in heart dynamic imaging, cerebral function imaging, human motion imaging and cardiovascular and cerebrovascular fast imaging, the diagnosis accuracy of the dynamic magnetic resonance imagings such as heart dynamic imaging, cerebral function imaging, human motion imaging and cardiovascular and cerebrovascular fast imaging will greatly be improved.

Because magnetic resonance imaging speed is slower, in imaging process usually because the physiological movement in examinee's health causes image fog, contrast distortion, traditional magnetic resonance imaging is in order to realize fast imaging, when obtaining MRI signal, often can only obtain limited a part of K spacing wave.The imperfect of K spacing wave will cause the generation of Fourier's gibbs artifact, wherein, comprise ring and fuzzy, and in the dynamic magnetic resonance imagings such as cerebral function imaging and cardiovascular and cerebrovascular fast imaging, seem particularly outstanding, and then make dynamic magnetic resonance imaging cannot obtain at short notice high-resolution dynamic magnetic resonance image.

Summary of the invention

Based on this, be necessary for obtaining at short notice the technical matters of high-resolution dynamic magnetic resonance image in traditional magnetic resonance imaging, the method for reconstructing in a kind of dynamic magnetic resonance imaging that can obtain fast high-resolution dynamic magnetic resonance image is provided.

In addition, be also necessary to provide the reconstructing device in a kind of dynamic magnetic resonance imaging that can obtain fast high-resolution dynamic magnetic resonance image.

A method for reconstructing in dynamic magnetic resonance imaging, comprises the steps:

The sparse magnetic resonance signal collecting is carried out in reception;

According to part separable function, estimate to obtain time basis function;

Combine and adopt part separable function and total variance constraint to obtain the space basis function of described magnetic resonance signal;

By the be restored dynamic magnetic resonance image of magnetic resonance signal of the part separable function model of the described time basis function obtaining and space basis function substitution low-rank.

In an embodiment, the step that the sparse magnetic resonance signal collecting is carried out in described reception comprises therein:

By part separable function sample mode, carry out data acquisition, to obtain described magnetic resonance signal.

Therein in an embodiment, describedly according to part separable function, estimate that the step that obtains time basis function comprises:

Gather navigation signal, according to described navigation signal, carry out unusual decomposition and obtain time basis function.

In an embodiment, the described step that adopts part separable function and total variance constraint to obtain the space basis function of described magnetic resonance signal of combining comprises therein:

Image measurement data and the time basis function of in the system of linear equations building at described part separable function introducing total variance Restricted operator, inputting described magnetic resonance signal obtain quadratic function to be solved;

Solve the space basis function that described quadratic function obtains described magnetic resonance signal.

Therein in an embodiment, the be restored step of dynamic magnetic resonance image of magnetic resonance signal of the described part separable function model by the described time basis function obtaining and space basis function substitution low-rank is:

The time basis function obtaining described in calculating and the product between the basis function of space, long-pending being of described time basis function and space basis function recovered the resulting dynamic magnetic resonance image of magnetic resonance signal.

A reconstructing device in dynamic magnetic resonance imaging, comprising:

Signal receiving module, carries out the sparse magnetic resonance signal collecting for receiving;

Estimation module, for estimating to obtain time basis function according to part separable function;

Space Base computing module, adopts part separable function and total variance constraint to obtain the space basis function of described magnetic resonance signal for combining;

Image generation module, for the dynamic magnetic resonance image of magnetic resonance signal that the part separable function model of the described time basis function obtaining and space basis function substitution low-rank is restored.

In an embodiment, described signal receiving module is also for carrying out data acquisition by part separable function sample mode, to obtain magnetic resonance signal therein.

In an embodiment, described estimation module, also for gathering navigation signal, is carried out unusual decomposition according to described navigation signal and is obtained time basis function therein.

In an embodiment, described space Base computing module comprises therein:

Input block, image measurement data and the time basis function of for introduce the system of linear equations of total variance Restricted operator structure at described part separable function, inputting described magnetic resonance signal obtain quadratic function to be solved;

Function solves unit, obtains the space basis function of described magnetic resonance signal for solving the described quadratic function of bag.

