CN111598963B - Quantitative magnetic susceptibility imaging method and device based on dictionary learning - Google Patents

Quantitative magnetic susceptibility imaging method and device based on dictionary learning Download PDF

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CN111598963B
CN111598963B CN202010381262.2A CN202010381262A CN111598963B CN 111598963 B CN111598963 B CN 111598963B CN 202010381262 A CN202010381262 A CN 202010381262A CN 111598963 B CN111598963 B CN 111598963B
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陈阳
杜嘉程
麦筱莉
申云鹏
顾宁
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Abstract

The invention discloses a quantitative magnetic susceptibility imaging method and device based on dictionary learning, wherein the method comprises the following steps: (1) acquiring magnetic resonance GRE sequence data, including GRE amplitude data and GRE phase data; (2) estimating a magnetic field map by adopting a least square fitting method according to the collected GRE phase data; (3) phase unwrapping for the estimated field map b (r); (4) removing a background field from the magnetic field map subjected to phase unwrapping by adopting a dipole field projection method; (5) performing dictionary training according to the collected GRE amplitude data to obtain a dictionary; (6) and (4) reconstructing the magnetic susceptibility by adopting a dictionary learning method according to the dictionary obtained by training and the magnetic field map with the background field removed to obtain the magnetic susceptibility distribution, thereby completing the quantitative magnetic susceptibility imaging. The reconstructed image quality is higher.

Description

Quantitative magnetic susceptibility imaging method and device based on dictionary learning
Technical Field
The invention relates to magnetic susceptibility reconstruction, in particular to a quantitative magnetic susceptibility imaging method and device based on dictionary learning.
Background
Magnetic Resonance Imaging (MRI) technology performs tomography on internal structures by detecting nuclear magnetic resonance signals of water protons in tissues to reflect changes of physiological information such as tissue functions and metabolism, wherein Quantitative magnetic Susceptibility imaging (Quantitative Susceptibility Mapping QSM) is an emerging new technology for quantitatively calculating tissue magnetic Susceptibility in MRI, is post-processing based on a magnetic field map obtained from phase data of gradient echo (GRE) MRI, and can be applied to Quantitative analysis of in vivo iron, calcification and blood oxygen saturation and concentration, and QSM has been applied to various biomedical problems including (1) demyelination, inflammation and overloading in multiple sclerosis; (2) neurodegeneration and iron overload in alzheimer's disease, parkinson's disease and huntington's disease; (3) changes in metabolic oxygen consumption, (4) bleeding, including microhemorrhages and blood degradation; (5) bone mineralization; (6) quantitative calculation of magnetic susceptibility in drug delivery using magnetic nanocarriers, and the like.
The QSM conventional algorithm flow is as follows:
(1) MRI phase signal processing
An estimated magnetic field map was fitted using the amplitude and phase maps:
Figure BDA0002482153350000011
wherein S is the complex signal of the jth echo, A is the amplitude signal of the jth echo, and TE is the echo time of the jth echo signal, thereby fitting the estimated magnetic field map b (r).
Since the phase signals are all wound between [ -pi, pi), phase unwrapping is required to obtain an unwrapped phase estimate.
And finally, removing a background field and filtering background components.
(2) Magnetic susceptibility inversion
The susceptibility distributions χ and b (r) can be expressed as a convolution of χ and a dipole kernel:
Figure BDA0002482153350000012
wherein the convolution kernel
Figure BDA0002482153350000021
R ═ x, y, z ∈ R denotes a spatial coordinate vector, transformed into the fourier domain b (k) ═ d (k) · x (k), where
Figure BDA0002482153350000022
Because the dipole is nucleated in
Figure BDA0002482153350000023
The two cone regions of (a) have a value of 0, and therefore the susceptibility distribution cannot be calculated directly by dividing x (k) ═ b (k)/d (k), and therefore calculating the susceptibility distribution is also an ill-defined inverse problem.
