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 PDF

Info

Publication number
CN110148193A
CN110148193A CN201910363197.8A CN201910363197A CN110148193A CN 110148193 A CN110148193 A CN 110148193A CN 201910363197 A CN201910363197 A CN 201910363197A CN 110148193 A CN110148193 A CN 110148193A
Authority
CN
China
Prior art keywords
image
dictionary
matrix
reconstruction
sampling
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
CN201910363197.8A
Other languages
Chinese (zh)
Inventor
王悦
汪洋
蒋慧敏
雷必成
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Taizhou University
Original Assignee
Taizhou University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Taizhou University filed Critical Taizhou University
Priority to CN201910363197.8A priority Critical patent/CN110148193A/en
Publication of CN110148193A publication Critical patent/CN110148193A/en
Pending legal-status Critical Current

Links

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T11/00—2D [Two Dimensional] image generation
    • G06T11/003—Reconstruction from projections, e.g. tomography
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T15/00—3D [Three Dimensional] image rendering
    • G06T15/005—General purpose rendering architectures
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
    • G06T2207/10—Image acquisition modality
    • G06T2207/10072—Tomographic images
    • G06T2207/10088—Magnetic resonance imaging [MRI]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
    • G06T2207/20—Special algorithmic details
    • G06T2207/20048—Transform domain processing
    • G06T2207/20056—Discrete and fast Fourier transform, [DFT, FFT]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
    • G06T2207/20—Special algorithmic details
    • G06T2207/20081—Training; Learning

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • Computer Graphics (AREA)
  • Magnetic Resonance Imaging Apparatus (AREA)