Therein in an embodiment, described image generation module is also for the time basis function that obtains described in calculating and the product between the basis function of space, and long-pending being of described time basis function and space basis function recovered the resulting dynamic magnetic resonance image of magnetic resonance signal.

Method for reconstructing in above-mentioned dynamic magnetic resonance imaging and device, after receiving and carrying out the sparse magnetic resonance signal collecting, to estimate to obtain time basis function according to part separable function, combine and adopt part separable function and total variance constraint to obtain the space basis function of magnetic resonance signal, and then the recovery that completes magnetic resonance signal by the time basis function that obtains and space basis function, obtain dynamic magnetic resonance image, on the basis of sparse sampling, by joining full employing part separable function and total variance constraint, image artifacts and noise have effectively been reduced, greatly improved the quality of rebuilding the dynamic magnetic resonance image obtaining, realized the raising of resolution, obtained the dynamic magnetic resonance image of high time resolution and high spatial resolution.

Accompanying drawing explanation

Fig. 1 is the process flow diagram of the method for reconstructing in dynamic magnetic resonance imaging in an embodiment;

Fig. 2 combines in Fig. 1 to adopt part separable function and total variance constraint to obtain the method flow diagram of the space basis function of magnetic resonance signal;

The dynamic magnetic resonance image that Fig. 3 obtains for the method for reconstructing reconstruction in application dynamic magnetic resonance imaging of the present invention;

Fig. 4 is that original dynamic magnetic resonance imaging is rebuild resulting dynamic magnetic resonance image;

Fig. 5 is the structural representation of the reconstructing device in dynamic magnetic resonance imaging in an embodiment;

Fig. 6 is the structural representation of Base computing module in space in Fig. 5.

Embodiment

In order to make object of the present invention, technical scheme and advantage clearer, below in conjunction with drawings and Examples, the present invention is further elaborated.Should be appreciated that specific embodiment described herein, only in order to explain the present invention, is not intended to limit the present invention.

As shown in Figure 1, in one embodiment, the method for reconstructing in a kind of dynamic magnetic resonance imaging, comprises the steps:

Step S110, receives and carries out the sparse magnetic resonance signal collecting.

In the present embodiment, the detailed process of this step S110 is: by part separable function sample mode, carry out data acquisition, to obtain magnetic resonance signal.The motive position employing part separable function sample modes such as heart, coronary artery are carried out to the signals collecting of a period of time, to receive the magnetic resonance signal from motive position.

Part separable function sample mode has very significantly advantage in numerous fast imaging methods, it has broken through the restriction of nyquist sampling theorem (Nyquist theorem) on imaging time, utilize the redundancy of frequency-domain and time-domain view data to reduce the needed data of collection imaging, and then the temporal resolution of raising imaging, in the dynamic magnetic resonance imaging that makes motive position carry out, do not used gating technology and in the situation that freely breathing, motion parts carried out to high resolution scanning, for the high resolving power of dynamic magnetic resonance imaging provides precondition.

Step S130, estimates to obtain time basis function according to part separable function.

In the present embodiment, the corresponding image function of dynamic magnetic resonance image that the magnetic resonance signal S (k, t) that actual reception obtains and reconstruction obtain is that the pass between ρ (x, t) is wherein, e (k, t) is for measuring noise.

In the signals collecting that motive position is carried out, the a certain panel data that the magnetic resonance signal collecting comprises has comprised the aliasing information from other each different parts outside motive position, therefore, for avoiding consequent fuzzy and motion artifacts, to utilize part separable function to carry out the estimation of time basis function, think image function ρ (x, t) it is that L rank are separated that spatial variations changed with the time, the L exponent part separable function model (PSF model) of definition magnetic resonance signal S (k, t) is:

Wherein, L is mode step, will get very little value, with be respectively space basis function and time basis function, S (k, t) is expressed as the Casorati matrix (Carcel draws base of a fruit matrix) of low order, that is:

Wherein, N is all pixel numbers in k space, order (S)≤L, and then S can be write as to following formula:

S＝U _kV _t

Wherein, (k, t) space is sparse sampling, has a lot of disappearances in magnetic resonance signal S, therefore, will carry out the recovery of magnetic resonance signal S by " rank " restriction, and then obtain time basis function V _t.

