CN110148193A - Dynamic magnetic resonance method for parallel reconstruction based on adaptive quadrature dictionary learning - Google Patents
Dynamic magnetic resonance method for parallel reconstruction based on adaptive quadrature dictionary learning Download PDFInfo
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Abstract
The invention discloses a kind of dynamic magnetic resonance method for parallel reconstruction based on adaptive quadrature dictionary learning, originally the relatively slow dictionary learning algorithm run in disconnection mode is applied in on-line mode, the first frame sampled with high precision is reference, it realizes and the real-time online of any n consecutive frame MR image is rebuild, using 3-D image fritter as reconstructed object, is improved using orthogonal dictionary as sparse constraint condition and singular value decomposition algorithm and rebuild speed and precision.
Description
Technical field:
The invention belongs to medical image reconstruction technique field, it is specifically related to a kind of based on adaptive quadrature dictionary learning
Dynamic magnetic resonance method for parallel reconstruction.
Background technique:
Magnetic resonance imaging (magnetic resonance imaging, MRI) technology is with no wound, radiationless, resolution
Rate height and can multiplanar imaging the advantages that, can not only show the anatomic information of tissue, but also can show its functional information.MRI
It is widely used in each system of clinical medicine, is the another important clinical detection method later after CT.But MR image taking speed
It slowly is the big disadvantage of one, especially dynamic magnetic resonance imaging (dynamic magnetic resonance imaging, dMRI),
The MRI image sequence for needing to obtain high-spatial and temporal resolution within a short period of time is currently a problem of medical field.Too long sweeps
The time is retouched plus organ movement's (as breathed, swallowing) of patient, will lead to image blur, while being also unable to satisfy dynamic realtime
The demand of imaging and functional imaging.It carries out down-sampled being a kind of method for improving image taking speed in k-space, but if directly from k
Space will lead to reconstruction image and generate aliasing effect against inner leaf inversion reconstruction image according to nyquist sampling theorem.Dynamic magnetic
Resonance image-forming data have very strong sparse characteristic time-space domain, so that compressed sensing (compressive sensing, CS)
Technology is widely applied in MR image reconstruction.CS theory is pointed out, if a signal is sparse in transform domain, and is become
It changes base and calculation matrix is incoherent (also known as limited equidistant property, RIP), then it can be from down-sampled (remote small using CS method
Under the conditions of nyquist sampling rate) data sample in, pass through non-linear algorithm for reconstructing perfect reconstruction signal.
DMRI method for reconstructing can be divided into online mode and offline mode.When rebuilding using off-line mode, need rebuilding
The sampled data of entire dMRI sequence is obtained before.Common offline method for reconstructing has motion correction, and dictionary learning and low-rank are close
Like etc..These methods make full use of entire dMRI sequence sparse characteristic to carry out high-precision reconstruction, the disadvantage is that reconstruction speed is slower,
And it needs to wait longer sweep time.Using when line method is rebuild, the reconstruction of each frame is only related with frame before,
Waiting time, but the complete information due to lacking entire sequence can be saved, reconstruction precision can not be protected to rebuild in scanning
Barrier, while being also put forward higher requirements to speed is rebuild.
There are two types of common schemes for online reconstruction: serial and concurrent.Serial scheme usually utilizes phase in image or transform domain
Sparsity between adjacent frame, this is also most of existing strategies common in line method.However, these methods frequently can lead to
Accumulated error.Chen C et al. uses a kind of concurrent reconstruction scheme of new dynamic total variation (dTV) to solve error accumulation
Problem.This method using first frame sampling with high precision as reference frame, remaining frame with its one by one compared with concurrent reconstruction.This method
Every time can only using between two frames it is sparse as rebuild priori knowledge, cause lower than off-line method precision.
Summary of the invention:
To solve problems of the prior art, the invention proposes a kind of realities based on adaptive quadrature dictionary learning
When dynamic magnetic resonance method for parallel reconstruction.