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

Dynamic magnetic resonance parallel reconstruction method based on adaptive orthogonal dictionary learning
The technical field is as follows:
the invention belongs to the technical field of medical image reconstruction, and particularly relates to a dynamic magnetic resonance parallel reconstruction method based on self-adaptive orthogonal dictionary learning.
Background art:
magnetic Resonance Imaging (MRI) technology has the advantages of no wound, no radiation, high resolution, capability of multi-dimensional imaging and the like, and can display not only anatomical information of human tissues, but also functional information of the human tissues. MRI is widely used in clinical medicine systems, and is another important clinical examination method following CT. However, the slow speed of MR imaging is a big disadvantage, and especially dynamic magnetic resonance imaging (dmiri), which requires obtaining an MRI image sequence with high spatial-temporal resolution in a short time, is a difficult problem in the medical field. The excessive scan time, coupled with the patient's organ motion (e.g., breathing, swallowing, etc.), can result in imaging blurring and also fails to meet the requirements for dynamic real-time imaging and functional imaging. Down-sampling in k-space is one method to increase imaging speed, but if the reconstructed image is inverted directly from k-space inverse-inner leaves, aliasing effects can be caused to the reconstructed image according to the nyquist sampling theorem. The dynamic magnetic resonance imaging data has strong sparsity in a time-space domain, so that a Compressed Sensing (CS) technology is widely applied to MR image reconstruction. CS theory states that if a signal is sparse in the transform domain and the transform basis and measurement matrix are uncorrelated (also known as finite equidistant property, RIP), then the CS method can perfectly reconstruct the signal from downsampled (much smaller than the nyquist sampling rate) data samples by a nonlinear reconstruction algorithm.
The dMRI reconstruction method can be divided into an online mode and an offline mode. With off-line mode reconstruction, it is necessary to obtain sample data for the entire dMRI sequence prior to reconstruction. Common off-line reconstruction methods include motion correction, dictionary learning, and low rank approximation. These methods fully utilize the sparsity of the whole dMRI sequence for high-precision reconstruction, and have the disadvantages of slow reconstruction speed and long waiting time for scanning. When the online method is adopted for reconstruction, the reconstruction of each frame is only related to the previous frame, and the reconstruction can be carried out while scanning, so that the waiting time is saved, but the reconstruction precision cannot be guaranteed due to the lack of complete information of the whole sequence, and meanwhile, higher requirements are also put forward on the reconstruction speed.
There are two common schemes for online reconstruction: serial and parallel. The serial approach typically exploits sparsity between adjacent frames in the image or transform domain, which is also a common strategy in most existing online approaches. However, these methods tend to result in cumulative errors. Chen C et al adopts a new parallel reconstruction scheme of dynamic total variation (dTV) to solve the error accumulation problem. The method adopts the high-precision sampling of the first frame as a reference frame, and the rest frames are compared with the reference frame one by one and reconstructed in parallel. The method can only use sparsity between two frames as the priori knowledge of reconstruction each time, resulting in lower precision than the offline method.
The invention content is as follows:
in order to solve the problems in the prior art, the invention provides a real-time dynamic magnetic resonance parallel reconstruction method based on self-adaptive orthogonal dictionary learning.
In order to achieve the purpose, the technical scheme of the invention is as follows:
a dynamic magnetic resonance parallel reconstruction method based on self-adaptive orthogonal dictionary learning comprises the following steps:
s1: inputting an original dMRI sequence X, inputting a measured value y, wherein the measured value y is undersampled data of a k-t space, inputting a first loop iteration frequency OutLoop of an algorithm and a second loop iteration frequency InnerLoop of the algorithm by adopting a pseudorandom ray undersampled mode, and inputting dictionary learning parameters;
s2: initializing, setting the initial value of the reconstructed image to beHere, theFor the MR sub-sequence image reconstructed after the kth iteration, xzfInitializing a dictionary D for the zero padding data after k-t space undersampling, wherein the dictionary D is a DCT dictionary;
s3: the update is carried out in an iterative manner,
for i＝1:OutLoop
forj＝InnerLoop
updating the self-adaptive dictionary D;
updating image block sparse representation coefficients αi；
Updating frequency-domain values of a reconstructed imageObtaining the j reconstructed subsequence by inverse Fourier transform
end
Outputting a reconstructed subsequence image Xs (j) and waiting for the next subsequence Xs (j + 1);
end
s4: the sub-sequence images xs (j) are recombined into a reconstructed dMRI sequence.
Preferably, in the step S3, the step of:
adaptive dictionary D and sparse representation coefficients αiComprises the following steps:
s310: given a dMRI sequence denoted X and its undersampled data in k-t space y, the compressed sensing dMRI reconstruction problem can be reduced to the following l0Norm minimization problem:
