CN108447102A - A kind of dynamic magnetic resonance imaging method of low-rank and sparse matrix decomposition - Google Patents
A kind of dynamic magnetic resonance imaging method of low-rank and sparse matrix decomposition Download PDFInfo
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- CN108447102A CN108447102A CN201810141334.9A CN201810141334A CN108447102A CN 108447102 A CN108447102 A CN 108447102A CN 201810141334 A CN201810141334 A CN 201810141334A CN 108447102 A CN108447102 A CN 108447102A
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- 238000000034 method Methods 0.000 title claims abstract description 42
- 239000011159 matrix material Substances 0.000 title claims abstract description 36
- 238000002595 magnetic resonance imaging Methods 0.000 title claims abstract description 33
- 238000000354 decomposition reaction Methods 0.000 title claims abstract description 31
- 238000005070 sampling Methods 0.000 claims abstract description 16
- 230000000694 effects Effects 0.000 claims description 8
- 239000004615 ingredient Substances 0.000 claims description 7
- 238000005457 optimization Methods 0.000 claims description 7
- 238000004088 simulation Methods 0.000 claims description 6
- 230000009466 transformation Effects 0.000 claims description 6
- 230000008602 contraction Effects 0.000 claims description 3
- 230000000452 restraining effect Effects 0.000 claims description 3
- 238000009795 derivation Methods 0.000 claims description 2
- 241000208340 Araliaceae Species 0.000 claims 1
- 235000005035 Panax pseudoginseng ssp. pseudoginseng Nutrition 0.000 claims 1
- 235000003140 Panax quinquefolius Nutrition 0.000 claims 1
- 235000008434 ginseng Nutrition 0.000 claims 1
- 238000003384 imaging method Methods 0.000 description 12
- 230000001133 acceleration Effects 0.000 description 3
- 230000000747 cardiac effect Effects 0.000 description 2
- 230000002708 enhancing effect Effects 0.000 description 2
- 238000002474 experimental method Methods 0.000 description 2
- 238000012986 modification Methods 0.000 description 2
- 230000004048 modification Effects 0.000 description 2
- 230000002107 myocardial effect Effects 0.000 description 2
- 230000010412 perfusion Effects 0.000 description 2
- 230000035945 sensitivity Effects 0.000 description 2
- 241000282414 Homo sapiens Species 0.000 description 1
- 230000003044 adaptive effect Effects 0.000 description 1
- 238000011161 development Methods 0.000 description 1
- 238000005259 measurement Methods 0.000 description 1
- 230000003068 static effect Effects 0.000 description 1
- 238000012800 visualization Methods 0.000 description 1
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- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T11/00—2D [Two Dimensional] image generation
- G06T11/003—Reconstruction from projections, e.g. tomography
- G06T11/005—Specific pre-processing for tomographic reconstruction, e.g. calibration, source positioning, rebinning, scatter correction, retrospective gating
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
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- G06T5/00—Image enhancement or restoration
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- G06V—IMAGE OR VIDEO RECOGNITION OR UNDERSTANDING
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Abstract
The invention discloses a kind of dynamic magnetic resonance imaging methods of low-rank and sparse matrix decomposition, are related to magnetic resonance imaging arts.Low-rank and sparse model are introduced dynamic magnetic resonance imaging by the present invention；It enables low-rank be analyzed by non-correlation requirement with sparse decomposition, and completes to improve；Improved low-rank and sparse decomposition are applied to the image reconstruction of lack sampling dynamic magnetic resonance imaging.It can ensure the quality and image taking speed of image reconstruction using the present invention；In the case of identical undersampling rate, image reconstruction quality is improved.
Description
Technical field
The present invention relates to imaging techniques, more particularly to a kind of method of dynamic magnetic resonance imaging.
