CN112526423B - Parallel magnetic resonance imaging algorithm based on conjugation and interlayer information - Google Patents
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Abstract
The invention discloses a parallel magnetic resonance imaging algorithm based on conjugation and interlayer information, which comprises the following steps of performing R times undersampling on a gradient positive high-frequency part and a gradient negative high-frequency part of an imaging object, and taking a middle low-frequency part as a calibration area to perform full sampling to obtain a matrix F; constructing a prediction matrix A of undersampled data; constructing a weight calculation matrix B by using the calibration areas of the matrix F of the layer and the adjacent layer; constructing a column vector matrix C of a weight calculation matrix B; obtaining a column vector matrix C according to the product of the weight calculation matrix B and the weight matrix W, and obtaining the weight matrix W in the interpolation window by adopting a least square method; constructing a prediction matrix D of undersampled line data; obtaining a column vector E according to the product of the prediction matrix D and the weight matrix W in the interpolation window; filling to obtain a reconstruction matrix H, and obtaining a parallel magnetic resonance imaging image after Fourier transformation. The method has the advantages of high imaging speed, rich information content of the prediction source matrix, higher signal-to-noise ratio and the like.
Description
Technical Field
The invention relates to the technical field of magnetic resonance imaging, in particular to a parallel magnetic resonance imaging algorithm based on conjugate and interlayer information.
Background
Parallel magnetic resonance imaging (p-MRI) is a major technological breakthrough in the fields of medical image high-speed imaging and image reconstruction, and has been applied to various large magnetic resonance devices. In the parallel magnetic resonance imaging process, magnetic resonance K space signals are acquired by a multi-channel phased array coil, and because each channel of the phased array coil contains information of an adjacent channel, the information of a downsampling part can be estimated through the information of the adjacent coil, and the magnetic resonance scanning speed is improved by reducing the frequency of phase encoding.
Currently, image reconstruction algorithms in the prior art are mainly divided into two categories:
firstly, based on reconstruction of an image domain, the algorithm mainly uses coil sensitivity to reconstruct an image to obtain an artifact-free image, the representative algorithm is SENSE (Sensitivity Encoding) and an expanding method SC-SENSE (Self-califying), PILS (Local Sensitivities) and the like which are developed later, the algorithm requires a channel coil to have more accurate sensitivity, coil sensitivity information is calculated by collecting low-frequency signals, when the sensitivity is known, chaari et al combine compressed sensing with SENSE, and a regularization term is added, so that a better reconstruction effect is obtained, but accurate estimation is often very difficult. The invention relates to a parallel magnetic resonance imaging method and device based on adaptive joint sparse coding and a computer readable medium, which are disclosed in Chinese patent application No. 201711246873.0.
Secondly, based on a K space-based coil-by-coil reconstruction technology, the technology collects middle line data as self-calibration signals (ACS), the final image is directly reconstructed by multiple channels, coil sensitivity is not required to be estimated, weight coefficients of the multiple channels of coils are calculated by undersampled K space data, undersampled missing data are fitted by the weight coefficients, the undersampled missing data are reconstructed into diagnostic images, and representative algorithms are AUTO-SMASH (Simulataneous Acquisition of Spatial Harmonics), GRAPPA (Generalized AUTO-calibrating Partially Parallel Acquisitions), VD-AUTO-SMASH algorithm and the like. The Chinese patent application No. 201510216413.8, named as a parallel magnetic resonance imaging phase processing method, is: performing Fourier inverse transformation on K space data acquired by the multichannel coils in parallel magnetic resonance imaging to obtain the amplitude and the phase of each coil image; constructing a reference coil image, and estimating the spatial sensitivity distribution of each coil of the multiple channels; performing two-dimensional Fourier transform on the spatial sensitivity of the reference coil image, and intercepting an intermediate matrix as a convolution kernel; constructing a K space data convolution model, and solving the joint weight W of the coil; obtaining a virtual coil K space value, and obtaining a virtual coil image through Fourier inverse transformation; the phase is unwound, and the phase of the virtual coil image background is removed; the mask image is used to extract the phase of the region of interest.
