WO2019104702A1 - 一种基于自适应联合稀疏编码的并行磁共振成像方法、装置及计算机可读介质 - Google Patents
一种基于自适应联合稀疏编码的并行磁共振成像方法、装置及计算机可读介质 Download PDFInfo
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- 238000002595 magnetic resonance imaging Methods 0.000 title claims abstract description 23
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- 239000011159 matrix material Substances 0.000 claims abstract description 36
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- 238000005259 measurement Methods 0.000 claims description 10
- GNFTZDOKVXKIBK-UHFFFAOYSA-N 3-(2-methoxyethoxy)benzohydrazide Chemical compound COCCOC1=CC=CC(C(=O)NN)=C1 GNFTZDOKVXKIBK-UHFFFAOYSA-N 0.000 claims description 5
- 238000011478 gradient descent method Methods 0.000 claims description 4
- FGUUSXIOTUKUDN-IBGZPJMESA-N C1(=CC=CC=C1)N1C2=C(NC([C@H](C1)NC=1OC(=NN=1)C1=CC=CC=C1)=O)C=CC=C2 Chemical compound C1(=CC=CC=C1)N1C2=C(NC([C@H](C1)NC=1OC(=NN=1)C1=CC=CC=C1)=O)C=CC=C2 FGUUSXIOTUKUDN-IBGZPJMESA-N 0.000 claims description 3
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R33/00—Arrangements or instruments for measuring magnetic variables
- G01R33/20—Arrangements or instruments for measuring magnetic variables involving magnetic resonance
- G01R33/44—Arrangements or instruments for measuring magnetic variables involving magnetic resonance using nuclear magnetic resonance [NMR]
- G01R33/48—NMR imaging systems
- G01R33/54—Signal processing systems, e.g. using pulse sequences ; Generation or control of pulse sequences; Operator console
- G01R33/56—Image enhancement or correction, e.g. subtraction or averaging techniques, e.g. improvement of signal-to-noise ratio and resolution
- G01R33/561—Image enhancement or correction, e.g. subtraction or averaging techniques, e.g. improvement of signal-to-noise ratio and resolution by reduction of the scanning time, i.e. fast acquiring systems, e.g. using echo-planar pulse sequences
- G01R33/5611—Parallel magnetic resonance imaging, e.g. sensitivity encoding [SENSE], simultaneous acquisition of spatial harmonics [SMASH], unaliasing by Fourier encoding of the overlaps using the temporal dimension [UNFOLD], k-t-broad-use linear acquisition speed-up technique [k-t-BLAST], k-t-SENSE
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- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
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- G01R33/20—Arrangements or instruments for measuring magnetic variables involving magnetic resonance
- G01R33/44—Arrangements or instruments for measuring magnetic variables involving magnetic resonance using nuclear magnetic resonance [NMR]
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- G01R33/56—Image enhancement or correction, e.g. subtraction or averaging techniques, e.g. improvement of signal-to-noise ratio and resolution
- G01R33/5608—Data processing and visualization specially adapted for MR, e.g. for feature analysis and pattern recognition on the basis of measured MR data, segmentation of measured MR data, edge contour detection on the basis of measured MR data, for enhancing measured MR data in terms of signal-to-noise ratio by means of noise filtering or apodization, for enhancing measured MR data in terms of resolution by means for deblurring, windowing, zero filling, or generation of gray-scaled images, colour-coded images or images displaying vectors instead of pixels
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Definitions
- the present invention relates to the field of magnetic resonance imaging, and in particular to a parallel magnetic resonance imaging method, apparatus and computer readable medium based on adaptive joint sparse coding.
- the calibration-free reconstruction method does not require special calibration information to estimate sensitivity. They reconstruct images in the K-space or image domain through the relationship between the channels.
- the proposed calibration-free reconstruction method now only utilizes joint sparsity directly from the conversion domain.
- the present invention proposes a parallel magnetic resonance imaging method and apparatus based on adaptive joint sparse coding, which can improve sparsity based on block sparsity and can further improve the acceleration multiple. To ensure the quality of reconstruction.
- the invention provides a parallel magnetic resonance imaging method based on adaptive joint sparse coding, comprising the following steps:
- Step a Construct a parallel magnetic resonance imaging model based on calibration-free joint sparse coding, ie reconstruction model, which is defined as:
- V represents the reconstructed image
- ⁇ represents the objective function
- F M represents the Fourier transform
- v j represents the image of each channel
- the matrix of all the channels v j merged together is V
- f j represents K-space data
- M represents the size of the atom
- N represents the vectorized size of the image
- P represents the number of atoms
- subscript F represents the Fourier transform
- ⁇ represents the data fitting weight
- ⁇ represents the joint sparse regularization weight
- 2,1 means joint sparse term
- Step b Temporarily fix X, and solve the dictionary D by using the gradient descent method.