In order to achieve the above objectives, technical scheme is as follows:
A kind of dynamic magnetic resonance method for parallel reconstruction based on adaptive quadrature dictionary learning, includes the following steps:
S1: inputting original dMRI sequence X, and input measurement value y, the measured value y are the lack sampling data in the space k-t, are adopted
With pseudorandom ray lack sampling mode, the first circulation the number of iterations OutLoop of algorithm is inputted, the second circulation for inputting algorithm changes
Generation number InnerLoop inputs dictionary learning parameter；
S2: reconstruction image initial value is set as by initializationHereFor MR rebuild after kth time iteration
Sequence image, xzfFor zero padding data after the lack sampling of the space k-t, dictionary D is initialized, the dictionary D is DCT dictionary；
S3: iteration updates,
For i=1:OutLoop
Forj=InnerLoop
Update self-adapting dictionary D；
Update image block rarefaction representation coefficient αi；
Update the frequency domain value of reconstruction imageInverse Fourier transform obtains j-th of reconstruct subsequence
end
Subsequence image Xs (j) is rebuild in output, waits next subsequence Xs (j+1)；
end
S4: each subsequence image Xs (j) is reassembled into the dMRI sequence after rebuilding.
As a preferred embodiment of the above technical solution, in the step S3:
Self-adapting dictionary D and rarefaction representation coefficient αiSolution include the following steps:
S310: the deficient data of adopting that a given dMRI sequence is expressed as the space X and its k-t are y, compressed sensing dMRI weight
The problem of building can be attributed to following l0Norm minimum problem:
Wherein, Fu=diag [Fu(1),Fu(2),...,Fu(Nt)] be the space k-t sampling matrix, Fu(t)=F2DPt,
Middle F2DFor two-dimensional Fourier transform operator, PtIt is t frame lack sampling matrix, y indicates the domain lack sampling k, | | x | |0It is the l of x0Norm,
Ψ is sparse transformation matrix, and λ is constant relevant to sampling noise；
S311: using the collected measured value of compression perceptual system as image observation sample data come training dictionary, will
Image to be processed is divided into the fritter of overlapping, and to replace entire image to carry out rarefaction representation, dictionary learning problem be can be described as:
Wherein, x is image sequence to be reconstructed, and D was complete dictionary, RiTo be overlapped the operator for taking block, αiFor the sparse table of x
Show coefficient, Γ={ α1,...,αIIt is rarefaction representation coefficient αiSet, T0Indicate degree of rarefication threshold constant, s.t. is to meet about
The meaning of beam condition, | | αi||0≤T0For constraint condition,For to arbitrary i, wherein first itemWith it is sparse about
Beam condition | | αi||0≤T0Ensured complete dictionary to the optimal sparse bayesian learning of each image block, Section 2For number
According to fidelity term, variable ν is constant, related with the standard deviation sigma for the white Gaussian noise being superimposed when k-t spatial sampling；
S312: orthogonal restriction D is added during dictionary learningTObjective function in D=I, step S311 becomes:
Wherein, ν and β is regularization parameter here, it is therefore an objective to which the contribution margin for reducing two below prevents equation from generating quasi-
It closes, I is unit diagonal matrix；
S313: each subsequence image Xs data remain unchanged, and convert D and α in solution procedure S312 formula for problemiMost
The subproblem of excellent solution:
S314: when carrying out first time iteration,Zero padding is directly carried out after k-space lack sampling for corresponding subsequence image Xs
The image data filled will be divided into 1 three-dimensional overlap partition first, randomly select between sampling subsequence image Xs overlap sampling
Partial amount image block, uses DCT dictionary as initial dictionary, and fixed D updates rarefaction representation coefficient α using following formula algorithmsi,
Hard threshold function can be used in the solution of the problem, embodies are as follows:
Wherein T (g) is hard threshold function,
S315: sparse coefficient α has been updatediAfter, fixed αi, dictionary D is updated using the method for singular value decomposition, dictionary is more
New problem can convert are as follows:
So that DTD=I
Here,
Wherein, X={ x1,x2,L xm}∈Rn×mFor image block matrix, V={ v1,v2,L vm}∈Rk×mFor sparse coefficient square
Battle array, Tr (g) are the operation of Matrix Calculating mark, then dictionary updating problem changes are as follows:
The problem is realized by singular value decomposition algorithm:
XVT=P ∑ QT,Dk+1=PQT
This is that the SVD of typical matrix is decomposed, and Σ is the matrix of a m × n, other than the element on leading diagonal
It is all 0, each element on leading diagonal is referred to as singular value, and P and Q are unitary matrice, that is, meets PTP=I, QTQ=I.