Background technology
With the development of mr imaging technique, the speed of dynamic magnetic resonance imaging will affect mr imaging technique
Practical application.Compressed sensing technology and parallel imaging technique have been applied to dynamic magnetic resonance imaging.Wherein, compressed sensing is imaged
Technology is the sparsity using magnetic resonance image, and by the K space data reconstruction image of lack sampling, parallel imaging technique is with mostly logical
Road phased-array coil receives magnetic resonance signal simultaneously, and the spatial sensitivities difference of receiving coil is recycled to carry out space encoder information simultaneously
Reconstruction image.
However, for compressed sensing imaging technique, magnetic resonance image is often only highly compressible, and not tight
Lattice are sparse, and this insufficient situation of sparsity will cause to generate discontinuous artefact in reconstruction image, to limit significantly
The application of compressed sensing imaging technique.
For parallel imaging technique, with the increase of receiving coil number, the susceptibility field of each coil is by height phase
It closes.This characteristic will amplify the noise in sampled data, and limitation parallel imaging technique is in practical magnetic resonance imaging application
Acceleration effect.
Invention content
The technical problem to be solved by the present invention is to：
A kind of dynamic magnetic resonance fast imaging side that image taking speed can be improved while ensureing reconstructed image quality is provided
Method.
The present invention uses following technical scheme to solve above-mentioned technical problem：
A kind of dynamic magnetic resonance imaging method of low-rank and sparse matrix decomposition, includes the following steps：
Step 1 introduces low-rank and sparse model, and the time series of image is converted into a matrix M；Then pass through solution
Convex optimization problem completes low-rank and sparse decomposition, and matrix M is resolved into the superposition of a low-rank matrix L and sparse matrix S, wherein
L corresponds to background component, and S corresponds to dynamic element；
The convex optimization problem is that is, min | | L | |*+λ||S||1S.t.M=L+S, wherein | | L | |*Be nuclear norm either
Matrix L singular value and, | | S | |1It is l1Norm either in S element absolute value and, λ is adjusting parameter；
Step 2, the improvement that completion low-rank and sparse decomposition after analysis are required by non-correlation, improvement type are：
min||L||*+λ||TS||1S.tE (L+S)=d
Wherein T is the sparse transformation of S, and E is coding or acquisition operations, and d is lack sampling k-t data；
Step 3, the image reconstruction that improved low-rank and sparse decomposition are applied to lack sampling dynamic magnetic resonance imaging.
Further, non-correlation described in step 2 includes：The spaces k-t and low-rank ingredient L describe irrelevant between space
Property, the spaces k-t and sparse ingredient S describe the non-correlation between non-correlation and the spaces L and the spaces S between space.
Further, the image reconstruction of step 3 is stated as follows：
It is solved using alternating direction method, the graceful disintegrating method of Donald Bragg or other convex optimization methods, λLAnd λSRepresent canonical
Change parameter.
Further, in the step 3, derivation algorithm uses the iteration soft-threshold algorithm based on singular value, specific steps
For：
DefinitionFor soft-threshold or contraction operator；Wherein x is complicated quantity, threshold value λ
It is actual value, singular value threshold operation operator is SVTλ(M)=U Λλ(∑)VH, wherein M=U ∑s VHIt is any singular value point of M
Solution；Iterations are set to 0, i.e. k=0 first, to realize initialization procedure；It, will not after completing initialization procedure
It is disconnected to be iterated operation, i.e.,：
When not restraining,
3、Mk=Lk+Sk-EH(E(Lk+Sk)-d)
Wherein, the associated change of algorithm iteration to solving result is less than 10-5, it is, | | Lk+Sk-(Lk-1+Sk-1)||2≤
10-5||Lk-1+Sk-1||2。
Further, is rebuild by effect and is estimated with root-mean-square error for simulation accelerated data set in step 3, for
The data set actually accelerated, the qualitative estimation in terms of remaining aliasing artefact and time fidelity.
The present invention has the following technical effects using above technical scheme is compared with the prior art：
Low-rank and sparse matrix decomposition are introduced into the fast imaging of dynamic magnetic resonance, after requiring analysis by non-correlation
The improvement of low-rank and sparse decomposition is completed, and improved low-rank and sparse decomposition are applied to lack sampling dynamic magnetic resonance imaging
In image reconstruction, the feasibility of the dynamic magnetic resonance imaging of low-rank and sparse decomposition is obtained, and tested in relevant medical experiment
With compare its rapidity.
