WO2023124971A1 - 基于跨域网络的磁共振成像降采样和重建方法 - Google Patents

基于跨域网络的磁共振成像降采样和重建方法 Download PDF

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WO2023124971A1
WO2023124971A1 PCT/CN2022/138662 CN2022138662W WO2023124971A1 WO 2023124971 A1 WO2023124971 A1 WO 2023124971A1 CN 2022138662 W CN2022138662 W CN 2022138662W WO 2023124971 A1 WO2023124971 A1 WO 2023124971A1
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sampling
downsampling
matrix
network
reconstruction
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白瑞良
程昭玮
金心宇
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浙江大学
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    • G—PHYSICS
    • G01—MEASURING; TESTING
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    • 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
    • G01R33/5608—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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    • 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
    • G01R33/4818—MR characterised by data acquisition along a specific k-space trajectory or by the temporal order of k-space coverage, e.g. centric or segmented coverage of k-space
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    • 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
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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
    • G01R33/561—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
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
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    • G06N3/045—Combinations of networks
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    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
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Definitions

  • the invention belongs to the technical field of magnetic resonance imaging, in particular to downsampling and reconstruction of magnetic resonance imaging based on a cross-domain network.
  • the mainstream deep learning-based MR image reconstruction methods all study how to design a complex neural network to achieve the expected improvement in the quality of the reconstructed image or the function of a complete inverse Fourier (Fourier) transform. They just use already undersampled k-space data or undersampled MR images as input to the model, while ignoring the importance of optimizing the undersampled trajectory.
  • Downsampling trajectories is a key factor to achieve fast MRI and ensure high-quality reconstruction.
  • the sparsity of the downsampling determines the speedup, for example, a 10% downsampling ratio corresponds to a 10x speedup, and a 20% downsampling ratio corresponds to a 5x speedup.
  • MRI downsampling only occurs in the phase-encoded dimension, not in the frequency-encoded dimension.
  • two-dimensional magnetic resonance imaging which contains a frequency encoding and a phase encoding dimension
  • only one-dimensional downsampling can be adopted.
  • traditional three-dimensional magnetic resonance imaging it contains one frequency encoding dimension and two phase encoding dimensions, so downsampling is generally two-dimensional.
  • the existing two-dimensional downsampling trajectory includes radial downsampling [P C Lauterbur. Image formation by induced local interactions: examples employing nuclear magnetic resonance [J]. Nature, Mar 1973.242(5394): 190–191] Spiral downsampling [C B Ahn, J H Kim, Z H Cho.
  • the PFGMS method since there are no adjustable parameters (non-neural network structure) in the process of learning downsampled trajectories, the PFGMS method only relies on greedy iterative methods to amplify the downsampled trajectories, and it takes a lot of time to iteratively obtain the final downsampled trajectories , cannot be applied to large-scale data training.
  • the down-sampling trajectory optimization and the training of the CNN model are separated, and then alternately updated to obtain an approximate optimal solution, which cannot realize the mechanism of cross-domain joint training.
  • Huijben et al [Iris A.M.Huijben, Bastiaan S.Veeling, Ruud J.G.van Sloun.Deep probabilistic subsampling for task-adaptive compressed sensing[C]//International Conference for Learning Representations,2020:1 16] proposed a probabilistic representation of The sampling method (DPS), and the introduction of a two-layer fully connected network, a three-layer convolutional network or a generation network, realizes an end-to-end joint training mechanism.
  • DPS The sampling method
  • Huijben et al. only trained and validated on small-scale image sets of MNIST and CIFAR-10, and did not test on specific MR image sets.
  • J-MoDL downsampling trajectory and reconstruction model
  • the training model includes k-space data consistency operation (requires known downsampling trajectory) and U-Net[Olaf Ronneberger ,Philipp Fischer,Thomas Brox.U-Net:convolutional networks for biomedical image segmentation[C]//Nassir Navab,Joachim Hornegger,William M Wells,Alejandro F Frangi.International Conference on Medical Image Computing and Computer-Assisted Intervention .Cham: Springer International Publishing, 2015:234–241] Structure.
  • ⁇ is updated by ⁇ c by a hard threshold ( ⁇ ) method.
  • ⁇ hard threshold
  • the use of a single threshold method by Weiss et al. leads to inflexible changes in the downsampling trajectory.