Because the Casorati matrix of highly owing to adopt is ill, use least square method scheduling algorithm to be difficult to estimate exactly, therefore, for fear of adopting least square method, to gather extraly navigation signal to carry out the estimation of time basis function, according to the time basis function constraint space basis function of estimating to obtain, and then obtain high-quality dynamic magnetic resonance image.

In one embodiment, the detailed process of above-mentioned steps S130 is: gather navigation signal, navigation signal carries out unusual decomposition and obtains time basis function.

In the present embodiment, gather extraly navigation signal, by navigation signal being carried out to unusual decomposition to obtain time basis function.

Step S150, combines and adopts part separable function and total variance constraint to obtain the space basis function of magnetic resonance signal.

In the present embodiment, in L exponent part separable function model, carry out total variance (total variation) constrained of space basis function, to obtain new reconstruction model,

TV operator can be defined as following formula:

Wherein, represent the horizontal and vertical difference of i pixel in each image, i.e. gradient operator, represent V _fj row, representative is at the spatial gradient of i pixel of (x, f) space j frame, because new reconstruction model is a protruding optimization problem, the TV item that has comprised non-linear non-differentiability, therefore, by this by half secondary regularization method by the TV bound term of non-differentiability be converted into can be micro-TV bound term,

Wherein,

β is constrained parameters (generally getting very little), and when β →+∞, the regularization constraint item based on above formula has become original TV regular terms $\mathrm{TV}\left(U_s{V}_f\right)=\underset{j=1}{\overset{M}{\mathrm{\Σ}}}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}\left|\right|D_i{U}_s{V}_f^{\left(j\right)}{\left|\right|}_2.$

Further,

W _ijfor intermediate variable.

Comprehensive above-mentioned three formulas, by new reconstruction model approximate change into following protruding optimization problem:

$\{{\hat{U}}_s,{\hat{w}}_{\mathrm{ij}}\}=\arg \underset{\{U_s,w_{\mathrm{ij}}\}}{\min }{\left|\right|d-\mathrm{\Ω}\left(F_s{U}_s{V}_t\right)\left|\right|}_2^2+\mathrm{\μ}\underset{j=1}{\overset{M}{\mathrm{\Σ}}}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\left|\right|w_{\mathrm{ij}}\left|\right|}_2+\frac{\mathrm{\μ\β}}{2}\underset{j=1}{\overset{M}{\mathrm{\Σ}}}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\left|\right|w_{\mathrm{ij}}-D_i{U}_s{V}_f^{\left(j\right)}\left|\right|}_2^2$

By iteration optimization, process the reconstruction model with epirelief optimization problem, given one initial by following two formula, obtain ?

$w_{\mathrm{ij}}^{\left(l\right)}=\frac{D_i{U}_s^{\left(l\right)}{V}_f^{\left(j\right)}}{{\left|\right|D_i{U}_s^{\left(l\right)}{V}_f^{\left(j\right)}\left|\right|}_2}\max \{{\left|\right|D_i{U}_s^{\left(l\right)}{V}_f^{\left(j\right)}\left|\right|}_2-\frac{1}{\mathrm{\β}},0\}$

By above-mentioned iterative computation, obtain now, will be undertaken by second double optimization problem solve, obtain

For simplifying, calculate, will introduce variable $w_{\mathrm{ij}}=\left[\begin{array}{c}{W}_{i,j}^h\\ W_{i,j}^v\end{array}\right],D_i=\left[\begin{array}{c}{D}_i^h\\ D_i^v\end{array}\right];$

Wherein, with be respectively matrix W ^hand W ^v(i, j), with respectively D ^hand D ^vi capable, by above-mentioned second double optimization be reduced to following formula:

Now, will further simplify so that effectively calculate.

Due to with be block circulant matrix, therefore can change orthogonalization by two-dimentional Fourier.