Description of the drawings
Fig. 1 is the flow chart of L+S algorithm for reconstructing；
Fig. 2 is the root-mean-square error/structural similarity index for simulating lack sampling cardiac perfusion dataset；
Fig. 3 is myocardial wall enhancing stage image comparison.
Specific implementation mode
Technical scheme of the present invention is described in further detail below in conjunction with the accompanying drawings：
Those skilled in the art of the present technique are it is understood that unless otherwise defined, all terms used herein (including skill
Art term and scientific terminology) there is meaning identical with the general understanding of the those of ordinary skill in fields of the present invention.Also
It should be understood that those terms such as defined in the general dictionary should be understood that with in the context of the prior art
The consistent meaning of meaning, and unless defined as here, will not be explained with the meaning of idealization or too formal.
As shown in Figure 1, embodiment describes a kind of dynamic magnetic resonance imaging method of low-rank and sparse matrix decomposition, including
Following steps：
Step 1 is filled in dynamic magnetic resonance imaging according to compressed sensing and low-rank matrix and applies, introduce low-rank with it is sparse
Model；
Step 2, the improvement that completion low-rank and sparse decomposition after analysis are required by non-correlation；
Step 3, the image reconstruction that improved low-rank and sparse decomposition are applied to lack sampling dynamic magnetic resonance imaging.
Low-rank is extended to obtain with sparse model by compressed sensing thought.The application of compressed sensing improves Magnetic resonance imaging
Image taking speed and efficiency, it require image sparsity and acquisition space and describe space between non-correlation, in low-rank
Under the conditions of non-correlation, the compressed sensing idea of signal/image vector extend to can recover it is loss or damage
The matrix of matrix entries, thus low-rank matrix filling are applied to dynamic magnetic resonance imaging.The knot of compressed sensing and low-rank matrix filling
Conjunction improves image taking speed, and low-rank is very suitable for dynamic imaging with sparse model, therefore proposes the low-rank of dynamic magnetic resonance imaging
With sparse description.
In the present embodiment, low-rank and sparse model are that a matrix M is resolved into a low-rank matrix L and sparse matrix S
Superposition.Low-rank is completed with sparse decomposition by solving convex optimization problem, that is, min | | L | |*+λ||S||1S.t.M=L+S is wherein
||L||*Be nuclear norm either matrix L singular value and, | | S | |1It is l1Norm either in S element absolute value and, λ is adjustment
Parameter.If L and S are fully uncorrelated, this method can be detached uniquely.
In the present embodiment, the low-rank of dynamic magnetic resonance imaging is analogy video sequence with sparse description, dynamic magnetic resonance at
As constitutionally indicates the superposition of a background component and dynamic element.Background component corresponds to the altitude-related information between frame,
It slowly changes with the time, and dynamic element captures the new method introduced in each frame, it changes rapidly with the time, and
It is sparse.L+S decomposition is applied in Dynamic MRI, the time series of image is converted into a matrix M, wherein each row are
One time frame.The application that L+S is decomposed will generate a matrix L and represent background component, and matrix S is represented corresponding to the new of row to row
Method.
In one embodiment, non-correlation is the low-rank and in sparse reconstruction three of lack sampling dynamic magnetic resonance imaging data
Non- phase between the different classes of non-correlation of kind, including the spaces k-t and low-rank ingredient (L) and sparse ingredient (S) description space
Non-correlation between the spaces Guan Xing and L and the spaces S, the non-correlation of first two type need to remove aliasing artefact, finally
One is to need separating background and dynamic element.The k-t lack sampling modes of standard are used for compressed sensing dynamic magnetic resonance imaging,
Include the undersampled image of randomly selected different variable density k-space at every point of time, it can be non-for meeting first two
Correlation requirement.The third non-correlation is not constrained by sample mode, only depends on the sparse transformation in rebuilding.