wherein, Fu＝diag[Fu(1),Fu(2),...,Fu(Nt)]Is a sampling matrix of k-t space, Fu(t)＝F2DPtIn which F is2DAs a two-dimensional Fourier transform operator, PtIs the t-th frame undersampled matrix, y represents the undersampled k domain, | | x | | luminance0Is l of x0Norm, Ψ is the sparse transform matrix, λ is a constant related to the sampling noise;
s311: a dictionary is trained by using a measured value acquired by a compressed sensing system as image observation sample data, an image to be processed is divided into overlapped small blocks to replace the whole image for sparse representation, and the dictionary learning problem can be described as follows:
wherein x is an image sequence to be reconstructed, D is an over-complete dictionary, and RiOperator for fetching blocks for overlap, αiA sparse representation coefficient of x, Γ ═ α1,...,αICoefficient α is expressed as sparseiSet of (2), T0Represents a sparsity threshold constant, s.t. is a meaning of satisfying a constraint condition, | | αi||0≤T0In order to be a constraint condition, the method comprises the following steps of,is to any of i, wherein the first termAnd sparse constraint | | | αi||0≤T0The optimal sparse approximation of the overcomplete dictionary to each image block is ensured, and the second termThe variable v is a constant and is related to the standard deviation sigma of superimposed white Gaussian noise during sampling of k-t space;
s312: adding orthogonal constraint D in dictionary learning processTWhen D is equal to I, the objective function in step S311 becomes:
wherein, ν and β are regularization parameters for reducing contribution values of the latter two terms and preventing the equation from generating overfitting, and I is a unit diagonal matrix;
s313, keeping the data of each subsequence image Xs unchanged, and converting the problem into D and α in the formula of the solving step S312iSub-problem of optimal solution:
s314: in the course of the first iteration,for image data obtained by directly carrying out zero filling after the sub-sequence image Xs is subjected to k-space undersampling, firstly, three-dimensional overlapped blocks with the sampling sub-sequence image Xs overlapped sampling interval of 1 are divided into blocks, partial quantity image blocks are randomly selected, a DCT dictionary is used as an initial dictionary, D is fixed, and the sparse representation coefficient α is updated by adopting the following formula algorithmi，
The solution of the problem can adopt a hard threshold function, which is embodied as:
where T (g) is a hard threshold function,
s315, updating the sparse coefficient αiThereafter, α are fixediAnd updating the dictionary D by adopting a singular value decomposition method, wherein the dictionary updating problem can be converted into:
so that DTD＝I
Here, ,
wherein X ═ { X ═ X1,x2,L xm}∈Rn×mFor the image block matrix, V ═ V1,v2,L vm}∈Rk×mFor sparse coefficient matrix, tr (g) is matrix tracing operation, the dictionary update problem is changed into:
this problem is realized by the singular value decomposition algorithm:
XVT＝P∑QT,Dk+1＝PQT
this is a typical SVD of the matrix, Σ being an m × n matrix with all 0's except the elements on the main diagonal, each element on the main diagonal being called a singular value, P and Q being unitary, i.e. satisfying PTP＝I，QTQ＝I。
Preferably, in the step S3, the step of:
updating frequency-domain values of a reconstructed imageObtaining the j reconstructed subsequence by inverse Fourier transformThe method specifically comprises the following steps:
s321: the reconstruction model is learned by the compressed sensing dictionary to obtain:
s322, D and α in the formula of step S321iThe image reconstruction sub-problem becomes a common least square method problem for a unique variable xsTaking the derivative and making it equal to 0 yields:
wherein:is FuThe conjugate transpose matrix of (a);
s323: fourier transform is performed on both sides of the formula in step S322 to obtain:
i represents a unit diagonal matrix, n is the number of any pixel contained by different three-dimensional image small blocks, when the block interval takes the minimum value of 1, n is the vector dimension of the image block,for downsampling zero-padded k-space data, it can be expressed as Is a diagonal matrix of P × P, P being the dimension of the whole sub-sequence image arranged as a vector;
the above equation can be simplified as:
wherein,corresponding in k-space for the sequence to be reconstructedThe value of the position (kx, ky), omega is the set of the position with the value of 1 in the sampling matrix, lambda is q/sigma and is determined by the standard deviation of sampling noise of k space, sigma is the noise variance, q is an adjustable parameter under the sampling condition with noise, lambda is infinite under the sampling condition without noise, and the reconstructed signal of the sampling point can directly order the reconstructed signal of the sampling point to be the same as the original signal of the sampling point
The invention has the beneficial effects that: the invention provides a real-time dynamic magnetic resonance parallel reconstruction method based on adaptive orthogonal dictionary learning, which applies a relatively slow dictionary learning algorithm originally running in an off-line mode to an on-line mode, realizes real-time on-line reconstruction of MR images of any n adjacent frames by taking a first frame sampled with high precision as a reference, takes a three-dimensional image small block as a reconstruction object, and adopts an orthogonal dictionary as a sparse constraint condition and Singular Value Decomposition (SVD) algorithm to improve the reconstruction speed and precision.
Description of the drawings:
the drawings are only for purposes of illustrating and explaining the present invention and are not to be construed as limiting the scope of the present invention. Wherein:
FIG. 1 is a schematic diagram of parallel adaptive dictionary learning dMRI reconstruction according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a first frame sampling matrix and other frame sampling matrices according to an embodiment of the present invention;
FIG. 3 is a diagram illustrating the relationship between iteration count and PSNR according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of image comparison before and after reconstruction according to one embodiment of the present invention;
FIG. 5 is a schematic diagram showing comparison of an error image and an MR image reconstructed by each algorithm according to an embodiment of the present invention;
FIG. 6 is a diagram illustrating a reconstructed RMS error as a function of q according to an embodiment of the invention.
The specific implementation mode is as follows:
the invention discloses a dynamic magnetic resonance parallel reconstruction method based on self-adaptive orthogonal dictionary learning, which comprises the following steps:
s1: inputting an original dMRI sequence X, inputting an under-sampled data of a measured value y k-t space, adopting a pseudo-random ray under-sampling mode (shown in an attached figure 2), inputting a first loop iteration frequency OutLoop of an algorithm, inputting a second loop iteration frequency InnerLoop of the algorithm, and inputting dictionary learning parameters;
s2: initializing, setting the initial value of the reconstructed image to beHere, theFor the MR sub-sequence image reconstructed after the kth iteration, xzfAnd initializing the dictionary D as a DCT dictionary for the zero padding data after k-t space undersampling.
S3: the update is carried out in an iterative manner,
for i＝1:OutLoop
for j＝1：InnerLoop
updating the self-adaptive dictionary D;
updating image block sparse representation coefficients αi；
Updating frequency-domain values of a reconstructed imageObtaining the j reconstructed subsequence by inverse Fourier transform
end
Outputting a reconstructed subsequence image Xs (j) and waiting for the next subsequence Xs (j + 1);
end
s4: the sub-sequence images xs (j) are recombined into a reconstructed dMRI sequence.
Adaptive dictionary D and sparse representation coefficients αiComprises the following steps:
s310: given a dMRI sequence denoted X and its undersampled data in k-t space y, the compressed sensing dMRI reconstruction problem can be reduced to the following l0Norm minimization problem:
wherein, Fu＝diag[Fu(1),Fu(2),...,Fu(Nt)]Is a sampling matrix of k-t space, Fu(t)＝F2DPtIn which F is2DAs a two-dimensional Fourier transform operator, PtIs the t-th frame undersampled matrix, | | x | | non-woven phosphor0Is l of x0The norm, Ψ, is the sparse transform matrix and λ is a constant associated with the sampling noise.
MRI acquires k-domain (fourier transform domain) signals, and reconstructs spatial domain signals through inverse fourier transform. The fourier transform is a linear transform requiring that the number of k-domain signals must equal the number of pixels in the image domain. Lustig et al, 2007, proposed the concept of Compressed Sensing Magnetic Resonance Imaging (CSMRI) to acquire k-space signals at a sampling frequency well below the Nyquist frequency, thereby greatly reducing the imaging time and perfectly reconstructing the original image by a nonlinear reconstruction algorithm.
CSMRI needs to satisfy 3 conditions:
(1) the sparse matrix Ψ, such that the original MR image has only a few non-zero coefficients in the sparse domain;
(2) the matrix Fu Ψ -1 satisfies the RIP condition, and typically employs a random or pseudorandom sampling matrix to reduce the correlation of the sampled data.
(3) The nonlinear reconstruction algorithm can rapidly and accurately reconstruct the original image.
S311: overcomplete dictionaries have wide application in sparse representations of signals. Various non-adaptive image reconstruction methods based on image library training are gradually replaced by image reconstruction algorithms based on adaptive dictionary learning due to the defects of poor adaptability, general reconstruction effect and the like. The self-adaptation refers to that measured values collected by a compressed sensing system are used as image observation sample data to train a dictionary. Since the computation amount of dictionary learning increases rapidly with the increase of the size of the dictionary, we usually divide the image to be processed into overlapping small blocks to perform sparse representation instead of the whole image. The dictionary learning problem can be described as:
wherein x is an image sequence to be reconstructed, D is an over-complete dictionary, and RiOperator for fetching blocks for overlap, αiA sparse representation coefficient of x, Γ ═ α1,...,αICoefficient α is expressed as sparseiSet of (1), (T)0S.t. represents a sparsity threshold constant, i.e., α, which means that a constraint condition is satisfied (the same applies below)i||0≤T0In order to be a constraint condition, the method comprises the following steps of,for any i. The first item ofAnd sparse constraint | | | αi||0≤T0And the optimal sparse approximation of the overcomplete dictionary to each image block is ensured. Second itemThe variable v is a constant and is related to the standard deviation sigma of superimposed white Gaussian noise during k-space sampling, and is a data fidelity term;
because the relative position of the main organs of each frame is approximately unchanged during dMRI dynamic scanning, the first frame image of the sequence is selected as a high-precision sample (generally, the sampling rate is more than 50 percent), and a high-precision reference is provided for the reconstruction of the subsequent frame, which can be completed by one pre-scanning of the magnetic resonance machine. The first frame and any other adjacent n-1 frame image form a series of n-frame subsequence images xs (j), taking 3 frames as an example, as shown in fig. 1, Xs(j)＝[x1,x2j,x2j+1]，j＝1,2,3…，x2jRepresenting the 2j frame image in the original dMRI sequence x. As long as two adjacent frames are sampled, real-time parallel reconstruction can be carried out without waiting for the completion of the sampling of the subsequent frames. The reconstruction of each sub-sequence is independent of the other sub-sequences.