Wherein

∧ ^hand ∧ ^vbe the diagonal matrix of N * N, make U _k=F _su _s, so

Wherein $W_k^h=F_s{W}^h,W_k^v=F_s{W}^v$

$\mathrm{\Ω}\left(U_k{V}_t\right)=\left[\begin{array}{c}{\mathrm{\Ω}}_1\left(u_k^1{V}_t\right)\\ {\mathrm{\Ω}}_2\left(u_k^2{V}_t\right)\\ .\\ .\\ .\\ {\mathrm{\Ω}}_N\left(u_k^N{V}_t\right)\end{array}\right]$

u _ki capable, Ω _iu _kv _tthe capable sample operator of i, will change into following formula:

Wherein, d _ithat i in image measurement data (k, t) space is capable, with be respectively with i capable, therefore, will build for solving the quadratic function of time basis function, i.e. above formula with $[A_i^{*}{A}_i+\frac{\mathrm{\μ\β}{\left|{\mathrm{\λ}}_i^h\right|}^2}{2}I+\frac{\mathrm{\μ\β}\left|{\mathrm{\λ}}_i^v\right|}{2}I]u_k^i=A_i^{*}\left(d_i\right)+\frac{\mathrm{\μ\βconj}\left({\mathrm{\λ}}_i^h\right)}{2}\stackrel{-}{w_i^h}{V}_f^H+\frac{\mathrm{\μ\βconj}\left({\mathrm{\λ}}_i^v\right)}{2}\stackrel{-}{w_i^v}{V}_f^H$ Form system of equations, in this system of equations, exponent number L and time basis function solve as unknown number.

A _i()=Ω _i(V _t), represent A _iadjoint operator, be unit operator, conj () represents complex conjugate, and at this, we suppose V _for V _trow be quadrature.

As shown in Figure 2, in one embodiment, above-mentioned steps S150 comprises the steps:

Step S151, image measurement data and the time basis function of in the system of linear equations building at part separable function introducing total variance Restricted operator, inputting magnetic resonance signal obtain quadratic function to be solved.

In the present embodiment, by the image measurement data of magnetic resonance signal and time basis function input with $[A_i^{*}{A}_i+\frac{\mathrm{\μ\β}{\left|{\mathrm{\λ}}_i^h\right|}^2}{2}I+\frac{\mathrm{\μ\β}\left|{\mathrm{\λ}}_i^v\right|}{2}I]u_k^i=A_i^{*}\left(d_i\right)+\frac{\mathrm{\μ\βconj}\left({\mathrm{\λ}}_i^h\right)}{2}\stackrel{-}{w_i^h}{V}_f^H+\frac{\mathrm{\μ\βconj}\left({\mathrm{\λ}}_i^v\right)}{2}\stackrel{-}{w_i^v}{V}_f^H$ Form in quadratic function system of equations, so that only there are exponent number L and these two unknown numbers of time basis function in system of equations.

Step S153, solves the space basis function that this quadratic function obtains magnetic resonance signal.

In the present embodiment, use conjugate gradient algorithm to carry out iteration optimization to system of equations and solve the unique locally optimal solution obtaining in quadratic function system of equations, obtain the space basis function of final constraint solving.

Step S170, obtains the dynamic magnetic resonance image of magnetic resonance signal by the time basis function obtaining and the low part separable function model that enters low-rank of space basis function.

In one embodiment, the detailed process of above-mentioned steps S170 is: the time basis function calculating and the product between the basis function of space, long-pending being of this time basis function and space basis function recovered the resulting dynamic magnetic resonance image of magnetic resonance signal.

Concrete, by time basis function V _twith space basis function U _ksubstitution formula S=U _kv _tthe dynamic magnetic resonance image that can obtain rebuilding in dynamic magnetic resonance imaging.

Method for reconstructing in above-mentioned dynamic magnetic resonance imaging has obtained preferably temporal resolution and spatial resolution, aspects such as making cerebral function imaging, heart dynamic imaging, cardiovascular and cerebrovascular fast imaging can be held to the super-resolution reconstruction image that gets certain section within a short period of time, avoided fuzzy and generation motion artifacts.