In one embodiment, in above-mentioned steps three lack sampling dynamic magnetic resonance imaging low-rank and sparse reconstruction specific mistake
Cheng Wei：
Low-rank and sparse decomposition are improved, improvement type is：
min||L||*+λ||TS||1S.tE (L+S)=d
Wherein T is the sparse transformation of S, and E is coding or acquisition operations, and d is lack sampling k-t data.
In the present embodiment, equation uses regularization rather than hard constraints, states as follows：
It can be solved by a common method, for example, using alternating direction method, the graceful disintegrating method of Donald Bragg or its
His convex optimization method.Parameter lambdaLAnd λSPass through nuclear norm and l1Norm and weighed data consistency and solving complexity.
Specifically, in the present invention, being solved using the iteration method based on singular value.
DefinitionFor soft-threshold or contraction operator.Wherein x is complicated quantity, and threshold value λ is true
Real value, singular value threshold operation operator is SVTλ(M)=U Λλ(∑)VH, wherein M=U ∑s VHIt is any singular value decomposition of M.
Iterations are set to 0, i.e. k=0 first, to realize initialization procedure.
After completing initialization procedure, will it constantly be iterated operation, i.e.,：
When not restraining,
3、Mk=Lk+Sk-EH(E(Lk+Sk)-d)
Wherein, the associated change of algorithm iteration to solving result is less than 10-5, it is, | | Lk+Sk-(Lk-1+Sk-1)||2≤
10-5||Lk-1+Sk-1||2。
Algorithm Convergence in the present embodiment is the particular example of the approximate gradient method by considering general type convex problem
Analysis obtains.General type convex problem is as follows：
ming(x)+h(x).
Here, g is convex and smooth, and h is convex, but is not necessarily smooth.Approximate gradient method form is such as
Under：
Wherein tkIt is step series, proxhIt is the approximate function of h：
When h (x) expression nuclear norms, approximate function can be equal to singular value soft-threshold, when h (x) indicates l1Norm, it is approximate
Function is determined by coefficient soft-threshold.Using fixed step size t, the approximate gradient method of this patent algorithm becomes：
If：
The then object function in the iteration energy minimization present invention in approximate gradient method.
In the present embodiment, image reconstruction is completed in Matlab, and low-rank specifically uses iteration threshold with sparse (L+S) reconstruction
Method realizes that algorithmic procedure is as shown in Figure 1.Wherein multi-coil encoding operation operator E is become in Descartes with fast Fourier
Realization is changed, is realized with nonuniform fast Fourier in non-Cartesian, coil sensitivity field uses adaptive coil combination skill
Art is calculated from the average time for accelerating data.It requires to calculate n in iteration singular value threshold steps×ntThe singular value of matrix point
Solution, wherein nsIt is the pixel number of each time frame, ntIt is to count out the time.Due to ntConsiderably small, algorithm is not to inhibit
, it can operably quickly.
Regularization parameter λLAnd λSFor comparing the reconstruction effect in numberical range.For simulation accelerated data set, rebuild
Effect is estimated with root-mean-square error (RMSE), for the data set actually accelerated, in remaining aliasing artefact and time fidelity
The qualitative estimation of aspect.Selection for L+S parameters, CS and L＆S rebuild effect and are tested and deposited with simulation accelerated root-mean-square error
It is tested in the qualitative estimation of the practical acceleration of aliasing artefact and time fidelity to compare.