In order to solve the ill-conditioned problem in the magnetic susceptibility inversion, the following conventional methods are adopted:
COSMOS: namely, a multi-directional sampling susceptibility computing method (COSMOS), which is the most effective QSM reconstruction algorithm and can effectively suppress streak artifacts in a reconstructed image, but the method needs to acquire data in multiple directions, is time-consuming and labor-consuming, and is basically not clinically implemented, and the reconstruction of a susceptibility distribution map by using data acquired in a single direction is more meaningful, such as TKD algorithm and MEDI algorithm, which are respectively reconstructed from a fourier domain and a spatial domain, so that the result of the COSMOS method is mostly used as a gold standard to verify the reconstruction accuracy of other reconstruction algorithms.
TKD: thresholded Truncation (TKD) which replaces the value of the dipole core D (k) which is less than the threshold value, namely DTKD(k) Max (d (k), thr), then by
Figure BDA0002482153350000024
The magnetic susceptibility distribution is calculated. The algorithm has the advantages of simple implementation, but the disadvantages are obvious, namely, it is difficult to find a proper threshold, if the threshold is small, the streak artifact cannot be effectively inhibited, if the threshold is large, the calculation of the overall susceptibility value is small, and other artifacts may be introduced by an unreasonable threshold.
MEDI: a morphological similarity based dipole nuclear inversion algorithm (MEDI) with the following objective function:
Figure BDA0002482153350000025
wherein W is a diagonal weighting matrix to reflect the reliability of each voxel value in a magnetic field map b (r), namely the higher the signal-to-noise ratio is, the higher the reliability is, to prevent the noise in b (r) from being transmitted to the subsequent calculation of magnetic susceptibility distribution, M is an anatomical prior, which is a gradient weighting matrix, the value of the tissue boundary is 0, and the value of the non-boundary is 1, so as to prevent over-smoothing, thereby blurring the tissue boundary, and G is a gradient operator.
The method introduces prior knowledge, namely the anatomical structures of the amplitude map and the magnetic susceptibility distribution map are consistent, and through the constraint of the gradient weighting matrix and the diagonal weighting matrix, the MEDI algorithm can effectively inhibit artifacts in the magnetic susceptibility distribution map compared with the TKD algorithm, so that the quality of reconstructed images is effectively improved, but the total reconstruction quality still has a liftable space.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the problems in the prior art, the invention provides a quantitative magnetic susceptibility imaging method and device based on dictionary learning, and the reconstruction quality is higher.
The technical scheme is as follows: the quantitative magnetic susceptibility imaging method based on dictionary learning comprises the following steps:
(1) acquiring magnetic resonance GRE sequence data, including GRE amplitude data and GRE phase data;
(2) estimating a magnetic field map b (r) by adopting a least square fitting method according to the collected GRE phase data;
(3) performing phase unwrapping on the estimated magnetic field map b (r);
(4) removing a background field from the magnetic field map subjected to phase unwrapping by adopting a dipole field projection method;
(5) performing dictionary training according to the collected GRE amplitude data to obtain a dictionary;
(6) and according to the dictionary obtained by training and the magnetic field map with the background field removed, reconstructing the magnetic susceptibility by adopting a dictionary learning method to obtain magnetic susceptibility distribution, and completing quantitative magnetic susceptibility imaging.
Further, GRE amplitude data is used as a training picture for dictionary training in the step (5), and a KSVD algorithm based on blocks is used for training the dictionary to obtain the dictionary.
Further, the step (6) specifically comprises:
(6.1) establishing an objective function:
Figure BDA0002482153350000031
wherein χ represents the magnetic susceptibilityDistribution, D denotes dipole nuclei, B denotes the fourier transform of the magnetic field map with the background field removed, and B ═ DX, X denotes the fourier transform of χ, W is a diagonal weighting matrix, λ1、λ2For regularizing coefficients, Ei,j,kAn extraction operator representing a block centered on a three-dimensional coordinate (i, j, k) in the susceptibility distribution, Z representing a trained dictionary, αi,j,kRepresenting the sparse coefficient of a block taking a three-dimensional coordinate (i, j, k) as the center in the magnetic susceptibility distribution, wherein M is boundary information extracted from GRE amplitude data, and G is a gradient operator;
and (6.2) solving the objective function through a conjugate gradient descent algorithm to obtain the magnetic susceptibility distribution x.