- ⁇ represents the learning rate and k represents the number of iterations.
- Step c updating the joint sparse coefficient X
- Step d update v j by the following formula
- Step e Update the K-space data by the following formula:
- Step f performing inverse Fourier transform on the K-space data to update v j again
- Step g Obtain an updated image based on the image v j of all channels.
- constructing a reconstruction model is to solve one Minimum objective function, where
- the norm is a data fitting term.
- Norm represents sparse representation error
- the mixed norm represents a joint sparse constraint between each channel.
- step a the initialization X 0 , V 0 is included , A step of.
- the atoms are normalized to avoid ambiguity in the dictionary atomic scale.
- updating v j further comprises the following steps:
- Step d1 Obtain the following formula according to the least squares method:
- I a diagonal matrix
- the value of the element on the diagonal is equal to the number of blocks in which the image pixels of the corresponding position overlap; when it is assumed that these blocks are mapped at the edge of the image, the values of the elements on the diagonal are all equal,
- ⁇ M
- Step d2 The image domain is converted to the Fourier domain by normalizing the full-Fourier Fourier coding matrix to obtain:
- I a diagonal matrix of 0 and 1, where 1 represents the position of the point taken in K space, ⁇ represents the number of pixel repetitions, and I N represents the unit matrix of N*N, a Fourier measurement indicating zero padding of the j-th channel;
- Step d3 Transform the formula in step d2 into:
- Fv j (k x , k y ) represents the updated value of the K-space position (k x , k y ), Represents the zero-padded K-space measurement of the j-th channel; ⁇ represents a small scalar, and ⁇ represents the set of points that the K-space has acquired.
- Step d4 v j is obtained by inverse Fourier transform by the data in the frequency domain of the formula (9) of the step c3.
- step g the squares of the images v j of all the channels are summed, and then squared to obtain an updated image.
- Another aspect of the present invention provides a parallel magnetic resonance imaging apparatus based on adaptive joint sparse coding, comprising: a model construction module, and constructing a parallel magnetic resonance imaging model based on calibration-free joint sparse coding, that is, a reconstruction model,
- the model is defined as:
- V represents the reconstructed image
- ⁇ represents the objective function
- F M represents the Fourier transform
- v j represents the image of each channel
- the matrix of all the channels v j merged together is V
- f j represents K-space data
- M represents the size of the atom
- N represents the vectorized size of the image
- P represents the number of atoms
- subscript F represents the Fourier transform
- ⁇ represents the data fitting weight
- ⁇ represents the joint sparse regularization weight
- 2,1 means joint sparse term
- the update module includes: a module for updating the joint sparse code X, a module for updating the dictionary D, a module for updating the image v j of each channel, and a module for updating the K-space data f j ;
- ⁇ represents the learning rate and k represents the number of iterations.
- the module that updates the image v j of each channel updates v j by the following formula,
- the module that updates the K-space data f j updates the K-space data by the following formula:
- the imaging module obtains an updated image based on the image v j of all channels.
- the imaging device further comprises: an initialization module, configured to initialize X 0 , V 0 ,
- constructing a reconstruction model is solving one Minimum objective function, where
- the norm is a data fitting term.
- Norm represents sparse representation error,
- the mixed norm represents a joint sparse constraint between each channel.
- the update module normalizes the atom when updating the dictionary D to avoid the dictionary atomic scale blur.
- the module for updating the image v j of each channel further performs the following steps:
- Step d1 Obtain the following formula according to the least squares method:
- I a diagonal matrix
- the value of the element on the diagonal is equal to the number of blocks in which the pixel of the corresponding position overlaps; when it is assumed that these blocks are mapped at the edge of the image, the values of the elements on the diagonal are all equal.
- ⁇ M
- Step d2 The image domain is converted to the Fourier domain by normalizing the full-Fourier Fourier coding matrix to obtain:
- I a diagonal matrix of 0 and 1, where 1 represents the position of the point taken in K space, ⁇ represents the number of pixel repetitions, and I N represents the unit matrix of N*N, a Fourier measurement indicating zero padding of the j-th channel;
- Step d3 Transform the formula in step d2 into:
- Fv j (k x , k y ) represents the updated value of the K-space position (k x , k y ), Represents the zero-padded K-space measurement of the j-th channel; ⁇ represents a small scalar, and ⁇ represents the set of points that the K-space has acquired.
- Step d4 v j is obtained by inverse Fourier transform by the data in the frequency domain of the formula (9) of the step d3.
- the imaging module sums the squares of the images v j of all channels and then squares to obtain an updated image.