It is above-mentioned low to illustrate with reference to the simulation lack sampling experiment of fully sampled Descartes's cardiac perfusion data
The dynamic magnetic resonance imaging method of order and sparse decomposition.The acquisition of experimental data is carried out in 3T whole-body scanner, using 12-
Matrix of elements coil array to short axle area acquisition among the ventricle of the diastole mid-term of healthy volunteer, obtain one 128 ×
128 image array and 40 time frames.Fully sampled Cartesian data with one it is different be thinned out random lack sampling pattern,
Along the k of each time pointyDirection with 6,8,10 factor lack samplings, uses multi-coil CS, L＆S and L+S methods retrospectively
It completes to rebuild, sparse transformation is replaced with time Fourier transformation.It is completed using root-mean-square error measurement and structuring similar index
Quantitative image quality measure, fully sampled reconstruction is as reference.Regularization parameter λLAnd λSThe heart of 8 times of acceleration of simulation is filled
The L+S reconstructions of note data have an impact.λLValue it is high, correspondingly eliminate static background substantially, λLValue it is very low, phase
The multidate information for accordingly containing a large amount of L ingredients, increases root-mean-square error and also reduces effect.Subsequent low-rank with it is dilute
Dredge λ in rebuildingL=0.01 and λS=0.01, provide minimum root-mean-square error.L+S is rebuild provides lower remaining aliasing puppet than CS
Mark has better time fidelity than L＆S, as a result obtains the description of better myocardial wall enhancing, as shown in Figure 3.These are fixed
Property find be confirmed in root-mean-square error and structural similarity index, such as Fig. 2.L+S rebuild another important feature be
The visualization of Contrast enhanced is improved in S ingredients, wherein background is inhibited by.
The above is only some embodiments of the present invention, it is noted that for the ordinary skill people of the art
For member, various improvements and modifications may be made without departing from the principle of the present invention, these improvements and modifications are also answered
It is considered as protection scope of the present invention.
Claims (6)
1. a kind of dynamic magnetic resonance imaging method of low-rank and sparse matrix decomposition, which is characterized in that include the following steps：
Step 1 introduces low-rank and sparse model, and the time series of image is converted into a matrix M；Then convex excellent by solving
Change problem completes low-rank and sparse decomposition, and matrix M is resolved into the superposition of a low-rank matrix L and sparse matrix S, wherein L pairs
Background component, S is answered to correspond to dynamic element；
Step 2, the improvement that completion low-rank and sparse decomposition after analysis are required by non-correlation, improvement type are：
min||L||*+λ||TS||1S.tE (L+S)=d
Wherein T is the sparse transformation of S, and E is coding or acquisition operations, and d is lack sampling k-t data；
Step 3, the image reconstruction that improved low-rank and sparse decomposition are applied to lack sampling dynamic magnetic resonance imaging.
2. the dynamic magnetic resonance imaging method of low-rank according to claim 1 and sparse matrix decomposition, which is characterized in that institute
Convex optimization problem is stated that is, min | | L | |*+λ||S||1S.t.M=L+S, wherein | | L | |*It is nuclear norm either matrix L singular value
With, | | S | |1It is l1Norm either in S element absolute value and, λ is adjusting parameter.
3. the dynamic magnetic resonance imaging method of low-rank according to claim 1 and sparse matrix decomposition, which is characterized in that step
Rapid 2 non-correlation includes：The spaces k-t and low-rank ingredient L describe the non-correlation between space, the spaces k-t with it is sparse at
S is divided to describe the non-correlation between non-correlation and the spaces L and the spaces S between space.
4. the dynamic magnetic resonance imaging method of low-rank according to claim 1 and sparse matrix decomposition, which is characterized in that step
Rapid 3 image reconstruction is expressed as follows：
It is solved using alternating direction method, the graceful disintegrating method of Donald Bragg or other convex optimization methods, λLAnd λSRepresent regularization ginseng
Number.
5. the dynamic magnetic resonance imaging method of low-rank according to claim 1 or 4 and sparse matrix decomposition, feature exist
In, in the step 3, derivation algorithm uses the iteration soft-threshold algorithm based on singular value, the specific steps are：
DefinitionFor soft-threshold or contraction operator；Wherein x is complicated quantity, and threshold value λ is true
Real value, singular value threshold operation operator is SVTλ(M)=U Λλ(∑)VH, wherein M=U ∑s VHIt is any singular value decomposition of M；
Iterations are set to 0, i.e. k=0 first, to realize initialization procedure；After completing initialization procedure, will constantly into
Row iteration is run, i.e.,：
When not restraining,
Mk=Lk+Sk-EH(E(Lk+Sk)-d)
Wherein, the associated change of algorithm iteration to solving result is less than 10-5, i.e.,：
||Lk+Sk-(Lk-1+Sk-1)||2≤10-5||Lk-1+Sk-1||2。
6. the dynamic magnetic resonance imaging method of low-rank according to claim 1 and sparse matrix decomposition, which is characterized in that step
For simulation accelerated data set in rapid 3, rebuilds effect and estimated with root-mean-square error, for the data set actually accelerated,
Qualitative estimation in terms of remaining aliasing artefact and time fidelity.
