CN104569880A - Magnetic resonance fast imaging method and system - Google Patents

Abstract

The invention provides a magnetic resonance fast imaging method and system. The method includes the steps that under-sampled magnetic resonance data are acquired; according to the under-sampled magnetic resonance data, K spatial data corresponding to various magnetic resonance image features to be acquired are calculated through multiple convolution kernel functions; according to the K spatial data corresponding to the magnetic resonance image features to be acquired, magnetic resonance image features are reconstructed through the compressed sensing technology, and the reconstructed image features are acquired; the reconstructed image features are combined and reconstructed magnetic resonance images are generated. By the adoption of the magnetic resonance fast imaging method and system, the image features corresponding to the convolution kernel functions are reconstructed through the compressed sensing technology, the image features may be more sparse and may be higher in signal to noise ratio, and therefore utilization of the compressed sensing technology for reconstruction is further facilitated; finally, noise and artifacts in the reconstructed image features can be further restrained through combination of the image features, and high-quality image reconstruction is achieved.

Description

A kind of magnetic resonance fast imaging method and system

Technical field

The present invention relates to mr imaging technique field, particularly a kind of magnetic resonance fast imaging method and system.

Background technology

In recent years, based on the MR imaging method of compressed sensing technology be the hot issue in FastMRI field.Compressed sensing technology mainly utilizes the openness of signal to rebuild to realize lack sampling.

The physical mechanism of magnetic resonance imaging can be expressed as:

D=F ρ+n (formula 1)

Wherein, d represents the MR data gathered on magnetic resonance device, and F represents Fourier-encoded matrix, and ρ is magnetic resonance image (MRI) to be asked, and n is assumed to white complex gaussian noise usually.Compressive sensing theory is thought, if signal is sparse in a certain transform domain, so by a kind of and the noncoherent sampling pattern of this transform domain, just can reconstruct real signal accurately from a small amount of sampled data.Further, signal is more sparse, and the sampled data of needs is fewer.MR imaging method based on compressed sensing technology can be expressed as:

$\widehat{\mathrm{\ρ}}=\underset{\mathrm{\ρ}}{\arg \min }{\left|\right|y-F_u\mathrm{\ρ}\left|\right|}_2^2+\mathrm{\λ}{\left|\right|{\mathrm{\Ψ}}_{\mathrm{\ρ}}\left|\right|}_1$ (formula 2)

Wherein, represent the magnetic resonance imaging based on compressed sensing reconstruction, ρ represents magnetic resonance image (MRI) to be asked, and y is the lack sampling data of k-space, F _ufor Fourier's encoder matrix of lack sampling, Ψ is sparse transformation matrix (such as wavelet transformation), and λ is regularization coefficient, || || ₁represent and ask L1 norm, || || ₂represent and ask L2 norm.

But medical magnetic resonance image is often just highly compressible, and also non-critical is sparse.This openness deficiency and sampling in noise can cause rebuild image in produce serious artifact, reduce the image quality of image, thus limit compression know the practical application of sense technology in accelerating magnetic resonance imaging.

Summary of the invention

Based on the mr imaging technique of compressed sensing, not enough and more serious image artifacts can be produced when having and make an uproar at image sparse.For foregoing problems, the present invention utilizes a series of convolution kernel function to extract the feature of image, and these characteristics of image need more sparse than magnetic resonance image (MRI) or have higher signal to noise ratio (S/N ratio).Concrete, the method first utilizes these characteristics of image of compressed sensing reconstruction, then these is rebuild the characteristics of image merging obtained, to generate the image of reconstruction.

For achieving the above object, the present invention proposes a kind of magnetic resonance fast imaging method, comprising: the MR data obtaining lack sampling; According to the MR data of described lack sampling, utilize multiple convolution kernel function, calculate the K space data corresponding to magnetic resonance image (MRI) feature multiple to be asked; According to the K space data corresponding to described multiple magnetic resonance image (MRI) feature to be asked, utilize compressed sensing reconstruction magnetic resonance image (MRI) feature, obtain the characteristics of image rebuild; The characteristics of image of described reconstruction is merged, generates the magnetic resonance image (MRI) of rebuilding.