The orthogonal dictionary can ensure the irrelevance between dictionary atoms to the maximum extent, thereby ensuring the efficiency maximization in the sparse coding process. The dMRI parallel reconstruction algorithm based on the adaptive orthogonal dictionary is provided, and aims to shorten scanning waiting time, improve reconstruction speed and improve image reconstruction quality.
S312: adding orthogonal constraint D in dictionary learning processTWhen D is equal to I, the objective function in step S311 becomes:
where ν and β are regularization parameters, in order to reduce the contribution of the latter two terms and prevent the equation from over-fitting, I is the unit diagonal matrix (the same below).
The reconstruction model provided by the above formula can be decomposed into a sub-problem for solving adaptive orthogonal dictionary learning, sparse optimization of image sparse coefficients and an image reconstruction sub-problem, and the solution of the optimal solution of the objective function is realized.
S313, keeping the data of each subsequence image Xs unchanged, and converting the problem into D and α in the formula of the solving step S312iSub-problem of optimal solution:
s314: in the course of the first iteration,for image data obtained by directly carrying out zero filling after the sub-sequence image Xs is subjected to k-space undersampling, firstly, three-dimensional overlapped blocks with the sampling sub-sequence image Xs overlapped sampling interval of 1 are divided into blocks, partial quantity image blocks are randomly selected, a DCT dictionary is used as an initial dictionary, D is fixed, and the sparse representation coefficient α is updated by adopting the following formula algorithmi，
The solution of the problem can adopt a hard threshold function, which is embodied as:
where T (g) is a hard threshold function.
S315, updating the sparse coefficient αiLater (the superscript k +1 is the representation of α after updatingi) And fixing the sparse coefficient unchanged, updating the dictionary D by adopting a singular value decomposition method, and converting the dictionary updating problem into:
here, ,
wherein X ═ { X ═ X1,x2,L xm}∈Rn×mFor the image block matrix, V ═ V1,v2,L vm}∈Rk×mFor sparse coefficient matrix, tr (g) is matrix tracing operation, the dictionary update problem is changed into:
this problem is realized by the singular value decomposition algorithm:
XVT＝P∑QT,Dk+1＝PQT。
this is a typical SVD of the matrix, Σ being an m × n matrix with all 0's except the elements on the main diagonal, each element on the main diagonal being called a singular value, P and Q being unitary, i.e. satisfying PTP＝I，QTQ＝I。
Image reconstruction sub-problem: updating frequency-domain values of a reconstructed imageObtaining the j reconstructed subsequence by inverse Fourier transformThe method specifically comprises the following steps:
S321：
the formula is a classic compressed sensing dictionary learning reconstruction model, superscripts represent the meaning of the (k +1) th iteration updating, and parameter indexes refer to S311.
S322, D and α in the formula of step S321iThe image reconstruction sub-problem becomes a common least square method problem for a unique variable xsTaking the derivative and making it equal to 0 yields:
wherein:is FuThe conjugate transpose matrix of (2).
S323: solving the above equation directly is quite computationally intensive, since the reconstruction results are obtained by inverting a P × P matrix, which makes the time complexity of solving the problem O (P)3). We can transform the image space into fourier space, and perform fourier transform on both sides of the formula in step S322 to obtain:
n is the number of any pixel contained by different three-dimensional image blocks, when the block interval takes the minimum value of 1, n is the vector dimension of the image block,is FuThe conjugate transpose matrix of (a) is,for downsampling zero-padded k-space data, it can be expressed as Is a diagonal matrix of P × P, P being the dimension of the whole sub-sequence image arranged as a vector;
the above equation can be simplified as:
wherein,for the value of the sequence to be reconstructed at the corresponding position (kx, ky) in k-space, Ω is the set of positions with value 1 in the sampling matrix. And λ q/σ is an adjustable parameter under the noise-containing sampling condition, wherein σ is determined by k-space sampling noise standard deviation and is a noise variance, and q is an adjustable parameter under the noise-containing sampling condition. Under the condition of noiseless sampling, lambda is infinite, and the reconstructed signal of sampling point can be directly orderedThe reconstruction sequence is obtained by inverse Fourier transform after the data is updated in k space, the parameter q is crucial to reconstruction performance under the condition of noise-containing sampling, and the reconstruction result is insensitive to the value of q under the condition of no noise.
As shown in fig. 1, in the present embodiment, a first frame sampled with high precision is used as a reference, and real-time online reconstruction of MR images of any n adjacent frames is implemented. A three-dimensional image small block is used as a reconstruction object, and an orthogonal dictionary is used as a sparse constraint condition and a Singular Value Decomposition (SVD) algorithm to improve the reconstruction speed and accuracy.