As a preferred embodiment of the above technical solution, in the step S3:
Update the frequency domain value of reconstruction imageInverse Fourier transform obtains j-th of reconstruct subsequence
Specifically comprise the following steps:
S321: it can be obtained by compressed sensing dictionary learning reconstruction model:
S322: D and α in the formula of step S321iIt immobilizes, image reconstruction subproblem becomes a common minimum two
Multiplication problem, to unique variable xsDerivation simultaneously enables it obtain equal to 0:
Wherein:For FuAssociate matrix；
S323: Fourier transformation is carried out to the formula both sides in step S322 and is obtained:
I represents unit diagonal matrix, and n is that any one pixel includes by different 3-D image fritters
Number, when piecemeal interval is minimized 1, n is the vector dimension of image block,For the k-space of down-sampled zero padding
Data can be expressed as It is the diagonal matrix of a P × P, P is the dimension that entire subsequence image lines up vector
Number；
Above formula can simplify are as follows:
Wherein,For value of the sequence to be reconstructed at k-space corresponding position (kx, ky), Ω is in sampling matrix
The set for the position that value is 1, λ=q/ σ are determined by k-space sampling noise criteria difference, and σ is noise variance, and q is noisy sampling
Under the conditions of adjustable parameter, λ is infinity under noiseless sampling condition, and the reconstruction signal of sampled point can enable directly
The beneficial effects of the present invention are: a kind of real-time dynamic based on adaptive quadrature dictionary learning proposed by the present invention
Originally the relatively slow dictionary learning algorithm run in disconnection mode is applied to online by magnetic resonance parallel method for reconstructing
Come in mode, the first frame sampled with high precision is reference, realizes the real-time online weight to any n consecutive frame MR image
It builds, using 3-D image fritter as reconstructed object, using orthogonal dictionary as sparse constraint condition and singular value decomposition
(Singular Value Decomposition, SVD) algorithm, which improves, rebuilds speed and precision.
Detailed description of the invention:
The following drawings are only intended to schematically illustrate and explain the present invention, not delimit the scope of the invention.Wherein:
Fig. 1 is that a kind of parallel adaptive dictionary learning dMRI of one embodiment of the invention rebuilds schematic diagram；
Fig. 2 is that the first frame sampling matrix of one embodiment of the invention and other frames use matrix schematic diagram；
Fig. 3 is the number of iterations and PSNR relation schematic diagram of one embodiment of the invention；
Fig. 4 is the reconstruction front and back image comparison schematic diagram of one embodiment of the invention；
Fig. 5 is that each algorithm of one embodiment of the invention rebuilds MR image and error image comparison schematic diagram；
Fig. 6 is the reconstruction root-mean-square error of one embodiment of the invention and the relation schematic diagram of q.
Specific embodiment:
A kind of dynamic magnetic resonance method for parallel reconstruction based on adaptive quadrature dictionary learning of the invention, including walk as follows
It is rapid:
S1: original dMRI sequence X is inputted, input measurement value y is the lack sampling data in the space k-t, using pseudorandom ray
Lack sampling mode (see attached drawing 2) inputs the first circulation the number of iterations OutLoop of algorithm, inputs the second circulation iteration of algorithm
Number InnerLoop inputs dictionary learning parameter；
S2: reconstruction image initial value is set as by initializationHereFor MR rebuild after kth time iteration
Sequence image, xzfFor zero padding data after the lack sampling of the space k-t, initialization dictionary D is DCT dictionary.