For achieving the above object, the invention allows for a kind of magnetic resonance fast imaging system, comprising: MR data acquisition module, for obtaining the MR data of lack sampling; K space data computing module, for the MR data according to described lack sampling, utilizes multiple convolution kernel function, calculates the K space data that magnetic resonance image (MRI) feature multiple to be asked is corresponding; Characteristics of image rebuilds module, for the K space data corresponding to described multiple magnetic resonance image (MRI) feature to be asked, utilizes compressed sensing reconstruction magnetic resonance image (MRI) feature, obtains the characteristics of image rebuild; Rebuilding Computer image genration module, for being merged by the characteristics of image of described reconstruction, generating the magnetic resonance image (MRI) of rebuilding.

First the magnetic resonance fast imaging method that the present invention proposes and system utilize the characteristics of image corresponding to the multiple convolution kernel function of compressed sensing reconstruction, these characteristics of image or more sparse, or there is higher signal to noise ratio (S/N ratio), be thus more conducive to use compressed sensing technology to rebuild; Finally, the merging of characteristics of image can suppress noise in the characteristics of image rebuild and artifact further, and then realizes high-quality image reconstruction.

Accompanying drawing explanation

Accompanying drawing described herein is used to provide a further understanding of the present invention, forms a application's part, does not form limitation of the invention.In the accompanying drawings:

Fig. 1 is the magnetic resonance fast imaging method process flow diagram of one embodiment of the invention.

Fig. 2 is the structural representation of the magnetic resonance fast imaging system of one embodiment of the invention.

Embodiment

Below coordinating preferred embodiment graphic and of the present invention, setting forth the technological means that the present invention takes for reaching predetermined goal of the invention further.

The present invention proposes a kind of magnetic resonance fast imaging method and system, compare the existing imaging effect utilizing the mr imaging technique of the compressed sensing of standard, first the present invention utilizes the characteristics of image corresponding to the multiple convolution kernel function of compressed sensing reconstruction; Again the characteristics of image of reconstruction is merged, obtain the magnetic resonance image (MRI) of rebuilding, and then realize high-quality image reconstruction.

Fig. 1 is the magnetic resonance fast imaging method process flow diagram of one embodiment of the invention.As shown in Figure 1, the method comprises:

Step 1, obtains the MR data of lack sampling;

Step 2, according to the MR data of lack sampling, utilizes multiple convolution kernel function, calculates the K space data corresponding to magnetic resonance image (MRI) feature multiple to be asked;

Step 3, according to the K space data corresponding to magnetic resonance image (MRI) feature multiple to be asked, utilizes compressed sensing reconstruction magnetic resonance image (MRI) feature, obtains the characteristics of image rebuild;

Step 4, merges the characteristics of image of reconstruction, generates the magnetic resonance image (MRI) of rebuilding.

Further, in step 2, the K space data corresponding to magnetic resonance image (MRI) feature multiple to be asked is:

y ₁＝F{K ₁}⊙y

y ₂＝F{K ₂}⊙y

.

.

.

y _p＝F{K _p}⊙y

Wherein, y ₁, y ₂..., y _prepresent the K space data corresponding to magnetic resonance image (MRI) feature multiple to be asked, K ₁, K ₂..., K _prepresent multiple convolution kernel function, ⊙ is point multiplication operation symbol, and F{} represents Fourier transform, and y is the MR data of lack sampling, and p is the number of convolution kernel function.

Wherein, convolution kernel function can be edge extracting kernel function or gaussian kernel function.The characteristics of image utilizing edge extracting kernel function to rebuild can be more sparse, and the characteristics of image utilizing gaussian kernel function to rebuild has higher signal to noise ratio (S/N ratio).Therefore, the method for the direct reconstruction magnetic resonance image (MRI) of background technology of comparing formula 2, the present invention utilizes compressed sensing technology can reconstruct these characteristics of image more accurately.