- the present invention also provides a computer readable medium having a program stored therein, the program being computer executable to cause a computer to perform the parallel magnetic resonance imaging method based on adaptive joint sparse coding described above Each step.
- the method of the invention is utilized
- the joint sparseness of the norm development channel, while developing information sparsity can be free of calibration, and the method has strong robustness.
- FIG. 1 is a flow chart of a parallel magnetic resonance imaging method based on adaptive joint sparse coding of the present invention.
- FIG. 2 is a block diagram of a parallel magnetic resonance imaging apparatus based on adaptive joint sparse coding of the present invention.
- step a construct a parallel magnetic co-synthesis based on joint-free sparse coding.
- the vibration imaging model is the reconstruction model, which is defined as:
- V represents the reconstructed image
- ⁇ represents the objective function
- F M represents the Fourier transform
- v j represents the image of each channel
- the matrix of all the channels v j merged together is V
- f j represents K-space data
- M represents the size of the atom
- N represents the vectorized size of the image
- P represents the number of atoms
- subscript F represents the Fourier transform
- ⁇ represents the data fitting weight
- ⁇ represents the joint sparse regularization weight
- 2,1 means joint sparse term
- step a constructing a reconstruction model is to solve one Minimum objective function, where
- the norm is a data fitting term.
- Norm represents sparse representation error
- the mixed norm represents a joint sparse constraint between each channel.
- the method further includes initializing X 0 , V 0 , A step of.
- step b temporarily fix X, and solve the dictionary D by using the gradient descent method.
- ⁇ represents the learning rate and k represents the number of iterations.
- step b the atoms are normalized to avoid ambiguity in the dictionary atomic scale.
- step c update the joint sparse coefficient X until the inner layer iteration reaches the specified number of times
- q is the number of loops in which the inner loop is nested
- B is the auxiliary variable
- ⁇ is the auxiliary parameter
- step d update the image v j of each channel by the following formula
- updating v j further includes the following steps:
- Step d1 Obtain the following formula according to the least squares method:
- I a diagonal matrix
- the value of the element on the diagonal is equal to the number of blocks in which the image pixels of the corresponding position overlap; when it is assumed that these blocks are mapped at the edge of the image, the values of the elements on the diagonal are all equal,
- ⁇ M
- Step d2 The image domain is converted to the Fourier domain by normalizing the full-Fourier Fourier coding matrix to obtain:
- I a diagonal matrix of 0 and 1, where 1 represents the position of the point taken in K space, ⁇ represents the number of pixel repetitions, and I N represents the unit matrix of N*N, a Fourier measurement indicating zero padding of the j-th channel;
- Step d3 Transform the formula in step d2 into:
- Fv j (k x , k y ) represents the updated value of the K-space position (k x , k y ), Represents the zero-padded K-space measurement of the j-th channel; ⁇ represents a small scalar, and ⁇ represents the set of points that the K-space has acquired.
- Step d4 v j is obtained by inverse Fourier transform by the data in the frequency domain of the formula (9) of the step d3.
- step e update the K-space data by the following formula:
- step f performing inverse Fourier transform on the K-space data to update v j again
- step g is performed: summing the squares of the images v j of all the channels, and then prescribing to obtain the updated image.
- the method proposed by the present invention can achieve high-quality magnetic resonance image reconstruction with 4 times acceleration through the overall model and algorithm.
- the joint sparse norm can better suppress the noise
- the dictionary update can adaptively acquire the structural information of the image
- the accurate iterative loop solution of the overall algorithm can achieve the reconstruction quality of the minimum error.
- the present invention also provides a computer readable medium having a program stored therein that is computer executable to cause a computer to perform processing including the steps described above.
- the present invention also provides a parallel joint magnetic resonance imaging apparatus based on adaptive joint sparse coding for the above method.
- the device includes different modules for implementing the various steps mentioned in the above method.
- the apparatus can include a model building module, an update module, and an imaging module.
- the model building module constructs a parallel magnetic resonance imaging model based on calibration-free joint sparse coding, ie reconstruction model.
- the update module includes a module for updating the joint sparse code X, a module for updating the dictionary D, a module for updating the image v j of each channel, and a module for updating the K-space data f j .
- the imaging module obtains an updated image based on the image v j of all channels.
- the imaging device further comprises: an initialization module, configured to initialize X 0 , V 0 ,
- constructing a reconstruction model is to solve one Minimum objective function, where
- the norm is a data fitting term.
- Norm represents sparse representation error
- the mixed norm represents a joint sparse constraint between each channel.
- the update module updates the dictionary D
- the atom needs to be normalized to avoid the dictionary atomic scale blur.
- the imaging module sums the squares of the images v j of all channels and then squares to obtain an updated image.