S3: iteration updates,
For i=1:OutLoop
For j=1:InnerLoop
Update self-adapting dictionary D；
Update image block rarefaction representation coefficient αi；
Update the frequency domain value of reconstruction imageInverse Fourier transform obtains j-th of reconstruct subsequence
end
Subsequence image Xs (j) is rebuild in output, waits next subsequence Xs (j+1)；
end
S4: each subsequence image Xs (j) is reassembled into the dMRI sequence after rebuilding.
Self-adapting dictionary D and rarefaction representation coefficient αiSolution include the following steps:
S310: the deficient data of adopting that a given dMRI sequence is expressed as the space X and its k-t are y, compressed sensing dMRI weight
The problem of building can be attributed to following l0Norm minimum problem:
Wherein, Fu=diag [Fu(1),Fu(2),...,Fu(Nt)] be the space k-t sampling matrix, Fu(t)=F2DPt,
Middle F2DFor two-dimensional Fourier transform operator, PtIt is t frame lack sampling matrix, | | x | |0It is the l of x0Norm, Ψ are sparse transformation squares
Battle array, λ are constants relevant to sampling noise.
MRI acquires the domain k (Fourier transform domain) signal, then rebuilds airspace signal by inverse Fourier transform.Fourier becomes
Changing is a kind of linear transformation, it is desirable that the domain k signal number is necessarily equal to the pixel number of image area.Lustig in 2007 et al. proposes pressure
The concept of contracting perception magnetic resonance imaging (CSMRI) adopts k-space signal with the sample frequency far below nyquist frequency
Collection to greatly reduce imaging time, and passes through non-linear algorithm for reconstructing perfect reconstruction original image.
CSMRI needs to meet 3 conditions:
(1) sparse matrix Ψ, so that original MR image only has a small amount of nonzero coefficient in sparse domain；
(2) matrix F u Ψ -1 meets RIP condition, general using randomly or pseudo-randomly sampling matrix, reduces sampled data
Correlation.
(3) non-linear algorithm for reconstructing can quick and precisely rebuild original image.
S311: excessively complete dictionary has a wide range of applications in the rarefaction representation of signal.It is various to be trained based on image library
Non-adaptive image rebuilding method because its adaptability is poor, rebuild effect it is general the disadvantages of gradually by be based on self-adapting dictionary
Replaced the image reconstruction algorithm of habit.Adaptively referring to here is seen by the collected measured value of compression perceptual system as image
Test sample notebook data carrys out training dictionary.Since the calculation amount of dictionary learning can be quicklyd increase with the increase of dictionary size, we
Image to be processed is usually divided into the fritter of overlapping, to replace entire image to carry out rarefaction representation.Dictionary learning problem can retouch
It states are as follows:
Wherein, x is image sequence to be reconstructed, and D was complete dictionary, RiTo be overlapped the operator for taking block, αiFor the sparse table of x
Show coefficient, Γ={ α1,...,αIIt is rarefaction representation coefficient αiSet (, T0Indicate degree of rarefication threshold constant.It s.t. is satisfaction
The meaning (similarly hereinafter) of constraint condition, | | αi||0≤T0For constraint condition,For to arbitrary i.Wherein first item
With sparse constraint condition | | αi||0≤T0Ensured complete dictionary to the optimal sparse bayesian learning of each image block.Section 2For data fidelity term, variable ν is constant, and the standard deviation sigma for the white Gaussian noise being superimposed when sampling with k-space is related；
When due to dMRI dynamic scan, the major organs relative position approximation of each frame is constant, we choose the of sequence
One frame image is sampling with high precision (generally taking the sample rate greater than 50%), provides high-precision reference for the reconstruction of subsequent frame, this
It can be completed by a prescan of magnetic resonance machine.The n-1 frame image of first frame and remaining arbitrary neighborhood forms a series of son of n frames
Sequence image Xs (j), by taking 3 frames as an example, as shown in Figure 1, Xs(j)=[x1,x2j,x2j+1], j=1,2,3 ..., x2jIndicate original dMRI
2j frame image in sequence x.As long as adjacent two frame sampling finishes, real-time parallel reconstruction can be carried out, without waiting for subsequent frame
Sampling is completed.The reconstruction of each subsequence is uncorrelated to other subsequences.