The embodiment also provides an experiment of the dynamic magnetic resonance parallel reconstruction method based on the adaptive orthogonal dictionary learning, which comprises the following steps:
all experiments were simulated on a laptop computer with 3.0GHz Intel i7CPU using MATLAB2013 a. We chose a set of myocardial perfusion dMRI sequences (resolution 192 × 192 × 30 frames) for evaluating the performance of the algorithm. The pseudo-ray sampling matrix is used for undersampling the test image in a k-t space and simulating the accelerated imaging of a magnetic resonance machine. As shown in fig. 2, the first frame sampling rate is 50%, and the other frame sampling rate is 15%. The Peak Signal-to-Noise Rate (PSNR) is adopted as an objective evaluation method of image quality, and the unit is dB. The PSNR calculation formula is as follows:
PSNR(x,y)＝20lg(Imax/RMSE(x,y))
where x and y are the original and reconstructed images, I, respectivelymaxFor the maximum value of the image pixel, generally, to reduce the matrix operation amount, the image is normalized, and then Imax1. RMSE is the root mean square error of the two images.
Setting experimental parameters: in order to reconstruct dMRI sequences quickly and parallelly, the algorithm sets the size of a three-dimensional image block to be 3 × 3, which is the smallest, and experimental tests show that the relationship between the quality of a reconstructed image and the size of the image block is not large, but the reconstruction speed is rapidly reduced along with the increase of the size of the image block. The dictionary size is set to 27 × 108, and the number of atoms learned online each time is 5000. The comparison algorithms include three types, namely k-t SLR in an off-line mode and TV in an on-line mode and DTV, and the parameters of the three comparison experimental algorithms are all set according to the optimal parameters of the paper.
Fig. 3 shows the process of reconstructing a dMRI sub-sequence (taking 3 frames as an example) by the algorithm herein. After 14 iterations, it takes 2.8 seconds to reconstruct a low signal-to-noise ratio image (PSNR: 31.1dB) with zero padding after k-space undersampling into an image with a high signal-to-noise ratio (PSNR: 36.3 dB). Fig. 4 shows the visual contrast of the image before and after reconstruction, and it can be seen that the artifact caused by undersampling is completely removed from the reconstructed image.
Fig. 5 compares the reconstruction effect of various algorithms (under the condition of no sampling noise), and takes columns as a unit, the first row is the respective reconstructed image, the second row is the error map of the reconstructed image and the original image, and the error is amplified by 5 times for comparison in order to highlight the effect. Obviously, the visual effect is most realistic with the least error of the algorithm, especially the key heart parts.
In the presence of sampling noise, assuming that the standard deviation of white gaussian noise superimposed on k-space is σ, the value of λ q/σ in formula (9) is closely related to the reconstruction effect. Fig. 6 shows the relationship between the parameter q and the RMSE of the reconstructed image. The sampling signal-to-noise ratios were 23dB (strong noise environment), 37dB (medium noise environment) and 57dB (low noise environment), respectively. It can be seen that q is 0.005, which is an optimal choice under different sampling noise environments. Especially, under a strong noise environment, the reconstruction effect is best when q is 0.005.
The algorithm can be applied to parallel reconstruction consisting of any adjacent n frame subsequences, and the relation between the number n of the subsequence frames, the reconstructed PSNR value and the algorithm reconstruction time (under the condition of 20% sampling rate) is given in table 1. It can be seen that, with 3 frames as a sub-sequence reconstruction unit, the reconstruction accuracy (PSNR value) is the highest, and the reconstruction time is the least. And under various parameters, the reconstruction precision is within a controllable error range, so that the stability of the algorithm is reflected.
TABLE 1 relationship between number of reconstructed sub-sequence frames and reconstruction effect
The comparison results of the reconstructed PSNR values of the present algorithm with the three comparison algorithms are shown in table 1. The algorithm herein is optimal at different sampling rates. Especially under the condition of 15% low sampling rate, the performance is improved by more than 0.4dB compared with other algorithms. Taking 3 frames as an example of a dMRI subsequence, the algorithm can reconstruct one frame of image every 1.4 seconds on average, and the reconstruction speed is far faster than that of an off-line mode (k-t SLR) but slower than that of two algorithms adopting a TV method.
TABLE 2 PSNR values (dB) of reconstructed images at different sampling rates
The dynamic magnetic resonance parallel reconstruction method based on the adaptive orthogonal dictionary learning is provided. And an online parallel reconstruction mode is adopted, so that real-time high-precision reconstruction of the dMRI image is realized, and the parameter q under a noisy environment is optimized. The experimental result verifies the superiority of the method in reconstruction precision and speed. The method provides a solution for real-time online reconstruction of dMRI.
It should be understood that the above examples are only for clarity of illustration and are not intended to limit the embodiments. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. And are neither required nor exhaustive of all embodiments. And obvious variations or modifications therefrom are within the scope of the invention.