In a specific embodiment, the method for reconstructing of applying in above-mentioned dynamic magnetic resonance imaging carries out off-line reconstruction model, and resulting dynamic magnetic resonance image as shown in Figure 3.

The resulting reconstruction image of method for reconstructing of original dynamic magnetic resonance imaging as shown in Figure 4, Fig. 3 and Fig. 4 are compared known, the resulting dynamic magnetic resonance image of method for reconstructing in above-mentioned dynamic magnetic resonance imaging has suppressed noise really effectively, has obtained better picture quality under the prerequisite of high time resolution and high spatial resolution.

As shown in Figure 5, in one embodiment, the reconstructing device in a kind of dynamic magnetic resonance imaging, comprises signal receiving module 110, estimation module 130, space Base computing module 150 and image generation module 170.

Signal receiving module 110, carries out the sparse magnetic resonance signal collecting for receiving.

In the present embodiment, above-mentioned signal receiving module 110 is also for carrying out data acquisition by part separable function sample mode, to obtain magnetic resonance signal.To motive position such as heart, coronary arteries, adopt part separable function sample mode to carry out the signals collecting of a period of time, signal receiving module 110 is by the magnetic resonance signal receiving from motive position.

Part separable function sample mode has very significantly advantage in numerous fast imaging methods, it has broken through the restriction of nyquist sampling theorem on imaging time, utilize the redundancy of frequency-domain and time-domain image to reduce the needed data of collection imaging, and then the temporal resolution of raising imaging, in the dynamic magnetic resonance imaging that makes motion parts carry out, do not used gating technology and in the situation that freely breathing, motion parts carried out to high resolution scanning, for the high resolving power of dynamic magnetic resonance imaging provides precondition.

Estimation module 130, for estimating to obtain time basis function according to part separable function.

In the present embodiment, the corresponding image function of dynamic magnetic resonance image that the magnetic resonance signal S (k, t) that the actual reception of signal receiving module 110 obtains and reconstruction obtain is that the pass between ρ (x, t) is $S(k,t)={\∫}_{-\∞}^{+\∞}\mathrm{\ρ}(x,t)e^{-i2\mathrm{\πk}\·x}\mathrm{dx}+e(k,t),$ Wherein, e (k, t) is for measuring noise.

In the signals collecting that motive position is carried out, the a certain panel data that the magnetic resonance signal collecting comprises has comprised the aliasing information from other each different parts outside motive position, therefore, for avoiding consequent fuzzy and motion artifacts, estimation module 130 will utilize part separable function to carry out the estimation of time basis function, think image function ρ (x, t) it is that L rank are separated that spatial variations changed with the time, the L exponent part separable function model (PSF model) of definition magnetic resonance signal S (k, t) is:

Wherein, L is mode step, will get very little value, with be respectively space basis function and time basis function, S (k, t) is expressed as the Casorati matrix (Carcel draws base of a fruit matrix) of low order, that is:

Wherein, N is all pixel numbers in k space, order (S)≤L, and then S can be write as to following formula:

S＝U _kV _t

Wherein, (k, t) space is sparse sampling, has a lot of disappearances in magnetic resonance signal S, therefore, will carry out the recovery of magnetic resonance signal S by " rank " restriction, and then obtain time basis function V _t.

Because the Casorati matrix of highly owing to adopt is ill, use least square method scheduling algorithm to be difficult to estimate exactly, therefore, for fear of adopting least square method, to gather extraly navigation signal to carry out the estimation of time basis function, according to the time basis function constraint space basis function of estimating to obtain, and then obtain high-quality dynamic magnetic resonance image.

In one embodiment, above-mentioned estimation module 130, also for gathering navigation signal, is carried out unusual decomposition according to navigation signal and is obtained time basis function.

In the present embodiment, estimation module 130 gathers navigation signal extraly, by navigation signal being carried out to unusual decomposition to obtain time basis function.

Space Base computing module 150, adopts part separable function and total variance constraint to obtain the space basis function of magnetic resonance signal for combining.