At present, in the process of calculating a reconstructed coefficient matrix by using the GRAPPA algorithm in the prior art, as the acceleration multiple is increased, the condition number of the equation coefficient matrix is increased, the available information quantity is reduced, and the pathological degree of the equation is increased. So that noise is amplified during the inversion matrix process.
In addition, the GRAPPA algorithm in the prior art can well avoid the convolution artifact for 2 times of acceleration, but has poor reconstruction effect under the condition of acceleration exceeding 2 times, obvious noise and still has the convolution artifact residues. The method is a problem to be solved in the application fields of magnetic resonance three-dimensional acquisition, dynamic imaging, real-time imaging, plane echo imaging and the like which are sensitive to the scanning speed.
In the chinese patent application No. 2020111409917.9, entitled "an improved algorithm for parallel magnetic resonance imaging", although the quality of reconstruction for parallel magnetic resonance imaging is 3 times and less, the amount of empty information is too large under the acceleration condition of 3 times or more, and if only the conjugate information in the layer is still used to add to the interpolation window, although the imaging effect can be significantly improved, there is still a problem that the amount of information is too small, the signal-to-noise ratio is insufficient, and the ideal imaging quality cannot be achieved.
Therefore, it is highly desirable to provide a parallel magnetic resonance imaging algorithm based on conjugate and interlayer information, which uses conjugate corresponding line data and adjacent layers to increase the data volume in the interpolation window, increase the information volume of the prediction source matrix, and improve the signal to noise ratio while accelerating.
Disclosure of Invention
Aiming at the problems, the invention aims to provide a parallel magnetic resonance imaging algorithm based on conjugation and interlayer information, and adopts the following technical scheme:
the parallel magnetic resonance imaging algorithm based on conjugate and interlayer information utilizes K space data received by a phased array coil, wherein the phased array coil is provided with L, L is a positive integer greater than 1, and the method comprises the following steps:
the method comprises the steps of performing R times undersampling on a gradient positive high-frequency part and a gradient negative high-frequency part of an imaging object, and performing full sampling by taking a middle low-frequency part as a calibration area to obtain a matrix F; the sampling scanning is performed on Z layers in total, wherein Z is a positive integer greater than 1;
constructing a prediction matrix A of a matrix F: filling the ith row sampling data of the z+1th layer adjacent to the z layer in the matrix F, and filling conjugate symmetrical data in the z layer;
constructing a weight calculation matrix B by using the calibration areas of the matrix F of the layer and the adjacent layers: the weight calculation matrix B is a transformation combination of K space data of L phased array coils of a z-th layer at a position x (i, j, L) and interpolation window data of a position x (-i, j, L), and a transformation combination of K space data of L phased array coils of a z+1-th layer at a position x (i, j, L) and interpolation window data of a position x (-i, j, L);
moving the position of x (i, j, 1) in the calibration area to obtain any row of data of the weight calculation matrix B, and recording the data of the position x (i, j, l), wherein any data is one row to obtain a column vector matrix C;
obtaining a column vector matrix C according to the product of the weight calculation matrix B and the weight matrix W, and obtaining the weight matrix W in the interpolation window by fitting through a least square method;
querying the data which is not sampled in the matrix F and recording the position as
Position in prediction matrix a
An interpolation window is arranged at the position, and a prediction matrix D of undersampled line data is formed;
obtaining a column vector E according to the product of the prediction matrix D and the weight matrix W in the interpolation window;
position is to
Corresponding positions in the matrix F in the data filling of (a), and removing the originally filled 0 to obtain a reconstructed matrix H, and obtaining a parallel magnetic resonance imaging image after Fourier transformation.
Further, the construction process of the matrix F is as follows:
dividing K space data received by any phased array coil into two symmetrical parts of positive gradient and negative gradient;
sampling is started from a low-frequency part of the gradient in the forward direction, and in the z-th layer, if the gradient is in the forward direction, the q+z% R line is sampled; the q satisfies q% r=1;
if the gradient is negative, sampling the- (q+z% R+1) row;
and filling the non-sampled rows with 0, and fully sampling the middle low-frequency part to obtain a matrix F.