Further, the sparse coefficient αi,j,kIs found by an orthogonal matching pursuit algorithm so that xi,j,k＝Zαi,j,k，χi,j,kRepresenting a block centered on a three-dimensional coordinate (i, j, k) in the susceptibility distribution.
The invention discloses a quantitative magnetic susceptibility imaging device based on dictionary learning, which comprises:
the data acquisition module is used for acquiring magnetic resonance GRE sequence data, including GRE amplitude data and GRE phase data;
the magnetic field map estimation module is used for estimating a magnetic field map b (r) by adopting a least square fitting method according to the collected GRE phase data;
a phase unwrapping module for phase unwrapping the estimated magnetic field map b (r);
the background field removing module is used for removing the background field from the magnetic field image after phase unwrapping by adopting a dipole field projection method;
the dictionary training module is used for carrying out dictionary training according to the collected GRE amplitude data to obtain a dictionary;
and the magnetic susceptibility reconstruction module is used for reconstructing magnetic susceptibility by adopting a dictionary learning method according to the dictionary obtained by training and the magnetic field map with the background field removed to obtain magnetic susceptibility distribution and finish quantitative magnetic susceptibility imaging.
Further, GRE amplitude data is used as a training picture in the dictionary training module, and a KSVD algorithm based on blocks is used for training the dictionary to obtain the dictionary.
Further, the magnetic susceptibility reconstruction module specifically includes:
an objective function establishing unit, configured to establish an objective function:
Figure BDA0002482153350000041
wherein χ represents a magnetic susceptibility distribution, D represents a dipole core, B represents a fourier transform of a magnetic field map from which a background field is removed, B ═ DX, X represents the fourier transform of χ, W is a diagonal weighting matrix, and λ1、λ2For regularizing coefficients, Ei,j,kAn extraction operator representing a block centered on a three-dimensional coordinate (i, j, k) in the susceptibility distribution, Z representing a trained dictionary, αi,j,kRepresenting the sparse coefficient of a block taking a three-dimensional coordinate (i, j, k) as the center in the magnetic susceptibility distribution, wherein M is boundary information extracted from GRE amplitude data, and G is a gradient operator;
and the solving unit is used for solving the objective function through a conjugate gradient descent algorithm to obtain the susceptibility distribution x.
Further, the sparse coefficient αi,j,kIs found by an orthogonal matching pursuit algorithm so that xi,j,k＝Zαi,j,k，χi,j,kRepresenting a block centered on a three-dimensional coordinate (i, j, k) in the susceptibility distribution.
Has the advantages that: compared with the prior art, the invention has the following remarkable advantages: the susceptibility inversion has lower mean square error and lower high frequency error, so that the reconstructed image quality is higher; and the training data of the dictionary is the self amplitude diagram, and no additional training data is needed.
Drawings
FIG. 1 is a schematic flow chart of a dictionary learning-based quantitative magnetic susceptibility imaging method provided by the present invention;
FIG. 2 is gold standard data of the QSM reconstruction results;
FIG. 3 is a graph showing the results of comparing the method of the present invention with MEDI and TKD algorithms.
Detailed Description
The embodiment provides a quantitative magnetic susceptibility imaging method based on dictionary learning, as shown in fig. 1, including:
(1) magnetic resonance GRE sequence data is acquired, including GRE amplitude data and GRE phase data.
(2) And estimating the magnetic field map b (r) by adopting a least square fitting method according to the collected GRE phase data.