Orthogonal dictionary can guarantee the irrelevance between dictionary atom to greatest extent, to ensure that sparse coding mistake
Efficiency in journey maximizes.Set forth herein a kind of dMRI concurrent reconstruction algorithm based on adaptive quadrature dictionary, it is intended to which shortening is swept
It retouches the waiting time, is promoted and rebuild speed, improve the quality of image reconstruction.
S312: orthogonal restriction D is added during dictionary learningTObjective function in D=I, step S311 becomes:
Wherein, ν and β is regularization parameter here, it is therefore an objective to which the contribution margin for reducing two below prevents equation from generating quasi-
It closes, I is unit diagonal matrix (similarly hereinafter).
The reconstruction model proposed in above formula can be analyzed to solve adaptive quadrature dictionary learning, image sparse coefficient it is sparse
Optimize subproblem and image reconstruction subproblem, realizes the solution to objective function optimal solution.
S313: each subsequence image Xs data remain unchanged, and convert D and α in solution procedure S312 formula for problemiMost
The subproblem of excellent solution:
S314: when carrying out first time iteration,Zero padding is directly carried out after k-space lack sampling for corresponding subsequence image Xs
The image data filled will be divided into 1 three-dimensional overlap partition first, randomly select between sampling subsequence image Xs overlap sampling
Partial amount image block, uses DCT dictionary as initial dictionary, and fixed D updates rarefaction representation coefficient α using following formula algorithmsi,
Hard threshold function can be used in the solution of the problem, embodies are as follows:
Wherein T (g) is hard threshold function.
S315: sparse coefficient α has been updatediAfter (subscript k+1 is exactly to represent updated αi), fixed sparse coefficient is constant,
Dictionary D is updated using the method for singular value decomposition, dictionary updating problem can convert are as follows:
Here,
Wherein, X={ x1,x2,L xm}∈Rn×mFor image block matrix, V={ v1,v2,L vm}∈Rk×mFor sparse coefficient square
Battle array, Tr (g) are the operation of Matrix Calculating mark, then dictionary updating problem changes are as follows:
The problem is realized by singular value decomposition algorithm:
XVT=P ∑ QT,Dk+1=PQT。
This is that the SVD of typical matrix is decomposed, and Σ is the matrix of a m × n, other than the element on leading diagonal
It is all 0, each element on leading diagonal is referred to as singular value, and P and Q are unitary matrice, that is, meets PTP=I, QTQ=I.
Image reconstruction subproblem: the frequency domain value of reconstruction image is updatedInverse Fourier transform obtains j-th of weight
Structure subsequenceSpecifically comprise the following steps:
S321:
This formula is classical compressed sensing dictionary learning reconstruction model, and subscript represents the meaning of+1 iteration of kth update
Think, parameter index refers to S311.
S322: D and α in the formula of step S321iIt immobilizes, image reconstruction subproblem becomes a common minimum two
Multiplication problem, to unique variable xsDerivation simultaneously enables it obtain equal to 0:
Wherein:For FuAssociate matrix.
S323: directly solving above formula, and calculation amount is sizable, because to ask the matrix of a P × P
Inverse that reconstructed results just can be obtained, this makes the time complexity for solving this problem reach O (p3).We can be by operation by image sky
Between transform to Fourier space progress, in step S322 formula both sides carry out Fourier transformation obtain:
N is the number that any one pixel includes by different 3-D image fritters, when piecemeal interval takes most
When small value 1, n is the vector dimension of image block,For FuAssociate matrix,For the k of down-sampled zero padding
Spatial data can be expressed as The diagonal matrix of a P × P, P be entire subsequence image line up to
The dimension of amount；
Above formula can simplify are as follows:
Wherein,For value of the sequence to be reconstructed at k-space corresponding position (kx, ky), Ω is in sampling matrix
The set for the position that value is 1.λ=q/ σ is to determine that σ is noise variance by k-space sampling noise criteria difference, and q is noisy sampling
Under the conditions of adjustable parameter.λ is infinity under noiseless sampling condition, and the reconstruction signal of sampled point can be enabled directlyReconstruction sequence is that inverse Fourier transform obtains after k-space more new data, in Noise
Under sampling condition, parameter q is most important for reconstruction performance, and under noise free conditions, reconstructed results are to the value of q and insensitive.