  • the initialization steps of the vectors ⁇ and ⁇ c used in J-UCR are too complicated, and manual design is required to allocate the low-frequency and high-frequency parts according to a specific sampling ratio. Since the downsampled trajectory is heavily dependent on specific initialization values, it does not change significantly during joint training, where the continuous-valued vector ⁇ c is not theoretically analyzed as a probability distribution.
  • the training process of J-UCR also only uses an l 1 loss function, resulting in insufficient supervision information for the downsampling process, so the trained downsampling trajectory cannot be reconstructed to obtain the best quality MR image.
  • the purpose of the present invention is to provide a magnetic resonance imaging downsampling and reconstruction method based on a cross-domain network, which can effectively improve the reconstruction effect of magnetic resonance imaging.
  • a magnetic resonance imaging downsampling and reconstruction method based on a cross-domain network comprising:
  • the cross-domain network includes a downsampling layer, an inverse Fourier transform layer and a spatial domain reconstruction layer; the data in step (2) is used as input for training, and the downsampling layer simulates the downsampling trajectory pair
  • the simulated full-sampled k-space data is down-sampled, the inverse Fourier transform layer reconstructs the down-sampled k-space data to obtain a down-sampled MR image, and the spatial domain reconstruction network reconstructs the down-sampled MR image to restore the details, and obtains cross domain network;
  • step (3) Use the cross-domain network trained in step (3) to downsample and reconstruct the head MR image:
  • (4-1) Set the sampling ratio of the downsampling layer in step (3). By optimizing the cross-domain network, the probability matrix under different sampling ratios and the corresponding spatial domain reconstruction network are obtained. Based on the probability matrix and sampling interval constraints, the optimal downsampling trace;
  • step (4-4) Use the downsampling trajectory in step (4-3) to obtain k-space data for the MR image, the inverse Fourier transform layer will reconstruct the k-space data to obtain a downsampled MR image, and the spatial domain reconstruction network will downsample the MR image Image reconstruction recovers the details.
  • the spatial resolution of each group of data is 256 ⁇ 256 ⁇ (240-320) (dimension 256 ⁇ 256, ranging from 240-320 scanned slices).
  • the basic unit normalizes the data and performs 8 random angle rotations on each slice to minimize the interference caused by the edge mutation effect on the optimization and analysis of the downsampling trajectory, while taking into account the data diversity in the real scanning process , to improve the generalization ability of the method.
  • step (1) the present invention adopts the strategy of fast calculation of complex number separation.
  • the Fourier matrix used by the Fourier transform is expressed as:
  • F n represents the Fourier matrix
  • ( ) H represents the conjugate transpose Hermitian
  • the Fourier matrices F m and F n can be calculated and saved in advance, and do not need to be added to the training process as learning parameters.
  • the present invention has separated the real part and the imaginary part of the k-space data (complex number), and similarly separates the real part and the imaginary part of the Fourier matrix F n (F m ) before training, so as to avoid the format of the complex number and speed up the training.
  • step (3) the downsampling layer realizes the downsampling layer in the form of matrix element product:
  • M u represents the downsampling matrix/trajectory, and the dimensions are consistent with the row and column dimensions of k-space data, but the value range is only discrete values ⁇ 0, 1 ⁇ , "0" represents the part that is not sampled, and "1" represents the sampled part; Represents the input fully sampled k-space data, Indicates the downsampled k-space data.
  • step (3) the method of constructing the downsampling layer is:
  • step (3-1) all element values of the probability matrix P u in the probabilistic downsampling layer are initialized to the sampling ratio, and the constraints are kept during the training process
  • the initial state of the sampling matrix M u is obtained by the probability matrix P u through the Bernoulli distribution.
  • the elements of the downsampling matrix Mu in step (3-2) are all ⁇ 0, 1 ⁇ discrete values, which can be used for forward calculation, but the discrete values are non-differentiable, there is no gradient, and backpropagation cannot be realized update process. Therefore, the present invention proposes a strategy for automatic training of the network structure: M u is defined as a structural parameter, and P u is defined as a control parameter. That is, before each training iteration, the structural parameter M u used in the forward calculation process, its value is generated by the control parameter P u through the Bernoulli distribution to generate discrete values; then, the gradient update is performed using the control parameters during backpropagation; so Loop until the probability matrix P u converges:
  • This strategy not only retains the probability distribution characteristics of the sampling matrix Mu , but also adds randomness in the training process, so that the probability matrix Pu can be stabilized and easily analyzed after continuous optimization, and it is easy to find the general laws.