In step 3, based on compressed sensing reconstruction magnetic resonance image (MRI) character representation be:

$\begin{array}{c}{\widehat{\mathrm{\ρ}}}_1=\underset{{\mathrm{\ρ}}_1}{\arg \min }{\left|\right|y_1-F_u{\mathrm{\ρ}}_1\left|\right|}_2^2+{\mathrm{\λ}}_1{\left|\right|{\mathrm{\Ψ\ρ}}_1\left|\right|}_1\\ {\widehat{\mathrm{\ρ}}}_2=\underset{{\mathrm{\ρ}}_2}{\arg \min }{\left|\right|y_2-F_u{\mathrm{\ρ}}_2\left|\right|}_2^2+{\mathrm{\λ}}_2{\left|\right|{\mathrm{\Ψ\ρ}}_1\left|\right|}_1\\ .\\ .\\ .\\ {\widehat{\mathrm{\ρ}}}_p\underset{{\mathrm{\ρ}}_p}{\arg \min }{\left|\right|y_p-F_u{\mathrm{\ρ}}_p\left|\right|}_2^2+{\mathrm{\λ}}_p{\left|\right|{\mathrm{\Ψ\ρ}}_p\left|\right|}_1\end{array}$

Wherein, represent the characteristics of image rebuild, ρ ₁, ρ ₂..., ρ _prepresent magnetic resonance image (MRI) feature to be asked, F _ufor Fourier's encoder matrix of lack sampling, λ ₁, λ ₂..., λ _pfor regularization coefficient, Ψ represents sparse transformation matrix, || || ₁represent and ask L1 norm, || || ₂represent and ask L2 norm;

Wherein, the relation of magnetic resonance image (MRI) feature and magnetic resonance image (MRI) is expressed as:

ρ ₁＝K ₁*ρ

ρ ₂＝K ₂*ρ

.

.

.

ρ _p＝K _p*ρ

Wherein, * is convolution algorithm symbol, and ρ is magnetic resonance image (MRI) to be asked.

In step 4, mainly the reconstruction characteristics of image in step 3 is merged, generate the magnetic resonance image (MRI) of rebuilding.Wherein, the merging method utilized in the present embodiment is the method utilizing regularization constraint, and namely complete reconstruction image obtains by with under type:

$\begin{array}{c}\widehat{\mathrm{\ρ}}=\underset{\mathrm{\ρ}}{\arg \min }{\left|\right|y-F_u\mathrm{\ρ}\left|\right|}_2^2+{\mathrm{\γ}}_{1}R\left(\mathrm{\ρ}\right)+\\ {\mathrm{\γ}}_2({\mathrm{\α}}_1{\left|\right|K_1*\mathrm{\ρ}-{\widehat{\mathrm{\ρ}}}_1\left|\right|}_2^2+{\mathrm{\α}}_2{\left|\right|K_2*\mathrm{\ρ}-{\widehat{\mathrm{\ρ}}}_2\left|\right|}_2^2+...+{\mathrm{\α}}_p{\left|\right|K_p*\mathrm{\ρ}-{\widehat{\mathrm{\ρ}}}_p\left|\right|}_2^2)\end{array}$

Wherein, for the magnetic resonance image (MRI) of rebuilding, function R () is for retraining the openness of magnetic resonance image (MRI), γ ₁for controlling the openness regularization parameter of magnetic resonance image (MRI) to be asked, γ ₂for controlling the regularization parameter of similarity between magnetic resonance image (MRI) feature to be asked and the characteristics of image of reconstruction, α ₁, α ₂..., α _prepresent the weight of each magnetic resonance image (MRI) feature.

Function R () for retraining the openness of magnetic resonance image (MRI), wherein, R (ρ)=|| Ψ ρ || ₁.

In other embodiments, the merging method utilized in step 4 is not limited in this, just one of the optimized method provided in above-described embodiment.

Just can obtain rebuilding image by above-mentioned steps 1-4, the quality of this reconstruction image will be much better than the image directly utilizing compressed sensing technology (formula 2) to obtain.

Based on same inventive concept, additionally provide a kind of magnetic resonance fast imaging system in the embodiment of the present invention, as the following examples.The principle of dealing with problems due to this system is similar to said method, and therefore the enforcement of this system see the enforcement of said method, can repeat part and repeat no more.Following used, term " unit " or " module " can realize the software of predetermined function and/or the combination of hardware.Although the device described by following examples preferably realizes with software, hardware, or the realization of the combination of software and hardware also may and conceived.