In gradient echo MRI, the phase varies with echo time due to the non-uniform electric field. Although the phase noise distribution is complex, the noise in the real part and imaginary part of the complex MR signal is normally distributed. Therefore, the problem of estimating the magnetic field map b (r) from complex MR signals measured at multiple echo times can be expressed as a non-linear least squares fitting problem, from which the magnetic field map b (r) can be estimated:
Figure BDA0002482153350000051
wherein r represents three-dimensional space coordinates, S is a complex signal of the jth echo, A is an amplitude signal of the jth echo, and TE is an echo time of the jth echo signal, thereby fitting an estimated magnetic field map b (r), omega0Is the initial phase.
(3) Phase unwrapping is performed for the estimated magnetic field map b (r).
ω0Is the initial phase because
Figure BDA0002482153350000052
Middle omega0Periodicity exists, so the estimated b (r) jumps among voxels in the range of [ -pi, pi), so frequencies outside the range of [ -pi, pi) are wrapped in [ -pi, pi), resulting in a jump of j.2pi in the output phase signal, j is an integer, j.2pi needs to be added to estimate b (r) to represent phase wrapping, in the following formula, omega.2 piw(r) is a phase of winding, ω (r) is a phase after unwinding, and j (r) is an integer.
Figure BDA0002482153350000053
In this embodiment, a region growing method is used to perform phase unwrapping, a point at the center of a visual field is selected as a seed point, then neighboring points are traversed, 2 pi of integral multiples of phase values of the neighboring points is increased or decreased according to the difference between the neighboring points and the phase value of the point, and then the phase unwrapping is gradually expanded until all the points are traversed, thereby completing the phase unwrapping.
(4) And removing the background field from the magnetic field image after phase unwrapping by adopting a dipole field projection method.
The background field is caused by the nonuniformity of the magnetization source and the main magnetic field outside the ROI (region of interest) and can influence the calculation of the magnetic susceptibility in the ROI, so that the accurate magnetic susceptibility distribution needs to be calculated, and the background field components need to be filtered outBWherein d is a dipole nucleus,
Figure BDA0002482153350000061
for convolution operations:
Figure BDA0002482153350000062
(5) and performing dictionary training according to the collected GRE amplitude data to obtain a dictionary Z.
During training, GRE amplitude data is used as a training picture, and a block-based KSVD algorithm is used for training a dictionary to obtain the dictionary. The block size is [6,6,4], the number of dictionary atoms is 500, and the dictionary size is 144 × 500.
(6) And (4) reconstructing the magnetic susceptibility by adopting a dictionary learning method according to the dictionary obtained by training and the magnetic field map with the background field removed to obtain the magnetic susceptibility distribution, thereby completing the quantitative magnetic susceptibility imaging.
The magnetic susceptibility inversion is the most important of QSM algorithmAn important step, in the Fourier domain, the magnetic field map B (k) can be expressed as the product of the dipole kernel D (k) and the susceptibility distribution X (k), since D (k) is
Figure BDA0002482153350000063
The two cone values of (a) are 0 and the value near the cone is extremely small, even small noise is amplified when the susceptibility x (k) is directly solved by division, and streak artifacts are generated, so that proper regularization is required to solve the ill-posed inverse problem. B (k) is a fourier transform of a magnetic field map from which the background field is removed, abbreviated as B, D (k) is abbreviated as D, and a magnetic susceptibility distribution X (k) represents a fourier transform of χ, abbreviated as X.
In this embodiment, a dictionary learning-based reconstruction method is adopted to reconstruct the magnetic susceptibility, which specifically includes:
(6.1) establishing an objective function:
Figure BDA0002482153350000064
wherein χ represents a magnetic susceptibility distribution, D represents a dipole core, B represents a fourier transform of a magnetic field map from which a background field is removed, B ═ DX, X represents the fourier transform of χ, W is a diagonal weighting matrix, and λ1、λ2For regularizing coefficients, Ei,j,kAn extraction operator representing a block centered on a three-dimensional coordinate (i, j, k) in the susceptibility distribution, Z representing a trained dictionary, αi,j,kRepresenting the sparse coefficient of a block taking a three-dimensional coordinate (i, j, k) as the center in the magnetic susceptibility distribution, wherein M is boundary information extracted from GRE amplitude data, and G is a gradient operator; sparse coefficient alphai,j,kIs found by an orthogonal matching pursuit algorithm so that x isi,j,k＝Zαi,j,k，χi,j,kRepresenting a block centered on a three-dimensional coordinate (i, j, k) in the susceptibility distribution.