Preferably, R is 4 or 5 or 6.
Compared with the prior art, the invention has the following beneficial effects:
(1) The invention can increase the data in the interpolation window, not only utilizes the intra-layer conjugate information, but also adds the information of the adjacent layers to fit, thereby increasing the information quantity, increasing the signal-to-noise ratio and reducing the convolution artifact; for example, if information of adjacent 1 layer is added, 3 lines of fitting data can be added, and if data of upper and lower adjacent 2 layers is added, 5 lines can be added;
(2) The invention adopts undersampling to obtain high-frequency sampling data of positive and negative gradients, and adopts full sampling to obtain middle low-frequency part, thereby reducing sampling data, improving imaging speed and ensuring full information quantity;
(3) On the basis of conjugate symmetry, the invention can obtain more useful information under the condition of downsampling, thereby effectively improving the signal-to-noise ratio;
(4) The method utilizes the calibration area of the matrix F of the layer and the adjacent layer to obtain the weight matrix in the interpolation window, applies the weight matrix in the interpolation window to the undersampled area to obtain the data around the undersampled signal, and reconstructs undersampled points by using the prediction source matrix with larger information quantity;
in conclusion, the method has the advantages of abundant information quantity of the prediction source matrix, higher signal to noise ratio and the like, and has high practical value and popularization value in the technical field of magnetic resonance imaging.
Drawings
For a clearer description of the technical solutions of the embodiments of the present invention, the drawings to be used in the embodiments will be briefly described below, it being understood that the following drawings only illustrate some embodiments of the present invention and should not be considered as limiting the scope of protection, and other related drawings may be obtained according to these drawings without the need of inventive effort for a person skilled in the art.
Fig. 1 is a schematic diagram of the structure of a matrix F according to the present invention.
Fig. 2 is a schematic diagram of the structure of a prediction matrix a according to the present invention.
Detailed Description
For the purposes, technical solutions and advantages of the present application, the present invention will be further described with reference to the accompanying drawings and examples, and embodiments of the present invention include, but are not limited to, the following examples. All other embodiments, which can be made by one of ordinary skill in the art without undue burden from the present disclosure, are within the scope of the present application based on the embodiments herein.
Examples
As shown in fig. 1 to 2, the present embodiment provides a parallel magnetic resonance imaging algorithm based on conjugate and interlayer information, using K-space data received by a phased array coil, the phased array coil being provided with L, the parallel magnetic resonance imaging algorithm of the present embodiment includes the steps of:
the method comprises the steps that firstly, an imaging system of magnetic resonance equipment is utilized to perform R (4, 5 and 6) times undersampling on a gradient positive high-frequency part and a gradient negative high-frequency part of an imaging object, and a middle low-frequency part (16 rows) is used as a calibration area to perform full sampling to obtain a matrix F;
in this embodiment, K-space data received by any phased array coil is divided into two symmetrical parts, positive and negative, of the gradient; sampling from a low-frequency part of the positive direction of the gradient, and sampling the q+z% R line when the gradient is positive direction in the cross section of the z layer; the q satisfies q% r=1; if the gradient is negative, sampling- (q+z% R+1); and filling the non-sampled rows with 0, and fully sampling the middle low-frequency part to obtain a matrix F.
Secondly, constructing a prediction matrix A of a matrix F: in the undersampling region, filling the ith row sampling data of the z+1th layer adjacent to the z layer in the matrix F, and filling conjugate symmetrical data in the z layer; since it has been ensured in the first step that when the mth line is sampled data, then the-mth line must be undersampled data, intra-layer conjugate symmetric line data mutual filling is performed without overwriting existing data. The data in the interpolation window is changed from 2 lines of the original algorithm to 5 lines.
Thirdly, constructing a weight calculation matrix B in the calibration areas of the matrix F of the layer and the adjacent layers: the weight calculation matrix B is a transformation combination of K space data of L phased array coils of a z-th layer at a position x (i, j, L) (namely, the K space position is an ith row, a jth column, a first coil, i, j and L are positive integers larger than 1) and interpolation window data of a position x (-i, j and L), and a transformation combination of K space data of L phased array coils of a z+1 layer at a position x (i, j and L) and interpolation window data of a position x (-i, j and L); the positions of x (i, j, 1) are shifted in the calibration area, and one line of data is obtained for each position to construct a matrix B.