As shown in Figure 1, the first frame that the present embodiment samples with high precision is reference, realizes and any n consecutive frame MR is schemed
The real-time online of picture is rebuild.Using 3-D image fritter as reconstructed object, using orthogonal dictionary as sparse constraint condition and surprise
Different value decomposes (Singular Value Decomposition, SVD) algorithm and improves reconstruction speed and precision.
The present embodiment also provides a kind of reality of dynamic magnetic resonance method for parallel reconstruction based on adaptive quadrature dictionary learning
It tests as follows:
All experiments are all to use MATLAB2013a on a laptop with 3.0GHz Intel i7CPU
It is emulated.We choose one group of heart muscle perfusion dMRI sequence (resolution ratio is 192 × 192 × 30 frames) for assessment algorithm
Performance.Pseudo- ray sampling matrix is used to carry out lack sampling in the space k-t to test image, and simulation magnetic resonance machine accelerates imaging.Such as
Shown in Fig. 2, first frame sample rate is 50%, other frame sampling rates are 15%.The method for objectively evaluating of picture quality uses peak value
Signal-to-noise ratio (Peak Signal to Noise Rate, PSNR), unit dB.PSNR calculation formula is as follows:
PSNR (x, y)=20lg (Imax/RMSE(x,y))
Here x and y is respectively original image and reconstruction image, ImaxFor image pixel maximum value, generally in order to reduce matrix
Operand image will be normalized operation, then Imax=1.RMSE is the root-mean-square error of two images.
Experiment parameter setting: for fast parallel reconstruction dMRI sequence, this algorithm sets 3-D image block size to most
Small 3*3*3 is tested by experiment, and reconstructed image quality and image block size relationship are little, can be with figure but rebuild speed
As block size increase and decline rapidly.Dictionary size is set as 27*108, and the atom number of each on-line study is 5000.Comparison
Algorithm have a k-t SLR of the off-line mode and TV of on-line mode, DTV these three, the parameter of three comparative experiments algorithms is pressed
The optimized parameter of source paper is arranged.
Fig. 3 gives the process that this paper algorithm rebuilds a dMRI subsequence (by taking 3 frames as an example).By 14 iteration, consumption
When 2.8 seconds, just by the low signal-to-noise ratio (SNR) images (PSNR=31.1dB) of zero padding after k-space lack sampling, be redeveloped into high s/n ratio
Image (PSNR=36.3dB).Fig. 4 gives the image vision comparison for rebuilding front and back, it is seen then that the image after reconstruction is complete
Eliminate artifact caused by lack sampling.
Fig. 5 compared the reconstruction effect (under no sampling noise conditions) of various algorithms, and to arrange as unit, the first behavior is respectively
Reconstruction image, the Error Graph of the second behavior reconstruction image and original image, to highlight effect, we by error amplify 5 times into
Row compares.Obviously our Algorithm Error is the smallest, and especially crucial cardia, visual effect are the most true to nature.
In the case where there is sampling noise situations, it is assumed that the white Gaussian noise standard deviation of k-space superposition is σ, λ=q/ σ in formula (9)
Value just with rebuild effect it is closely bound up.Fig. 6 gives the relationship between parameter q and the RMSE of reconstruction image.Sample noise
Than taking 23dB (strong noise environment), 37dB (medium noise circumstance) and 57dB (low noise environment) respectively.As it can be seen that q=0.005 is
Consider an optimal selection under different sampling noise circumstances.Especially under strong noise environment, weight when q=0.005
It is best to build effect.