  • step (3-2) the probability matrix P u generates the sampling matrix M u through the Bernoulli distribution with rich randomness, the randomness in the training process helps the probability matrix P u to be fully trained, and the training ends Finally, the randomness makes the positions of the sampling points of Mu generated by the same Pu different each time, resulting in drastic changes in the performance of the reconstruction network, which is not conducive to further analysis of the law of the probability matrix Pu .
  • step (3) the input of the inverse Fourier transform layer (to realize the conversion of k-space data into MR images) is part of the down-sampled k-space data, and the inverse Fourier transform is used in the process of forward calculation.
  • the undersampled MR image can be obtained by leaf transform; among them, the calculation process of forward and inverse Fourier transform and inverse Fourier transform are as follows:
  • step (3) the spatial domain reconstruction network uses a common 10-layer convolutional network structure, and adds a global skip connection to realize the spatial domain reconstruction network, and restores the details of the downsampled MR image reconstruction:
  • Xu represents the downsampled MR image
  • f cnn represents the spatial domain reconstruction network
  • ⁇ represents the network parameters of f cnn to be optimized.
  • the spatial domain reconstruction network provided by the present invention significantly improves the signal-to-noise ratio of an image, and at the same time ensures the versatility of the cross-domain network.
  • the convolution kernel size of the first 9 layers in the spatial domain reconstruction network is 3 ⁇ 3, the number of channels is 16, and the step size is 1.
  • a ReLU activation function is followed; the tenth convolution layer For feature fusion, the size of the convolution kernel of this layer is 3 ⁇ 3, the number of channels is 1, and the step size is 1.
  • the trained loss function is based on the traditional Euclidean loss constraint, which consists of two parts: downsampling loss and reconstruction loss:
  • L joint ⁇ 1 ⁇ L IFT + ⁇ 2 ⁇ L rec , ⁇ 1 , ⁇ 2 ⁇ [0,1],
  • the loss function includes not only the reconstruction loss, but also the downsampling layer loss to provide deep supervision for the model, where the hyperparameters ⁇ 1 and ⁇ 2 are both The effect is best when it is set to 1, which means that the supervision information added by the two loss functions in the training process is equally important.
  • step (4-1) the sampling interval is constrained in the process of generating the sampling matrix M u based on the probability matrix P u .
  • the distance between all sampling points in the equal probability area is distributed as evenly as possible.
  • the minimum distance is r 0
  • the maximum The distance is 2r 0 :
  • step (4-3) the function expression satisfied by the section probability curve P center , the edge probability curve P margin and the three-dimensional surface graph P face is:
  • rate is the total sampling ratio
  • limit of the minimum sampling probability value z
  • z represents the coordinate value of the probability matrix P u
  • d represents the distance between the pixel point in the probability matrix P u and the center of the matrix.
  • a series of parameters ⁇ , t 0 , t 1 , P min can be calculated according to the required sampling ratio rate, then according to these parameters, the probability value of each point in the probability matrix P u can be calculated with the formula P face , Then the sampling matrix can be generated according to the probability matrix combined with the sampling interval constraints.
  • the section probability curve P center and the edge probability curve P margin are used to analyze the expression to obtain the three-dimensional surface graph P face , and then the probability matrix P u can be calculated according to the P face , and then the final drop is generated based on P u and the sampling interval constraints. Sample trace.
  • the function expressions of P face , P center , and P margin under different sampling ratios obtained by the present invention, combined with sampling interval constraints, can generate down-sampling trajectories under different sampling ratios, which can be a general two-dimensional down-sampling trajectory.
  • the down-sampling trajectory is used to down-sample only the sampling points (that is, the point with a value of 1 in the down-sampling matrix) when acquiring k-space data, and the inverse Fourier transform layer reconstructs the down-sampled k-space data to obtain the down-sampled Sampling the MR image, and then using the trained spatial domain reconstruction network to reconstruct the down-sampled MR image to restore the details.
  • the method for downsampling and reconstruction of magnetic resonance (MR) images based on the cross-domain network proposed by the present invention simultaneously optimizes the downsampling trajectory of the magnetic resonance (MR) image and the spatial domain reconstruction network, and quantitatively analyzes the cross-domain Functional expressions for the probability distribution of optimal downsampled trajectories in domain networks.
  • the present invention mainly includes three parts: the probabilistic downsampling layer simulates the downsampling trajectory; the inverse Fourier transform layer reconstructs the downsampled k-space data to obtain an MR image; the spatial domain reconstruction network reconstructs the fuzzy MR image to restore details content.