Fig. 2 is the structural representation of the magnetic resonance fast imaging system of one embodiment of the invention.As shown in Figure 2, this system comprises:

MR data acquisition module 1, for obtaining the MR data of lack sampling;

K space data computing module 2, for the MR data according to lack sampling, utilizes multiple convolution kernel function, calculates the K space data corresponding to magnetic resonance image (MRI) feature multiple to be asked;

Characteristics of image rebuilds module 3, for the K space data corresponding to magnetic resonance image (MRI) feature multiple to be asked, utilizes compressed sensing reconstruction magnetic resonance image (MRI) feature, obtains the characteristics of image rebuild;

Rebuilding Computer image genration module 4, for being merged by the characteristics of image of reconstruction, generating the magnetic resonance image (MRI) of rebuilding.

In K space data computing module 2, the K space data corresponding to magnetic resonance image (MRI) feature multiple to be asked is:

y ₁＝F{K ₁}⊙y

y ₂＝F{K ₂}⊙y

.

.

.

y _p＝F{K _p}⊙y

Wherein, y ₁, y ₂..., y _prepresent the K space data corresponding to magnetic resonance image (MRI) feature multiple to be asked, K ₁, K ₂..., K _prepresent multiple convolution kernel function, ⊙ is point multiplication operation symbol, and F{} represents Fourier transform, and y is the MR data of lack sampling, and p is the number of convolution kernel function.

Characteristics of image is rebuild in module 3, based on compressed sensing reconstruction magnetic resonance image (MRI) character representation is:

$\begin{array}{c}{\widehat{\mathrm{\ρ}}}_1=\underset{{\mathrm{\ρ}}_1}{\arg \min }{\left|\right|y_1-F_u{\mathrm{\ρ}}_1\left|\right|}_2^2+{\mathrm{\λ}}_1{\left|\right|{\mathrm{\Ψ\ρ}}_1\left|\right|}_1\\ {\widehat{\mathrm{\ρ}}}_2=\underset{{\mathrm{\ρ}}_2}{\arg \min }{\left|\right|y_2-F_u{\mathrm{\ρ}}_2\left|\right|}_2^2+{\mathrm{\λ}}_2{\left|\right|{\mathrm{\Ψ\ρ}}_1\left|\right|}_1\\ .\\ .\\ .\\ {\widehat{\mathrm{\ρ}}}_p\underset{{\mathrm{\ρ}}_p}{\arg \min }{\left|\right|y_p-F_u{\mathrm{\ρ}}_p\left|\right|}_2^2+{\mathrm{\λ}}_p{\left|\right|{\mathrm{\Ψ\ρ}}_p\left|\right|}_1\end{array}$

Wherein, represent the characteristics of image rebuild, ρ ₁, ρ ₂..., ρ _prepresent magnetic resonance image (MRI) feature to be asked, F _ufor Fourier's encoder matrix of lack sampling, λ ₁, λ ₂..., λ _pfor regularization coefficient, Ψ represents sparse transformation matrix, || || ₁represent and ask L1 norm, || || ₂represent and ask L2 norm;

Wherein, the relation of magnetic resonance image (MRI) feature and magnetic resonance image (MRI) is expressed as:

ρ ₁＝K ₁*ρ

ρ ₂＝K ₂*ρ

.

.

.

ρ _p＝K _p*ρ

Wherein, * is convolution algorithm symbol, and ρ is magnetic resonance image (MRI) to be asked.

Rebuild in Computer image genration module 4, complete reconstruction image obtains by with under type:

$\begin{array}{c}\widehat{\mathrm{\ρ}}=\underset{\mathrm{\ρ}}{\arg \min }{\left|\right|y-F_u\mathrm{\ρ}\left|\right|}_2^2+{\mathrm{\γ}}_{1}R\left(\mathrm{\ρ}\right)+\\ {\mathrm{\γ}}_2({\mathrm{\α}}_1{\left|\right|K_1*\mathrm{\ρ}-{\widehat{\mathrm{\ρ}}}_1\left|\right|}_2^2+{\mathrm{\α}}_2{\left|\right|K_2*\mathrm{\ρ}-{\widehat{\mathrm{\ρ}}}_2\left|\right|}_2^2+...+{\mathrm{\α}}_p{\left|\right|K_p*\mathrm{\ρ}-{\widehat{\mathrm{\ρ}}}_p\left|\right|}_2^2)\end{array}$

Wherein, for the magnetic resonance image (MRI) of rebuilding, function R () is for retraining the openness of magnetic resonance image (MRI), γ ₁for controlling the openness regularization parameter of magnetic resonance image (MRI) to be asked, γ ₂for controlling the regularization parameter of similarity between magnetic resonance image (MRI) feature to be asked and the characteristics of image of reconstruction, α ₁, α ₂..., α _prepresent the weight of each magnetic resonance image (MRI) feature respectively.