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- High Energy & Nuclear Physics (AREA)
- Health & Medical Sciences (AREA)
- General Health & Medical Sciences (AREA)
- Nuclear Medicine, Radiotherapy & Molecular Imaging (AREA)
- Radiology & Medical Imaging (AREA)
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Abstract
Description
Claims (13)
- 一种基于自适应联合稀疏编码的并行磁共振成像方法,其特征在于,包括以下步骤:步骤a:构建一个基于免校准的联合稀疏编码的并行磁共振成像模型即重建模型,所述模型定义为:式中,V代表重建的图像,代表过完备(P>>M)的字典,θ表示目标函数,代表稀疏矩阵,表示从第j-th通道的图像提取第l-th图像块,FM代表傅里叶变换,vj表示每个通道的图像,所有通道的图像vj合并在一起组成的矩阵即为V,fj代表K空间数据,代表块提取矩阵,M表示原子的尺寸,N表示图像的向量化尺寸,P表示原子的个数,下标F表示傅里叶变换,λ表示数据拟合项权重,β表示联合稀疏正则化权重,||·||2,1表示联合稀疏项,式中,表示第j-th通道的第l-th提取块中第p-th像素;步骤b:临时固定X,采用梯度下降的方法求解字典D,式中γ表示学习率,k表示迭代次数,因此获得下式:Dk+1=Dk-γ(DX-RlV)XH (3)步骤c:更新联合稀疏系数X;步骤d:通过下式更新vj,步骤e:通过下述公式更新K空间数据:步骤f:对K空间数据进行傅里叶反变换再次更新vj,获得步骤g:根据所有通道的图像vj,获得更新后的图像。
- 根据权利要求1所述的方法,其特征在于,步骤b中,对原子进行归一化处理,以避免字典原子尺度模糊。
- 根据权利要求1所述的方法,其特征在于,步骤d中,更新vj进一步包括如下步骤:步骤d1:根据最小二乘法获得下式:步骤d2:图像域通过归一化全采傅里叶编码矩阵转换到傅里叶域,获得:步骤d3:将步骤d2中的公式变换成:步骤d4:通过步骤d3的公式(9)中频域中的数据通过逆傅里叶变换求得vj。
- 根据权利要求1所述的方法,其特征在于,步骤g中,对所有通道的图像vj的平方进行求和,然后开方,获得更新后的图像。
- 一种基于自适应联合稀疏编码的并行磁共振成像装置,其特征在于,包括:模型构建模块,构建一个基于免校准的联合稀疏编码的并行磁共振成像模型即重建模型,所述模型定义为:式中,V代表重建的图像,代表过完备(P>>M)的字典,θ表示目标函数,代表稀疏矩阵,表示从第j-th通道的图像提取第l-th图像块,FM代表傅里叶变换,vj表示每个通道的图像,所有通道的图像vj合并在一起组成的矩阵即为V,fj代表K空间数据,代表块提取矩阵,M表示原子的尺寸,N表示图像的向量化尺寸,P表示原子的个数,下标F表示傅里叶变换,λ表示数据拟合项权重,β表示联合稀疏正则化权重,||·||2,1表示联合稀疏项,式中,表示第j-th通道的第l-th提取块中第p-th像素;更新模块,包括:更新联合稀疏编码X的模块、更新字典D的模块、更新每一个通道的图像vj的模块以及更新K空间数据fj的模块;其中, 更新字典D的模块临时固定X,采用梯度下降的方法求解字典D,式中γ表示学习率,k表示迭代次数,因此获得下式:Dk+1=Dk-γ(DX-RlV)XH (3)更新每一个通道的图像vj的模块通过下式更新vj,更新K空间数据fj的模块通过下述公式更新K空间数据:并且对K空间数据进行傅里叶反变换再次更新vj,获得成像模块,根据所有通道的图像vj,获得更新后的图像。
- 根据权利要求7所述的成像装置,其特征在于,所述更新模块在更新字典D时,对原子进行归一化处理,以避免字典原子尺度模糊。
- 根据权利要求7所述的成像装置,其特征在于,更新每一个通道的图像vj的模块进一步执行如下步骤:步骤d1:根据最小二乘法获得下式:步骤d2:图像域通过归一化全采傅里叶编码矩阵转换到傅里叶域,获得:步骤d3:将步骤d2中的公式变换成:步骤d4:通过步骤d3的公式(9)中频域中的数据通过逆傅里叶变换求得vj。
- 根据权利要求7所述的成像装置,其特征在于,所述成像模块对所有通道的图像vj的平方进行求和,然后开方,获得更新后的图像。
- 一种计算机可读介质,该计算机可读介质具有存储在其中的程序,该程序是计算机可执行的以使计算机执行权利要求1-6中任一项所述的基于自适应联合稀疏编码的并行磁共振成像方法的各步骤。
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