And (6.2) solving the objective function through a conjugate gradient descent algorithm to obtain a magnetic susceptibility distribution chi, and presenting the magnetic susceptibility distribution chi, namely the reconstructed magnetic susceptibility image.
The present embodiment also provides a quantitative magnetic susceptibility imaging device based on dictionary learning, including:
the data acquisition module is used for acquiring magnetic resonance GRE sequence data, including GRE amplitude data and GRE phase data;
the magnetic field map estimation module is used for estimating a magnetic field map b (r) by adopting a least square fitting method according to the collected GRE phase data;
a phase unwrapping module for phase unwrapping the estimated magnetic field map b (r);
the background field removing module is used for removing the background field from the magnetic field image after phase unwrapping by adopting a dipole field projection method;
the dictionary training module is used for carrying out dictionary training according to the collected GRE amplitude data to obtain a dictionary;
and the magnetic susceptibility reconstruction module is used for reconstructing the magnetic susceptibility by adopting a dictionary learning method according to the dictionary obtained by training and the magnetic field map with the background field removed to obtain magnetic susceptibility distribution and finish quantitative magnetic susceptibility imaging.
Further, the magnetic susceptibility reconstruction module specifically includes:
an objective function establishing unit, configured to establish an objective function:
Figure BDA0002482153350000071
wherein χ represents a magnetic susceptibility distribution, D represents a dipole core, B represents a fourier transform of a magnetic field map from which a background field is removed, B ═ DX, X represents the fourier transform of χ, W is a diagonal weighting matrix, and λ1、λ2For regularizing coefficients, Ei,j,kAn extraction operator representing a block centered on a three-dimensional coordinate (i, j, k) in the susceptibility distribution, Z representing a trained dictionary, αi,j,kRepresenting the sparse coefficient of a block taking a three-dimensional coordinate (i, j, k) as the center in the magnetic susceptibility distribution, wherein M is boundary information extracted from GRE amplitude data, and G is a gradient operator; the sparse coefficient αi,j,kIs found by an orthogonal matching pursuit algorithm so that x isi,j,k＝Zαi,j,k，χi,j,kRepresenting the three-dimensional seating in the susceptibility distributionThe block with index (i, j, k) as the center.
And the solving unit is used for solving the objective function through a conjugate gradient descent algorithm to obtain the magnetic susceptibility distribution x.
The device corresponds to the above methods one to one, and reference to the methods is not repeated for the parts which are not described in detail.
In order to verify the effect of the invention, data disclosed by a 2016 QSM reconstructed challenge race is used for verifying the improvement of the method disclosed by the invention relative to the traditional method, a gold standard data obtained by adopting a COSMOS algorithm is shown in figure 2, and TKD, MEDI and DL are shown in figure three.
While the invention has been described in connection with what is presently considered to be the most practical and preferred embodiment, it is to be understood that the invention is not to be limited to the disclosed embodiment, but on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims.