Function R () for retraining the openness of magnetic resonance image (MRI), wherein, R (ρ)=|| Ψ ρ || ₁.

First the magnetic resonance fast imaging method that the present invention proposes and system utilize the characteristics of image corresponding to the multiple convolution kernel function of compressed sensing reconstruction, these characteristics of image or more sparse, or there is higher signal to noise ratio (S/N ratio), be thus more conducive to use compressed sensing technology to rebuild; Finally, the merging of characteristics of image can suppress noise in the characteristics of image rebuild and artifact further, and then realizes high-quality image reconstruction.

Above-described specific embodiment; object of the present invention, technical scheme and beneficial effect are further described; be understood that; the foregoing is only specific embodiments of the invention; the protection domain be not intended to limit the present invention; within the spirit and principles in the present invention all, any amendment made, equivalent replacement, improvement etc., all should be included within protection scope of the present invention.

Claims (12)

1. a magnetic resonance fast imaging method, is characterized in that, comprising:

Obtain the MR data of lack sampling;

According to the MR data of described lack sampling, utilize multiple convolution kernel function, calculate the K space data corresponding to magnetic resonance image (MRI) feature multiple to be asked;

According to the K space data corresponding to described multiple magnetic resonance image (MRI) feature to be asked, utilize compressed sensing reconstruction magnetic resonance image (MRI) feature, obtain the characteristics of image rebuild;

The characteristics of image of described reconstruction is merged, generates the magnetic resonance image (MRI) of rebuilding.

2. magnetic resonance fast imaging method as claimed in claim 1, is characterized in that, according to the MR data of described lack sampling, utilize multiple convolution kernel function, calculate the K space data corresponding to magnetic resonance image (MRI) feature multiple to be asked, comprising:

K space data corresponding to magnetic resonance image (MRI) feature multiple to be asked is:

y ₁＝F{K ₁}⊙y

y ₂＝F{K ₂}⊙y

.

.

.

y _p＝F{K _p}⊙y

Wherein, y ₁, y ₂..., y _prepresent the K space data corresponding to magnetic resonance image (MRI) feature multiple to be asked, K ₁, K ₂..., K _prepresent multiple convolution kernel function, ⊙ is point multiplication operation symbol, and F{} represents Fourier transform, and y is the MR data of lack sampling, and p is the number of convolution kernel function.

3. magnetic resonance fast imaging method as claimed in claim 2, it is characterized in that, described convolution kernel function is edge extracting kernel function or gaussian kernel function.

4. magnetic resonance fast imaging method as claimed in claim 2, is characterized in that, according to the K space data corresponding to described multiple magnetic resonance image (MRI) feature to be asked, utilize compressed sensing reconstruction magnetic resonance image (MRI) feature, obtains the characteristics of image rebuild, comprising:

Based on compressed sensing reconstruction magnetic resonance image (MRI) character representation be:

${\widehat{\mathrm{\ρ}}}_1=\underset{{\mathrm{\ρ}}_1}{\arg \min }{\left|\right|y_1-F_u{\mathrm{\ρ}}_1\left|\right|}_2^2+{\mathrm{\λ}}_1{\left|\right|\mathrm{\Ψ}{\mathrm{\ρ}}_1\left|\right|}_1$

${\widehat{\mathrm{\ρ}}}_2=\underset{{\mathrm{\ρ}}_2}{\arg \min }{\left|\right|y_2-F_u{\mathrm{\ρ}}_2\left|\right|}_2^2+{\mathrm{\λ}}_2{\left|\right|\mathrm{\Ψ}{\mathrm{\ρ}}_2\left|\right|}_1$

.