Step four, moving the position of x (i, j, 1) in the calibration area to obtain any row of data of the weight calculation matrix B, and recording the data of the position x (i, j, l), wherein any data is one row to obtain a column vector matrix C;
fifthly, obtaining a column vector matrix C according to the product of the weight calculation matrix B and the weight matrix W, and obtaining the weight matrix W in the interpolation window by fitting through a least square method;
sixth, the data not sampled in the matrix F is inquired and the position is recorded as
Position in prediction matrix A +.>
An interpolation window is arranged at the position, and a prediction matrix D of undersampled line data is formed;
seventh, obtaining a column vector E according to the product of the prediction matrix D and the weight matrix W in the interpolation window;
eighth step, the position is adjusted
Corresponding positions in the matrix F in the data filling of (a), and removing the originally filled 0 to obtain a reconstructed matrix H, and obtaining a parallel magnetic resonance imaging image after Fourier transformation.
The above embodiments are only preferred embodiments of the present invention and are not intended to limit the scope of the present invention, but all changes made by adopting the design principle of the present invention and performing non-creative work on the basis thereof shall fall within the scope of the present invention.
Claims (3)
1. The parallel magnetic resonance imaging algorithm based on conjugate and interlayer information utilizes K space data received by a phased array coil, wherein the phased array coil is provided with L, L is a positive integer greater than 1, and the method is characterized by comprising the following steps of:
the method comprises the steps of performing R times undersampling on a gradient positive high-frequency part and a gradient negative high-frequency part of an imaging object, and performing full sampling by taking a middle low-frequency part as a calibration area to obtain a matrix F; sampling and scanning a total Z layer, wherein Z is a positive integer greater than 1;
constructing a prediction matrix A of a matrix F: filling the ith row sampling data of the z+1th layer adjacent to the high-frequency undersampling part in the matrix F into the ith row of the z layer, and filling conjugate symmetrical data in the z layer;
constructing a weight calculation matrix B by using the calibration area of the matrix F of the layer and the adjacent layers: the weight calculation matrix B is a transformation combination of K space data of L phased array coils of a z-th layer at a position x (i, j, L) and interpolation window data of a position x (-i, j, L), and a transformation combination of K space data of L phased array coils of a z+1-th layer at a position x (i, j, L) and interpolation window data of a position x (-i, j, L);
moving the position of x (i, j, 1) in the calibration area to obtain any row of data of the weight calculation matrix B, and recording the data of the position x (i, j, l), wherein any data is one row to obtain a column vector matrix C;
obtaining a column vector matrix C according to the product of the weight calculation matrix B and the weight matrix W, and obtaining the weight matrix W in the interpolation window by adopting a least square method;
querying the data which is not sampled in the matrix F and recording the position as
Position in prediction matrix A +.>
An interpolation window is arranged at the position, and a prediction matrix D of undersampled line data is formed;
obtaining a column vector E according to the product of the prediction matrix D and the weight matrix W in the interpolation window;
position is to
Filling the data of the matrix F to the corresponding position, and removing the originally filled 0 to obtain a reconstructed matrix H, and obtaining a parallel magnetic resonance imaging image after Fourier transformation.
2. The parallel magnetic resonance imaging algorithm based on conjugate and interlayer information according to claim 1, wherein the construction process of the matrix F is as follows:
dividing K space data received by any phased array coil into two symmetrical parts of positive gradient and negative gradient;
sampling is started from a low-frequency part of the gradient in the forward direction, and in the z-th layer, if the gradient is in the forward direction, the q+z% R line is sampled; the q satisfies q% r=1;
if the gradient is negative, sampling the- (q+z% R+1) row;
and filling the non-sampled rows with 0, and fully sampling the middle low-frequency part to obtain a matrix F.
3. The parallel magnetic resonance imaging algorithm based on conjugate and interlayer information according to claim 1, wherein R is 4 or 5 or 6.
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