  • the cross-domain reconstruction network proposed by the present invention uses the k-space data obtained after Fourier transform based on real MR data, and fully trains the 2D probabilistic downsampling layer and the reconstruction network model only under the traditional Euclidean loss constraints, and finds the best Probability distribution of optimal 2D downsampled trajectories versus sampling ratio (speedup factor).
  • the 2D probabilistic downsampling layer and the cross-domain joint training mechanism proposed by the present invention have stronger practicability and better effects for different MR acquisition and reconstruction scenarios.
  • the function expression of the probability distribution of the optimal sampling trajectory learned by the method provided by the present invention can provide a theoretical basis for the down-sampling trajectory in the 3D MR scanning magnetic resonance imaging (MRI) scene.
  • the present invention uses real MR images of 3D scans of different modalities and different health conditions for testing, which proves the robustness and universality of the downsampling trajectory of the present invention.
  • the reconstruction effect of the probabilistic down-sampling trajectory proposed by the present invention obviously exceeds the reconstruction effect of several existing down-sampling trajectories.
  • Figure 1 is a structural diagram of a cross-domain network.
  • Fig. 2 is the analysis result of the probability matrix curve of the 2D probabilistic downsampling layer optimized by the present invention: three-dimensional surface graph P face , the cross-sectional probability curve (solid line) P center of the row (column) direction passing through the center point, and row The margin probability curve (dotted line) P margin in the (column) direction, the downsampling ratios are (a) 10%, (b) 20%, (c) 30%, (d) 40%.
  • Fig. 3 is the performance display of the sampling interval constraints proposed by the present invention, and the sampling results of uniform distribution with a downsampling probability of 10% are as follows: (a) is a sampling matrix randomly generated by Bernoulli; (b) is generated under constraints sampling matrix.
  • Fig. 4 is an example of several downsampling trajectories compared in the present invention: (a) J-CUR; (b) PFGMS; (c) J-MoDL; (d) LOUPE; (e) Gaussian; (f) Poisson.
  • Figure 5 is the result of the 2D probabilistic downsampling layer proposed by the present invention using only undersampling loss training results in a non-reconstructed network.
  • the first row represents the probability matrix
  • the second row represents the sampling matrix generated under stability constraints: downsampling
  • the ratios are: (a) 10%; (b) 20%; (c) 30%; (d) 40%.
  • Fig. 6 is a test example of the downsampling trajectory and reconstruction network optimized by the present invention in the MICCAI2013 test set and the dynamic contrast-enhanced magnetic resonance image data set of high-grade glioma patients.
  • the present invention adopts the T1 weighted modal head MR image in the public data set MICCAI 2013 Grand Challenge on Multi-Atlas Labeling, and obtains the simulated full sampling k-space data through Fourier transform. Considering that in the MR image of the head, except for some tissues, the background is simple and has no content, in order to avoid the edge mutation effect of the restored image, the present invention adopts the preprocessing method of translating the tissue part in the image to the center of the image.
  • the present invention adopts the following data expansion strategy: all training images are randomly rotated 0°–360°, repeated 8 times, The morphological features of MR images are enriched by rotation in random directions to avoid biased convergence solutions and unexpected overfitting.
  • the model proposed by the present invention is realized jointly by Tensorflow and Keras high-level interface.
  • the experiment of the present invention is equipped with Intel Xeon (R) Platinum processor (CPU)@2.50GHz, 528GB internal memory, 4 NVIDIA Tesla V100 (32GB) GPUs and Ubuntu Linux distributions running on the server.
  • the cross-domain network magnetic resonance image downsampling trajectory and reconstruction network optimization method provided by the present invention mainly include the following steps:
  • this method can avoid the complex calculation in the frequency domain without any loss of information.
  • the cross-domain network includes a downsampling layer, an inverse Fourier transform layer, and a spatial domain reconstruction layer; the data in step (2) is used as input for training, and the downsampling layer simulates The down-sampling trajectory down-samples the simulated full-sampled k-space data, the inverse Fourier transform layer reconstructs the down-sampled k-space data to obtain a down-sampled MR image, and the spatial domain reconstruction network reconstructs the down-sampled MR image to restore details.
  • the specific process is:
  • step (4-1) Based on the probability matrix P u designed in step (4-1), generate a sampling matrix M u according to the Bernoulli distribution.
  • step (4-4) Design an inverse Fourier transform layer, transform the downsampled k-space data obtained in step (4-3) into the image domain, and obtain a downsampled MR image.