.

.

${\widehat{\mathrm{\ρ}}}_p=\underset{{\mathrm{\ρ}}_p}{\arg \min }{\left|\right|y_p-F_u{\mathrm{\ρ}}_p\left|\right|}_2^2+{\mathrm{\λ}}_p{\left|\right|\mathrm{\Ψ}{\mathrm{\ρ}}_p\left|\right|}_1$

Wherein, represent the characteristics of image rebuild, ρ ₁, ρ ₂..., ρ _prepresent magnetic resonance image (MRI) feature to be asked, F _ufor Fourier's encoder matrix of lack sampling, λ ₁, λ ₂..., λ _pfor regularization coefficient, Ψ represents sparse transformation matrix, || || ₁represent and ask L1 norm, || || ₂represent and ask L2 norm;

Wherein, the relation of magnetic resonance image (MRI) feature and magnetic resonance image (MRI) is expressed as:

ρ ₁＝K ₁*ρ

ρ ₂＝K ₂*ρ

.

.

.

ρ _p＝K _p*ρ

Wherein, * is convolution algorithm symbol, and ρ is magnetic resonance image (MRI) to be asked.

5. magnetic resonance fast imaging method as claimed in claim 4, is characterized in that, merged by the characteristics of image of described reconstruction, generate complete reconstruction image, comprising:

Complete reconstruction image obtains by with under type:

$\begin{array}{c}\widehat{\mathrm{\ρ}}=\underset{\mathrm{\ρ}}{\arg \min }{\left|\right|y-F_u\mathrm{\ρ}\left|\right|}_2^2+{\mathrm{\γ}}_{1}R\left(\mathrm{\ρ}\right)+\\ {\mathrm{\γ}}_2({\mathrm{\α}}_1{\left|\right|K_1*\mathrm{\ρ}-{\widehat{\mathrm{\ρ}}}_1\left|\right|}_2^2+{\mathrm{\α}}_2{\left|\right|K_2*\mathrm{\ρ}-{\widehat{\mathrm{\ρ}}}_2\left|\right|}_2^2+...+{\mathrm{\α}}_p{\left|\right|K_p*\mathrm{\ρ}-{\widehat{\mathrm{\ρ}}}_p\left|\right|}_2^2)\end{array}$

Wherein, for the magnetic resonance image (MRI) of rebuilding, function R () is for retraining the openness of magnetic resonance image (MRI), γ ₁for controlling the openness regularization parameter of magnetic resonance image (MRI) to be asked, γ ₂for controlling the regularization parameter of similarity between magnetic resonance image (MRI) feature to be asked and the characteristics of image of reconstruction, α ₁, α ₂..., α _prepresent the weight of magnetic resonance image (MRI) feature described in each respectively.

6. magnetic resonance fast imaging method as claimed in claim 5, is characterized in that, described function R () for retraining the openness of magnetic resonance image (MRI), R (ρ)=|| Ψ ρ || ₁.

7. a magnetic resonance fast imaging system, is characterized in that, comprising:

MR data acquisition module, for obtaining the MR data of lack sampling;

K space data computing module, for the MR data according to described lack sampling, utilizes multiple convolution kernel function, calculates the K space data that magnetic resonance image (MRI) feature multiple to be asked is corresponding;

Characteristics of image rebuilds module, for the K space data corresponding to described multiple magnetic resonance image (MRI) feature to be asked, utilizes compressed sensing reconstruction magnetic resonance image (MRI) feature, obtains the characteristics of image rebuild;

Rebuilding Computer image genration module, for being merged by the characteristics of image of described reconstruction, generating the magnetic resonance image (MRI) of rebuilding.

8. magnetic resonance fast imaging system as claimed in claim 7, is characterized in that, described in magnetic resonance image (MRI) feature calculation module to be asked, the K space data corresponding to magnetic resonance image (MRI) feature multiple to be asked is:

y ₁＝F{K ₁}⊙y

y ₂＝F{K ₂}⊙y

.

.

.

y _p＝F{K _p}⊙y

Wherein, y ₁, y ₂..., y _prepresent the K space data corresponding to magnetic resonance image (MRI) feature multiple to be asked, K ₁, K ₂..., K _prepresent multiple convolution kernel function, ⊙ is point multiplication operation symbol, and F{} represents Fourier transform, and y is the MR data of lack sampling, and p is the number of convolution kernel function.