In the present embodiment, space Base computing module 150 is carried out total variance (total variation) constrained of space basis function in L exponent part separable function model, to obtain new reconstruction model,

TV operator can be defined as following formula:

Wherein, represent the horizontal and vertical difference of i pixel in each image, i.e. gradient operator, represent V _fj row, representative is at the spatial gradient of i pixel of (x, f) space j frame, because new reconstruction model is a protruding optimization problem, the TV item that has comprised non-linear non-differentiability, therefore, by this by half secondary regularization method by the TV bound term of non-differentiability be converted into can be micro-TV bound term,

Wherein,

β is for being constrained parameters (generally getting very little), and when β →+∞, the regularization constraint item based on above formula has become original TV regular terms $\mathrm{TV}\left(U_s{V}_f\right)=\underset{j=1}{\overset{M}{\mathrm{\Σ}}}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\left|\right|D_i{U}_s{V}_f^{\left(j\right)}\left|\right|}_2.$

Further,

W _ijfor intermediate quantity.

Comprehensive above-mentioned three formulas, by new reconstruction model approximate change into following protruding optimization problem:

$\{{\hat{U}}_s,{\hat{w}}_{\mathrm{ij}}\}=\arg \underset{\{U_s,w_{\mathrm{ij}}\}}{\min }{\left|\right|d-\mathrm{\Ω}\left(F_s{U}_s{V}_t\right)\left|\right|}_2^2+\mathrm{\μ}\underset{j=1}{\overset{M}{\mathrm{\Σ}}}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\left|\right|w_{\mathrm{ij}}\left|\right|}_2+\frac{\mathrm{\μ\β}}{2}\underset{j=1}{\overset{M}{\mathrm{\Σ}}}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\left|\right|w_{\mathrm{ij}}-D_i{U}_s{V}_f^{\left(j\right)}\left|\right|}_2^2$

By iteration optimization, process the reconstruction model with epirelief optimization problem, given one initial by following two formula, obtain ?

$w_{\mathrm{ij}}^{\left(l\right)}=\frac{D_i{U}_s^{\left(l\right)}{V}_f^{\left(j\right)}}{{\left|\right|D_i{U}_s^{\left(l\right)}{V}_f^{\left(j\right)}\left|\right|}_2}\max \{{\left|\right|D_i{U}_s^{\left(l\right)}{V}_f^{\left(j\right)}\left|\right|}_2-\frac{1}{\mathrm{\β}},0\}$

By above-mentioned iterative computation, obtain now, will be undertaken by second double optimization problem solve, obtain

For simplifying, calculate, will introduce variable $w_{\mathrm{ij}}=\left[\begin{array}{c}{W}_{i,j}^h\\ W_{i,j}^v\end{array}\right],D_i=\left[\begin{array}{c}{D}_i^h\\ D_i^v\end{array}\right];$

Wherein, with be respectively matrix W ^hand W ^v(i, j), with respectively D ^hand D ^vi capable, by above-mentioned second double optimization be reduced to following formula:

Now, will further simplify so that effectively calculate.

Due to with be block circulant matrix, therefore can change orthogonalization by two-dimentional Fourier.

Wherein

∧ ^hand ∧ ^vbe the diagonal matrix of N * N, make U _k=F _su _s, so

Wherein $W_k^h=F_s{W}^h,W_k^v=F_s{W}^v$

$\mathrm{\Ω}\left(U_k{V}_t\right)=\left[\begin{array}{c}{\mathrm{\Ω}}_1\left(u_k^1{V}_t\right)\\ {\mathrm{\Ω}}_2\left(u_k^2{V}_t\right)\\ .\\ .\\ .\\ {\mathrm{\Ω}}_N\left(u_k^N{V}_t\right)\end{array}\right]$

u _ki capable, Ω _iu _kv _tthe capable sample operator of i, will change into following formula:

Wherein, d _ithat i in image measurement data (k, t) space is capable, with be respectively with i capable, therefore, will build for solving the quadratic function of time basis function, i.e. above formula with $[A_i^{*}{A}_i+\frac{\mathrm{\μ\β}{\left|{\mathrm{\λ}}_i^h\right|}^2}{2}I+\frac{\mathrm{\μ\β}\left|{\mathrm{\λ}}_i^v\right|}{2}I]u_k^i=A_i^{*}\left(d_i\right)+\frac{\mathrm{\μ\βconj}\left({\mathrm{\λ}}_i^h\right)}{2}\stackrel{-}{w_i^h}{V}_f^H+\frac{\mathrm{\μ\βconj}\left({\mathrm{\λ}}_i^v\right)}{2}\stackrel{-}{w_i^v}{V}_f^H$ Form system of equations, in this system of equations, space Base computing module 150 exponent number L and time basis function solve as unknown number.

A _i()=Ω _i(V _t), represent A _iadjoint operator, be unit operator, conj () represents complex conjugate, and at this, we suppose V _for V _trow be quadrature.

As shown in Figure 6, in one embodiment, above-mentioned space Base computing module 150 comprises that input block 151 and function solve unit 153.

Input block 151, image measurement data and the time basis function of for introduce the system of linear equations of total variance Restricted operator structure at part separable function, inputting magnetic resonance signal obtain quadratic function to be solved.

In the present embodiment, input block 151 is by the image measurement data of magnetic resonance signal and time basis function input with $[A_i^{*}{A}_i+\frac{\mathrm{\μ\β}{\left|{\mathrm{\λ}}_i^h\right|}^2}{2}I+\frac{\mathrm{\μ\β}\left|{\mathrm{\λ}}_i^v\right|}{2}I]u_k^i=A_i^{*}\left(d_i\right)+\frac{\mathrm{\μ\βconj}\left({\mathrm{\λ}}_i^h\right)}{2}\stackrel{-}{w_i^h}{V}_f^H+\frac{\mathrm{\μ\βconj}\left({\mathrm{\λ}}_i^v\right)}{2}\stackrel{-}{w_i^v}{V}_f^H$ Form in quadratic function system of equations, so that only there are exponent number L and these two unknown numbers of time basis function in system of equations.

Function solves unit 153, obtains the space basis function of magnetic resonance signal for solving this quadratic function.

In the present embodiment, function solves unit 153 and uses conjugate gradient algorithm to carry out iteration optimization to system of equations to solve the unique locally optimal solution obtaining in quadratic function system of equations, obtain the space basis function of final constraint solving.

Image generation module 170, for the dynamic magnetic resonance image of magnetic resonance signal that the part separable function model of the time basis function obtaining and space basis function substitution low-rank is restored.

In one embodiment, above-mentioned image generation module 170 is also for the time basis function that calculates and the product between the basis function of space, and long-pending being of this time basis function and space basis function recovered the resulting dynamic magnetic resonance image of magnetic resonance signal.

Concrete, image generation module 170 is by time basis function V _twith space basis function U _ksubstitution formula S=U _kv _tthe dynamic magnetic resonance image that can obtain rebuilding in dynamic magnetic resonance imaging.

Reconstructing device in above-mentioned dynamic magnetic resonance imaging has obtained preferably temporal resolution and spatial resolution, aspects such as making cerebral function imaging, heart dynamic imaging, cardiovascular and cerebrovascular fast imaging can be held to the super-resolution reconstruction image that gets certain section within a short period of time, avoided fuzzy and generation motion artifacts.

Method for reconstructing in above-mentioned dynamic magnetic resonance imaging and device, after receiving and carrying out the sparse magnetic resonance signal collecting, to estimate to obtain time basis function according to part separable function, combine and adopt part separable function and total variance constraint to obtain the space basis function of magnetic resonance signal, and then the recovery that completes magnetic resonance signal by the time basis function that obtains and space basis function, obtain dynamic magnetic resonance image, on the basis of sparse sampling, by joining full employing part separable function and total variance constraint, image artifacts and noise have effectively been reduced, greatly improved the quality of rebuilding the dynamic magnetic resonance image obtaining, realized the raising of resolution, obtained the dynamic magnetic resonance image of high time resolution and high spatial resolution.