  • the undersampled MR image can be obtained by using the inverse Fourier transform;
  • the calculation process of the forward and inverse Fourier transform and the inverse Fourier transform are as follows:
  • step (4-3) Design a spatial domain reconstruction network, improve the signal-to-noise ratio of the downsampled MR image in step (4-4), and recover the details.
  • Xu represents the downsampled MR image
  • f cnn represents the spatial domain reconstruction network
  • ⁇ represents the network parameters of f cnn to be optimized.
  • the size of the convolution kernel of the first 9 layers in the spatial domain reconstruction network is 3 ⁇ 3, the number of channels is 16, and the step size is 1.
  • a ReLU activation function is followed; the tenth layer of convolution Layer for feature fusion, the size of the convolution kernel of this layer is 3 ⁇ 3, the number of channels is 1, and the step size is 1.
  • the training loss function is based on the traditional Euclidean loss constraint, which consists of two parts: downsampling loss and reconstruction loss:
  • L joint ⁇ 1 ⁇ L IFT + ⁇ 2 ⁇ L rec , ⁇ 1 , ⁇ 2 ⁇ [0,1],
  • sampling matrix is generated under the constraint of the sampling interval, and fixed as the probability matrix and sampling matrix in the cross-domain network.
  • the domain reconstruction network is fine-tuned to obtain the final sampling matrix and spatial domain reconstruction network.
  • the present invention proposes a constraint on the sampling interval, and the distance between all sampling points in the equal probability area is distributed as evenly as possible, the minimum distance is r 0 , and the maximum distance is 2r 0 .
  • step section probability curve P center The function expression satisfied by step section probability curve P center , edge probability curve P margin and three-dimensional surface graph P face is:
  • rate is the total sampling ratio
  • limit of the minimum sampling probability value z
  • z represents the coordinate value of the probability matrix P u
  • d represents the distance between the pixel point in the probability matrix P u and the center of the matrix.
  • the probability matrices under different sampling ratios obtained in step (5) have a high degree of regularity, and the quantitative analysis continues.
  • the present invention explores the three-dimensional surface graph P face of the probability matrix under different sampling ratios, and the rows (columns) passing through the central point
  • the present invention only needs to focus on any direction for curve analysis.
  • the maximum value of the cross-sectional probability curve P center is 1, and the minimum value is a preset P min ; as the sampling ratio increases, the shape of the curve becomes more and more "wider".
  • the maximum value of the edge probability curve P margin becomes larger as the sampling ratio increases, and the minimum value is a preset P min ; as the sampling ratio increases, the shape of the curve becomes more and more "higher” and "wider”.
  • step (6) Use the downsampling trajectory in step (5) to obtain k-space data from the MR image, the inverse Fourier transform layer reconstructs the k-space data to obtain a downsampled MR image, and the spatial domain reconstruction network reconstructs and restores the downsampled MR image to details.
  • step (6) when the sampling ratio in step (6) is the same as that in step (4), the spatial domain reconstruction network in step (4) is used; when the two are different, retraining is required to obtain the spatial domain reconstruction network under this sampling ratio.
  • the present invention selects some existing down-sampling methods, and compares the results corresponding to 10-2 times acceleration under the condition of 10%-50% sampling ratio.
  • the comparative methods include JCUR, PFGMS, J-MoDL, LOUPE, Gaussian, Poisson.
  • the present invention uses the above-mentioned down-sampling trajectory (one part is fixed and the other part is trainable) to replace the sampling matrix in the probabilistic down-sampling layer proposed by the present invention, and trains the reconstruction network, and finally quantitatively compares the signal-to-noise ratio of the MR reconstructed images. Since the model parameters of different sampling ratios cannot be shared, the present invention trains multiple models for testing according to the conditions of different sampling ratios.
  • Quantitative analysis of different sampling ratios and corresponding probability matrices data fitting to obtain the function expressions satisfied by the cross-section probability curve P center , edge probability curve P margin and three-dimensional surface graph P face , and can be generated according to the function expression and sampling interval constraints
  • the probability matrix and downsampling trajectory of different sampling ratios, the parameters that need to be manually configured in this process are only the limits of the total sampling ratio rate and the minimum sampling probability value There is no need for a large number of hyperparameter adjustments; and the sampling probability function and the optimal downsampling trajectory can be deployed in the MRI scanner as a real downsampling strategy, realizing the acquisition and reconstruction of MR images with high signal-to-noise ratio under limited sampling ratio Target.