This paper algorithm is applicable to the concurrent reconstruction that the n frame subsequence of arbitrary neighborhood is constituted, and table 1 gives subsequence frame
Relationship between number n and reconstruction PSNR value and algorithm reconstruction time (under the conditions of 20% sample rate).As it can be seen that using 3 frames as one
The precision (PSNR value) of a sub- rebuilding series unit, reconstruction is highest, and the time rebuild is least.And each seed ginseng
Under several, reconstruction precision embodies the stability of this algorithm all in controllable error range.
Table 1 rebuilds subsequence frame number and rebuilds relationship between effect
The reconstruction PSNR value comparing result that this paper algorithm compares algorithm with three is as shown in table 1.Under different sample rates,
The algorithm of this paper is optimal.Especially under the conditions of 15% low sampling rate, compared to the performance that other algorithms have 0.4dB or more
It is promoted.By taking 3 frames are a dMRI subsequence as an example, a frame image can be rebuild within this paper algorithm average every 1.4 seconds, it is remote to rebuild speed
Far faster than off-line mode (k-t SLR), but it is slower than two kinds of algorithms using TV method.
The PSNR value (dB) of reconstruction image under the different sample rates of table 2
A kind of method of dynamic magnetic resonance concurrent reconstruction based on adaptive quadrature dictionary learning proposed in this paper.Using
Line concurrent reconstruction mode realizes the real-time high-precision reconstruction to dMRI image, and excellent to there is the parameter q under noise circumstance to make
Change.Experiment show superiority of this method on reconstruction precision and speed.This method is that real-time online reconstruction dMRI is mentioned
A solution is supplied.
Obviously, the above embodiments are merely examples for clarifying the description, and does not limit the embodiments.It is right
For those of ordinary skill in the art, can also make on the basis of the above description it is other it is various forms of variation or
It changes.There is no necessity and possibility to exhaust all the enbodiments.And it is extended from this it is obvious variation or
It changes still within the protection scope of the invention.
Claims (3)
1. a kind of dynamic magnetic resonance method for parallel reconstruction based on adaptive quadrature dictionary learning, which is characterized in that including as follows
Step:
S1: original dMRI sequence X is inputted, input measurement value y, the measured value y is the lack sampling data in the space k-t, using puppet
Stochastic ray lack sampling mode inputs the first circulation the number of iterations OutLoop of algorithm, inputs the second circulation iteration time of algorithm
Number InnerLoop, inputs dictionary learning parameter；
S2: reconstruction image initial value is set as by initializationHereFor the MR subsequence rebuild after kth time iteration
Image, xzfFor zero padding data after the lack sampling of the space k-t, dictionary D is initialized, the dictionary D is DCT dictionary；
S3: iteration updates,
For i=1:OutLoop
For j=1: InnerLoop
Update self-adapting dictionary D；
Update image block rarefaction representation coefficient αi；
Update the frequency domain value of reconstruction imageInverse Fourier transform obtains j-th of reconstruct subsequence
end
Subsequence image Xs (j) is rebuild in output, waits next subsequence Xs (j+1)；
end
S4: each subsequence image Xs (j) is reassembled into the dMRI sequence after rebuilding.