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| CN109188326A (en) * | 2018-09-29 | 2019-01-11 | 上海联影医疗科技有限公司 | MR imaging method and magnetic resonance system |
| CN110652297A (en) * | 2019-10-10 | 2020-01-07 | 中国计量大学 | Lung function imaging processing method based on MRI technology |
| CN111932649A (en) * | 2020-08-04 | 2020-11-13 | 中国科学院深圳先进技术研究院 | Dynamic medical imaging method, device, equipment and storage medium |
| CN112710975A (en) * | 2021-01-25 | 2021-04-27 | 东北林业大学 | Magnetic resonance diffusion image reconstruction method based on sparse and local low-rank matrix decomposition |
| CN112881958A (en) * | 2021-02-04 | 2021-06-01 | 上海交通大学 | Magnetic resonance interventional imaging method, system and medium based on low rank and sparse decomposition |
| CN113971706A (en) * | 2021-10-15 | 2022-01-25 | 厦门大学 | Rapid magnetic resonance intelligent imaging method |
| TWI773603B (en) * | 2021-11-30 | 2022-08-01 | 國立清華大學 | Compressed sensing imaging method and compressed sensing imaging system |
| WO2024092387A1 (en) * | 2022-10-31 | 2024-05-10 | 中国科学院深圳先进技术研究院 | Adaptive dynamic magnetic resonance fast imaging method and device based on partially separable function |
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Cited By (13)
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| CN109188326B (en) * | 2018-09-29 | 2021-04-06 | 上海联影医疗科技股份有限公司 | Magnetic resonance imaging method and magnetic resonance system |
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| CN110652297A (en) * | 2019-10-10 | 2020-01-07 | 中国计量大学 | Lung function imaging processing method based on MRI technology |
| CN111932649B (en) * | 2020-08-04 | 2024-05-24 | 中国科学院深圳先进技术研究院 | Dynamic medical imaging method, device, equipment and storage medium |
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| WO2022027804A1 (en) * | 2020-08-04 | 2022-02-10 | 中国科学院深圳先进技术研究院 | Dynamic medical imaging method and apparatus, device and storage medium |
| CN112710975A (en) * | 2021-01-25 | 2021-04-27 | 东北林业大学 | Magnetic resonance diffusion image reconstruction method based on sparse and local low-rank matrix decomposition |
| CN112881958A (en) * | 2021-02-04 | 2021-06-01 | 上海交通大学 | Magnetic resonance interventional imaging method, system and medium based on low rank and sparse decomposition |
| CN112881958B (en) * | 2021-02-04 | 2022-02-25 | 上海交通大学 | Magnetic resonance interventional imaging method, system and medium based on low rank and sparse decomposition |
| CN113971706A (en) * | 2021-10-15 | 2022-01-25 | 厦门大学 | Rapid magnetic resonance intelligent imaging method |
| CN113971706B (en) * | 2021-10-15 | 2024-04-30 | 厦门大学 | Rapid magnetic resonance intelligent imaging method |
| TWI773603B (en) * | 2021-11-30 | 2022-08-01 | 國立清華大學 | Compressed sensing imaging method and compressed sensing imaging system |
| WO2024092387A1 (en) * | 2022-10-31 | 2024-05-10 | 中国科学院深圳先进技术研究院 | Adaptive dynamic magnetic resonance fast imaging method and device based on partially separable function |
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