Claims (6)

1. A quantitative magnetic susceptibility imaging method based on dictionary learning is characterized by comprising the following steps:
(1) acquiring magnetic resonance GRE sequence data, including GRE amplitude data and GRE phase data;
(2) estimating a magnetic field map b (r) by a least square fitting method according to the collected GRE phase data;
(3) phase unwrapping for the estimated field map b (r);
(4) removing a background field from the magnetic field graph subjected to phase unwrapping by adopting a dipole field projection method;
(5) performing dictionary training according to the collected GRE amplitude data to obtain a dictionary;
(6) according to the dictionary obtained by training and the magnetic field map with the background field removed, reconstructing the magnetic susceptibility by adopting a dictionary learning method to obtain magnetic susceptibility distribution and finish quantitative magnetic susceptibility imaging; the method specifically comprises the following steps:
(6.1) establishing an objective function:
Figure FDA0003604767550000011
wherein χ represents a magnetic susceptibility distribution, D represents a dipole core, B represents a fourier transform of a magnetic field map from which a background field is removed, B ═ DX, X represents the fourier transform of χ, W is a diagonal weighting matrix, and λ1、λ2For regularizing coefficients, Ei,j,kAn extraction operator representing a block centered on a three-dimensional coordinate (i, j, k) in the susceptibility distribution, Z representing a trained dictionary, αi,j,kRepresenting the sparse coefficient of a block taking a three-dimensional coordinate (i, j, k) as the center in the magnetic susceptibility distribution, wherein M is boundary information extracted from GRE amplitude data, and G is a gradient operator;
and (6.2) solving the objective function through a conjugate gradient descent algorithm to obtain the susceptibility distribution χ.
2. The dictionary learning-based quantitative magnetic susceptibility imaging method according to claim 1, wherein: and (5) adopting GRE amplitude data as a training picture for dictionary training, and adopting a KSVD algorithm based on blocks to train the dictionary to obtain the dictionary.
3. The dictionary learning-based quantitative magnetic susceptibility imaging method according to claim 1, characterized in that: the sparse coefficient αi,j,kIs found by an orthogonal matching pursuit algorithm so that x isi,j,k＝Zαi,j,k，χi,j,kRepresenting a block centered on a three-dimensional coordinate (i, j, k) in the susceptibility distribution.
4. A quantitative magnetic susceptibility imaging apparatus based on dictionary learning, characterized by comprising:
the data acquisition module is used for acquiring magnetic resonance GRE sequence data, including GRE amplitude data and GRE phase data;
the magnetic field map estimation module is used for estimating a magnetic field map b (r) by adopting a least square fitting method according to the collected GRE phase data;
a phase unwrapping module for phase unwrapping the estimated magnetic field map b (r);
the background field removing module is used for removing the background field from the magnetic field image after phase unwrapping by adopting a dipole field projection method;
the dictionary training module is used for carrying out dictionary training according to the collected GRE amplitude data to obtain a dictionary;
the magnetic susceptibility reconstruction module is used for reconstructing magnetic susceptibility by adopting a dictionary learning method according to the dictionary obtained by training and the magnetic field map with the background field removed to obtain magnetic susceptibility distribution and finish quantitative magnetic susceptibility imaging;
the magnetic susceptibility reconstruction module specifically comprises:
an objective function establishing unit, configured to establish an objective function:
Figure FDA0003604767550000021
wherein χ represents a magnetic susceptibility distribution, D represents a dipole core, B represents a fourier transform of a magnetic field map from which a background field is removed, B ═ DX, X represents the fourier transform of χ, W is a diagonal weighting matrix, and λ1、λ2For regularizing coefficients, Ei,j,kAn extraction operator representing a block centered on a three-dimensional coordinate (i, j, k) in the susceptibility distribution, Z representing a trained dictionary, αi,j,kExpressing the sparse coefficient of a block taking a three-dimensional coordinate (i, j, k) as a center in the magnetic susceptibility distribution, wherein M is boundary information extracted from GRE amplitude data, and G is a gradient operator;
and the solving unit is used for solving the objective function through a conjugate gradient descent algorithm to obtain the magnetic susceptibility distribution x.
5. The dictionary learning-based quantitative magnetic susceptibility imaging apparatus according to claim 4, wherein: and the dictionary training module adopts GRE amplitude data as a training picture and adopts a KSVD algorithm based on blocks to train a dictionary to obtain the dictionary.
6. Quantitative magnetic susceptibility imaging device based on dictionary learning according to claim 4The method is characterized in that: the sparse coefficient αi,j,kIs found by an orthogonal matching pursuit algorithm so that x isi,j,k＝Zαi,j,k，χi,j,kRepresenting a block centered on a three-dimensional coordinate (i, j, k) in the susceptibility distribution.
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