Claims (3)

1. A dynamic magnetic resonance parallel reconstruction method based on self-adaptive orthogonal dictionary learning is characterized by comprising the following steps:
s1: inputting an original dMRI sequence X, inputting a measured value y, wherein the measured value y is undersampled data of a k-t space, inputting a first loop iteration frequency OutLoop of an algorithm and a second loop iteration frequency InnerLoop of the algorithm by adopting a pseudorandom ray undersampled mode, and inputting dictionary learning parameters;
s2: initializing, setting the initial value of the reconstructed image to beHere, theFor the MR sub-sequence image reconstructed after the kth iteration, xzfInitializing a dictionary D for the zero padding data after k-t space undersampling, wherein the dictionary D is a DCT dictionary;
s3: the update is carried out in an iterative manner,
for i＝1:OutLoop
for j＝1∶InnerLoop
updating the self-adaptive dictionary D;
updating image block sparse representation coefficients αi；
Updating frequency-domain values of a reconstructed imageObtaining the j reconstructed subsequence by inverse Fourier transform
end
Outputting a reconstructed subsequence image Xs (j) and waiting for the next subsequence Xs (j + 1);
end
s4: the sub-sequence images xs (j) are recombined into a reconstructed dMRI sequence.
2. The dynamic magnetic resonance parallel reconstruction method based on adaptive orthogonal dictionary learning according to claim 1, wherein in the step S3:
adaptive dictionary D and sparse representation coefficients αiComprises the following steps:
s310: given a dMRI sequence denoted X and its undersampled data in k-t space y, the compressed sensing dMRI reconstruction problem can be reduced to the following l0Norm minimization problem:
wherein, Fu＝diag[Fu(1),Fu(2),...,Fu(Nt)]Is a sampling matrix of k-t space, Fu(t)＝F2DPtIn which F is2DAs a two-dimensional Fourier transform operator, PtIs the t-th frame undersampled matrix, y represents the undersampled k domain, | | x | | luminance0Is l of x0Norm, Ψ is the sparse transform matrix, λ is a constant related to the sampling noise;
s311: a dictionary is trained by using a measured value acquired by a compressed sensing system as image observation sample data, an image to be processed is divided into overlapped small blocks to replace the whole image for sparse representation, and the dictionary learning problem can be described as follows:
wherein x is an image sequence to be reconstructed, D is an over-complete dictionary, and RiOperator for fetching blocks for overlap, αiA sparse representation coefficient of x, Γ ═ α1,...,αICoefficient α is expressed as sparseiSet of (2), T0Represents a sparsity threshold constant, s.t. is a meaning of satisfying a constraint condition, | | αi||0≤T0In order to be a constraint condition, the method comprises the following steps of,is to any of i, wherein the first termAnd sparse constraint | | | αi||0≤T0The optimal sparse approximation of the overcomplete dictionary to each image block is ensured, and the second termThe variable v is a constant and is related to the standard deviation sigma of superimposed white Gaussian noise during sampling of k-t space;
s312: adding orthogonal constraint D in dictionary learning processTWhen D is equal to I, the objective function in step S311 becomes:
wherein, ν and β are regularization parameters for reducing contribution values of the latter two terms and preventing the equation from generating overfitting, and I is a unit diagonal matrix;
s313, keeping the data of each subsequence image Xs unchanged, and converting the problem into D and α in the formula of the solving step S312iSub-problem of optimal solution:
s314: in the course of the first iteration,for image data obtained by directly carrying out zero filling after corresponding subsequence image Xs is subjected to undersampling in k-t space, firstly, three-dimensional overlapped blocks with sampling subsequence image Xs overlapped sampling interval of 1 are divided, partial quantity image blocks are randomly selected, a DCT dictionary is used as an initial dictionary, D is fixed, and the following formula algorithm is adopted to update sparse representation coefficient αi，
The solution of the problem can adopt a hard threshold function, which is embodied as:
where T (g) is a hard threshold function,
s315, updating the sparse coefficient αiThereafter, α are fixediAnd updating the dictionary D by adopting a singular value decomposition method, wherein the dictionary updating problem can be converted into:
so that DTD＝I
Here, ,
wherein X ═ { X ═ X1,x2,L xm}∈Rn×mFor the image block matrix, V ═ V1,v2,L vm}∈Rk×mFor sparse coefficient matrix, tr (g) is matrix tracing operation, the dictionary update problem is changed into:
this problem is realized by the singular value decomposition algorithm:
XVT＝P∑QT,Dk+1＝PQT
this is a typical SVD of the matrix, Σ being an m × n matrix with all 0's except the elements on the main diagonal, each element on the main diagonal being called a singular value, P and Q being unitary, i.e. satisfying PTP＝I,QTQ＝I。
3. The dynamic magnetic resonance parallel reconstruction method based on adaptive orthogonal dictionary learning according to claim 2, wherein in the step S3:
updating frequency-domain values of a reconstructed imageObtaining the j reconstructed subsequence by inverse Fourier transformThe method specifically comprises the following steps:
s321: the reconstruction model is learned by the compressed sensing dictionary to obtain:
s322, D and α in the formula of step S321iThe image reconstruction sub-problem becomes a common least square method problem for a unique variable xsTaking the derivative and making it equal to 0 yields:
wherein:is FuThe conjugate transpose matrix of (a);
s323: fourier transform is performed on both sides of the formula in step S322 to obtain:
i represents a unit diagonal matrix, n is the number of any pixel contained by different three-dimensional image small blocks, when the block interval takes the minimum value of 1, n is the vector dimension of the image block,for downsampling zero-padded k-space data, it can be expressed as Is a diagonal matrix of P × P, P being the dimension of the whole sub-sequence image arranged as a vector;
the above equation can be simplified as:
wherein,for the value of a sequence to be reconstructed at a corresponding position (kx, ky) in a k space, omega is a set of positions with the value of 1 in a sampling matrix, lambda is q/sigma and is determined by a standard deviation of sampling noise in the k space, sigma is a noise variance, q is an adjustable parameter under a noisy sampling condition, lambda is infinite under a noiseless sampling condition, and a reconstruction signal of a sampling point can directly enable a reconstruction signal to be obtained
CN201910363197.8A 2019-04-30 2019-04-30 Dynamic magnetic resonance method for parallel reconstruction based on adaptive quadrature dictionary learning Pending CN110148193A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201910363197.8A CN110148193A (en) 2019-04-30 2019-04-30 Dynamic magnetic resonance method for parallel reconstruction based on adaptive quadrature dictionary learning