9. magnetic resonance fast imaging system as claimed in claim 8, it is characterized in that, described convolution kernel function is edge extracting kernel function or gaussian kernel function.

10. magnetic resonance fast imaging system as claimed in claim 8, is characterized in that, described characteristics of image is rebuild in module, based on compressed sensing reconstruction magnetic resonance image (MRI) character representation is:

${\widehat{\mathrm{\ρ}}}_1=\underset{{\mathrm{\ρ}}_1}{\arg \min }{\left|\right|y_1-F_u{\mathrm{\ρ}}_1\left|\right|}_2^2+{\mathrm{\λ}}_1{\left|\right|\mathrm{\Ψ}{\mathrm{\ρ}}_1\left|\right|}_1$

${\widehat{\mathrm{\ρ}}}_2=\underset{{\mathrm{\ρ}}_2}{\arg \min }{\left|\right|y_2-F_u{\mathrm{\ρ}}_2\left|\right|}_2^2+{\mathrm{\λ}}_2{\left|\right|\mathrm{\Ψ}{\mathrm{\ρ}}_2\left|\right|}_1$

.

.

.

${\widehat{\mathrm{\ρ}}}_p=\underset{{\mathrm{\ρ}}_p}{\arg \min }{\left|\right|y_p-F_u{\mathrm{\ρ}}_p\left|\right|}_2^2+{\mathrm{\λ}}_p{\left|\right|\mathrm{\Ψ}{\mathrm{\ρ}}_p\left|\right|}_1$

Wherein, represent the characteristics of image rebuild, ρ ₁, ρ ₂..., ρ _prepresent magnetic resonance image (MRI) feature to be asked, F _ufor Fourier's encoder matrix of lack sampling, λ ₁, λ ₂..., λ _pfor regularization coefficient, Ψ represents sparse transformation matrix, || || ₁represent and ask L1 norm, || || ₂represent and ask L2 norm;

Wherein, the relation of magnetic resonance image (MRI) feature and magnetic resonance image (MRI) is expressed as:

ρ ₁＝K ₁*ρ

ρ ₂＝K ₂*ρ

.

.

.

ρ _p＝K _p*ρ

Wherein, * is convolution algorithm symbol, and ρ is magnetic resonance image (MRI) to be asked.

11. magnetic resonance fast imaging systems as claimed in claim 10, is characterized in that, in described reconstruction Computer image genration module, complete reconstruction image obtains by with under type:

$\begin{array}{c}\widehat{\mathrm{\ρ}}=\underset{\mathrm{\ρ}}{\arg \min }{\left|\right|y-F_u\mathrm{\ρ}\left|\right|}_2^2+{\mathrm{\γ}}_{1}R\left(\mathrm{\ρ}\right)+\\ {\mathrm{\γ}}_2({\mathrm{\α}}_1{\left|\right|K_1*\mathrm{\ρ}-{\widehat{\mathrm{\ρ}}}_1\left|\right|}_2^2+{\mathrm{\α}}_2{\left|\right|K_2*\mathrm{\ρ}-{\widehat{\mathrm{\ρ}}}_2\left|\right|}_2^2+...+{\mathrm{\α}}_p{\left|\right|K_p*\mathrm{\ρ}-{\widehat{\mathrm{\ρ}}}_p\left|\right|}_2^2)\end{array}$

Wherein, for the magnetic resonance image (MRI) of rebuilding, function R () is for retraining the openness of magnetic resonance image (MRI), γ ₁for controlling the openness regularization parameter of magnetic resonance image (MRI) to be asked, γ ₂for controlling the regularization parameter of similarity between magnetic resonance image (MRI) feature to be asked and the characteristics of image of reconstruction, α ₁, α ₂..., α _prepresent the weight of magnetic resonance image (MRI) feature described in each respectively.

12. magnetic resonance fast imaging systems as claimed in claim 11, is characterized in that, described function R () for retraining the openness of magnetic resonance image (MRI), wherein, R (ρ)=|| Ψ ρ || ₁.