2. a kind of dynamic magnetic resonance method for parallel reconstruction based on adaptive quadrature dictionary learning according to claim 1,
It is characterized in that, in the step S3:
Self-adapting dictionary D and rarefaction representation coefficient αiSolution include the following steps:
S310: the deficient data of adopting that a given dMRI sequence is expressed as the space X and its k-t are y, and compressed sensing dMRI reconstruction is asked
Topic can be attributed to following l0Norm minimum problem:
Wherein, Fu=diag [Fu(1),Fu(2),...,Fu(Nt)] be the space k-t sampling matrix, Fu(t)=F2DPt, wherein F2D
For two-dimensional Fourier transform operator, PtIt is t frame lack sampling matrix, y indicates the domain lack sampling k, | | x | |0It is the l of x0Norm, Ψ are
Sparse transformation matrix, λ are constants relevant to sampling noise；
S311: using the collected measured value of compression perceptual system as image observation sample data come training dictionary, will be wait locate
The image of reason is divided into the fritter of overlapping, and to replace entire image to carry out rarefaction representation, dictionary learning problem be can be described as:
Wherein, x is image sequence to be reconstructed, and D was complete dictionary, RiTo be overlapped the operator for taking block, αiFor the rarefaction representation system of x
Number, Γ={ α1,...,αIIt is rarefaction representation coefficient αiSet, T0Indicate degree of rarefication threshold constant, s.t. is to meet constraint item
The meaning of part, | | αi||0≤T0For constraint condition,For to arbitrary i, wherein first itemWith sparse constraint item
Part | | αi||0≤T0Ensured complete dictionary to the optimal sparse bayesian learning of each image block, Section 2For data guarantor
True item, variable ν is constant, related with the standard deviation sigma for the white Gaussian noise being superimposed when k-t spatial sampling；
S312: orthogonal restriction D is added during dictionary learningTObjective function in D=I, step S311 becomes:
Wherein, ν and β is regularization parameter here, it is therefore an objective to which the contribution margin for reducing two below prevents equation from generating over-fitting, I
For unit diagonal matrix；
S313: each subsequence image Xs data remain unchanged, and convert D and α in solution procedure S312 formula for problemiOptimal solution
Subproblem:
S314: when carrying out first time iteration,Zero padding is directly carried out after the lack sampling of the space k-t for corresponding subsequence image Xs
Obtained image data will be divided into 1 three-dimensional overlap partition first, randomly select portion between sampling subsequence image Xs overlap sampling
Component image block, uses DCT dictionary as initial dictionary, and fixed D updates rarefaction representation coefficient α using following formula algorithmsi,
Hard threshold function can be used in the solution of the problem, embodies are as follows:
Wherein T (g) is hard threshold function,
S315: sparse coefficient α has been updatediAfter, fixed αi, dictionary D is updated using the method for singular value decomposition, dictionary updating is asked
Topic can convert are as follows:
So that DTD=I
Here,
Wherein, X={ x1,x2,L xm}∈Rn×mFor image block matrix, V={ v1,v2,L vm}∈Rk×mFor sparse coefficient matrix, Tr
It (g) is the operation of Matrix Calculating mark, then dictionary updating problem changes are as follows:
The problem is realized by singular value decomposition algorithm:
XVT=P ∑ QT,Dk+1=PQT
This is that the SVD of typical matrix is decomposed, and Σ is the matrix of a m × n, is all other than the element on leading diagonal
0, each element on leading diagonal is referred to as singular value, and P and Q are unitary matrice, that is, meet PTP=I, QTQ=I.
3. a kind of dynamic magnetic resonance method for parallel reconstruction based on adaptive quadrature dictionary learning according to claim 2,
It is characterized in that, in the step S3:
Update the frequency domain value of reconstruction imageInverse Fourier transform obtains j-th of reconstruct subsequenceSpecifically
Include the following steps:
S321: it can be obtained by compressed sensing dictionary learning reconstruction model:
S322: D and α in the formula of step S321iIt immobilizes, image reconstruction subproblem becomes a common least square method
Problem, to unique variable xsDerivation simultaneously enables it obtain equal to 0:
Wherein:For FuAssociate matrix；
S323: Fourier transformation is carried out to the formula both sides in step S322 and is obtained:
I represents unit diagonal matrix, and n is the number that any one pixel includes by different 3-D image fritters, when
When piecemeal interval is minimized 1, n is the vector dimension of image block,For the k-space data of down-sampled zero padding,
It can be expressed as It is the diagonal matrix of a P × P, P is the dimension that entire subsequence image lines up vector；
Above formula can simplify are as follows:
Wherein,For value of the sequence to be reconstructed at k-space corresponding position (kx, ky), Ω is value in sampling matrix
For the set of 1 position, λ=q/ σ is determined by k-space sampling noise criteria difference, and σ is noise variance, and q is noisy sampling condition
Under adjustable parameter, λ is infinity under noiseless sampling condition, and the reconstruction signal of sampled point can enable directly
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