One of ordinary skill in the art will appreciate that all or part of flow process realizing in above-described embodiment method, to come the hardware that instruction is relevant to complete by computer program, described program can be stored in a computer read/write memory medium, this program, when carrying out, can comprise as the flow process of the embodiment of above-mentioned each side method.Wherein, described storage medium can be magnetic disc, CD, read-only store-memory body (Read-Only Memory, ROM) or random store-memory body (Random Access Memory, RAM) etc.

The above embodiment has only expressed several embodiment of the present invention, and it describes comparatively concrete and detailed, but can not therefore be interpreted as the restriction to the scope of the claims of the present invention.It should be pointed out that for the person of ordinary skill of the art, without departing from the inventive concept of the premise, can also make some distortion and improvement, these all belong to protection scope of the present invention.Therefore, the protection domain of patent of the present invention should be as the criterion with claims.

Claims (10)

1. the method for reconstructing in dynamic magnetic resonance imaging, comprises the steps:

The sparse magnetic resonance signal collecting is carried out in reception;

According to part separable function, estimate to obtain time basis function;

Combine and adopt part separable function and total variance constraint to obtain the space basis function of described magnetic resonance signal;

By the be restored dynamic magnetic resonance image of magnetic resonance signal of the part separable function model of the described time basis function obtaining and space basis function substitution low-rank.

2. method according to claim 1, is characterized in that, the step that the sparse magnetic resonance signal collecting is carried out in described reception comprises:

By part separable function sample mode, carry out data acquisition, to obtain described magnetic resonance signal.

3. method according to claim 1, is characterized in that, describedly according to part separable function, estimates that the step that obtains time basis function comprises:

Gather navigation signal, according to described navigation signal, carry out unusual decomposition and obtain time basis function.

4. method according to claim 1, is characterized in that, the described step that adopts part separable function and total variance constraint to obtain the space basis function of described magnetic resonance signal of combining comprises:

Image measurement data and the time basis function of in the system of linear equations building at described part separable function introducing total variance Restricted operator, inputting described magnetic resonance signal obtain quadratic function to be solved;

Solve the space basis function that described quadratic function obtains described magnetic resonance signal.

5. method according to claim 1, is characterized in that, the be restored step of dynamic magnetic resonance image of magnetic resonance signal of the described part separable function model by the described time basis function obtaining and space basis function substitution low-rank is:

The time basis function obtaining described in calculating and the product between the basis function of space, long-pending being of described time basis function and space basis function recovered the resulting dynamic magnetic resonance image of magnetic resonance signal.

6. the reconstructing device in dynamic magnetic resonance imaging, is characterized in that, comprising:

Signal receiving module, carries out the sparse magnetic resonance signal collecting for receiving;

Estimation module, for estimating to obtain time basis function according to part separable function;

Space Base computing module, adopts part separable function and total variance constraint to obtain the space basis function of described magnetic resonance signal for combining;

Image generation module, for the dynamic magnetic resonance image of magnetic resonance signal that the part separable function model of the described time basis function obtaining and space basis function substitution low-rank is restored.

7. device according to claim 6, is characterized in that, described signal receiving module is also for carrying out data acquisition by part separable function sample mode, to obtain magnetic resonance signal.

8. device according to claim 6, is characterized in that, described estimation module, also for gathering navigation signal, is carried out unusual decomposition according to described navigation signal and obtained time basis function.

9. device according to claim 6, is characterized in that, described space Base computing module comprises:

Input block, image measurement data and the time basis function of for introduce the system of linear equations of total variance Restricted operator structure at described part separable function, inputting described magnetic resonance signal obtain quadratic function to be solved;

Function solves unit, obtains the space basis function of described magnetic resonance signal for solving the described quadratic function of bag.

10. device according to claim 6, it is characterized in that, described image generation module is also for the time basis function that obtains described in calculating and the product between the basis function of space, and long-pending being of described time basis function and space basis function recovered the resulting dynamic magnetic resonance image of magnetic resonance signal.