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201910363197.8A CN110148193A (en) 2019-04-30 2019-04-30 Dynamic magnetic resonance method for parallel reconstruction based on adaptive quadrature dictionary learning

Publications (1)

Publication Number Publication Date
CN110148193A true CN110148193A (en) 2019-08-20

Family

ID=67593943

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201910363197.8A Pending CN110148193A (en) 2019-04-30 2019-04-30 Dynamic magnetic resonance method for parallel reconstruction based on adaptive quadrature dictionary learning

Country Status (1)

Country Link
CN (1) CN110148193A (en)

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111292390A (en) * 2020-03-03 2020-06-16 台州学院 Dynamic magnetic resonance rapid reconstruction method
CN112834971A (en) * 2020-12-31 2021-05-25 苏州朗润医疗系统有限公司 MRI iterative self-calibration parallel imaging algorithm based on singular value decomposition
CN113267287A (en) * 2021-06-29 2021-08-17 中北大学 Method for reconstructing shock wave overpressure three-dimensional space-time field

Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105931242A (en) * 2016-04-22 2016-09-07 河海大学 Dynamic nuclear magnetic resonance image reconstruction method based on dictionary learning and time gradient
US20170053402A1 (en) * 2014-04-30 2017-02-23 Samsung Electronics Co., Ltd. Magnetic resonance imaging device and method for generating magnetic resonance image

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20170053402A1 (en) * 2014-04-30 2017-02-23 Samsung Electronics Co., Ltd. Magnetic resonance imaging device and method for generating magnetic resonance image
CN105931242A (en) * 2016-04-22 2016-09-07 河海大学 Dynamic nuclear magnetic resonance image reconstruction method based on dictionary learning and time gradient

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
张幼伟: "基于自适应字典学习的医学图像重建算法研究", 《张幼伟，中国优秀硕士学位论文全文数据库信息科技辑》 *

Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111292390A (en) * 2020-03-03 2020-06-16 台州学院 Dynamic magnetic resonance rapid reconstruction method
CN111292390B (en) * 2020-03-03 2023-04-11 台州学院 Dynamic magnetic resonance rapid reconstruction method
CN112834971A (en) * 2020-12-31 2021-05-25 苏州朗润医疗系统有限公司 MRI iterative self-calibration parallel imaging algorithm based on singular value decomposition
CN113267287A (en) * 2021-06-29 2021-08-17 中北大学 Method for reconstructing shock wave overpressure three-dimensional space-time field
CN113267287B (en) * 2021-06-29 2022-09-23 中北大学 Method for reconstructing shock wave overpressure three-dimensional space-time field

Similar Documents

Publication Publication Date Title
Qin et al. Convolutional recurrent neural networks for dynamic MR image reconstruction
Song et al. Coupled dictionary learning for multi-contrast MRI reconstruction
CN108090871B (en) Multi-contrast magnetic resonance image reconstruction method based on convolutional neural network
Ravishankar et al. MR image reconstruction from highly undersampled k-space data by dictionary learning
US8879852B2 (en) Non-contrast-enhanced 4D MRA using compressed sensing reconstruction
CN111951344B (en) Magnetic resonance image reconstruction method based on cascade parallel convolution network
CN106934778B (en) A kind of MR image rebuilding method based on small echo domain structure and non local grouping sparsity
Kelkar et al. Compressible latent-space invertible networks for generative model-constrained image reconstruction
US20210217213A1 (en) MRI image reconstruction from undersampled data using adversarially trained generative neural network
CN109345473B (en) Image processing method based on self-adaptive fast iterative shrinkage threshold algorithm
CN110148193A (en) Dynamic magnetic resonance method for parallel reconstruction based on adaptive quadrature dictionary learning
CN112991483B (en) Non-local low-rank constraint self-calibration parallel magnetic resonance imaging reconstruction method
Jacob et al. Improved model-based magnetic resonance spectroscopic imaging
CN105931242A (en) Dynamic nuclear magnetic resonance image reconstruction method based on dictionary learning and time gradient
CN109920017B (en) Parallel magnetic resonance imaging reconstruction method of joint total variation Lp pseudo norm based on self-consistency of feature vector
CN117011409B (en) Multi-position physical intelligent high-definition diffusion magnetic resonance data generation method
Yakkundi et al. Convolutional LSTM: A deep learning approach for dynamic MRI reconstruction
CN105976412A (en) Offline-dictionary-sparse-regularization-based CT image reconstruction method in state of low tube current intensity scanning
CN113866694B (en) Rapid three-dimensional magnetic resonance T1 quantitative imaging method, system and medium
Li et al. Highly undersampled MR image reconstruction using an improved dual-dictionary learning method with self-adaptive dictionaries
CN113674379B (en) MRI reconstruction method, system and computer readable storage medium based on co-sparse analysis model of reference support set
Wang et al. LANTERN: Learn analysis transform network for dynamic magnetic resonance imaging
CN113487507A (en) Dual-domain recursive network MR reconstruction method based on multi-module feature aggregation
Singh et al. Compressive sensing magnetic resonance image reconstruction and denoising using convolutional neural network
CN113298907B (en) Nuclear magnetic image reconstruction method based on gamma nuclear norm and total variation

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
RJ01 Rejection of invention patent application after publication

Application publication date: 20190820

RJ01 Rejection of invention patent application after publication