  • the present invention compares J-CUR downsampling (in (a) in Fig. 4), PFGMS downsampling (in (b) in Fig. 4 )), J-MoDL downsampling ((c) in Figure 4), LOUPE downsampling ((d) in Figure 4), Gaussian downsampling ((e) in Figure 4), Poisson downsampling ((f in Figure 4 )).
  • the down-sampling trajectory of the J-CUR method and the PFGMS method collect too little information on the high-frequency part, while the down-sampling trajectory of the J-MoDL method collects the information of the low-frequency and high-frequency parts in the same proportion, which leads to The signal-to-noise ratio of reconstructed MR images is relatively low.
  • the probabilistic downsampling trajectory obtained by the present invention (as shown in Figure 5: the 2D probabilized downsampling layer only uses the result of undersampling loss training in the non-reconstruction network, the first row represents the probability matrix, and the second row represents the stability
  • the probability matrix that the present invention trains and obtains is also considered as the importance distribution of k-space sampling points: the energy of the central low-frequency part is very high, which is very important for restoring the overall structure of the MR image; the energy of the high-frequency part is very low, but it is important for improving The intricate details of MR images are critical.

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Abstract

一种基于跨域网络的磁共振成像降采样轨迹及重建网络方法，包括：获取头部MR图像，经过预处理后，通过傅里叶变换得到仿真全采样k空间数据；将仿真全采样k空间数据的实部和虚部进行分离，独立保存在两个同维度的矩阵中，然后合并为两个通道作为跨域网络的输入；构建跨域网络，包括降采样层、逆傅里叶变换层和空间域重建层，概率化降采样层模拟降采样轨迹；逆傅里叶变换层将降采样后的k空间数据重建得到MR图像；空间域重建网络将模糊的MR图像重建恢复出细节内容：输入进行训练，得到训练完成后的跨域网络；使用训练完成后的跨域网络对头部MR图像进行来集和重建，这一方法可以有效提升磁共振成像的重建效果。

Description

基于跨域网络的磁共振成像降采样和重建方法 技术领域
本发明属于磁共振成像的技术领域，特别涉及基于跨域网络的磁共振成像降采样和重建。
背景技术
主流的基于深度学习的MR图像重建方法均是研究如何设计复杂的神经网络，从而实现预期的重建图像质量的提升或完整的逆傅里叶(Fourier)变换的功能。它们只是利用已经欠采样的k空间数据或欠采样的MR图像，作为模型的输入，而忽略了优化降采样轨迹(undersampled trajectory)的重要性。降采样轨迹是实现快速磁共振成像MRI并且保证高质量重建的关键因素。降采样的稀疏性决定了加速程度，例如，10％的降采样比例对应10倍加速，20％的降采样比例对应5倍加速。一般来说，MRI降采样只发生在相位编码维度上，不存在于频率编码维度。对于二维磁共振成像，包含一个频率编码和一个相位编码维度，只能采取一维降采样。对于传统三维磁共振成像，包含一个频率编码维度和两个相位编码维度，因而降采样一般是二维的。目前已有的二维降采样轨迹包括径向(radial)降采样[P C Lauterbur.Image formation by induced local interactions:examples employing nuclear magnetic resonance[J].Nature,Mar 1973.242(5394):190–191]螺旋(spiral)降采样[C B Ahn,J H Kim,Z H Cho.Highspeed spiral-scan echo planar NMR imaging[J].IEEE Transactions on Medical Imaging,Mar 1986.5(1):2–7]、高斯(Gaussian)降采样[Robert L.Cook.Stochastic sampling in computer graphics[J].ACM Transactions on Graphics(TOG),Jan 1986.5(1):51–72]和泊松(Poisson)降采样[Thouis R.Jones.Efficient generation of Poisson-disk sampling patterns[J].Journal of Graphics Tools,Jan 2006.11(2):27–36]。但是，这些方法只是遵循先前研究的选择，没有提出确定性的理论依据，或者分析出哪一种的降采样轨迹最适合于优化特定的k空间数据。目前，仅有少数研究开始关注降采样轨迹的优化，针对特定的k空间数据，在采集阶段最大程 度地提升MR图像的质量。
Figure PCTCN2022138662-appb-000001
ü等人[Baran
Figure PCTCN2022138662-appb-000002
ü,Rabeeh Karimi Mahabadi,YenHuan Li,Efe Ilicak,Tolga Cukur,Jonathan Scarlett,Volkan Cevher.Learning-based compressive MRI[J].IEEE Transactions on Medical Imaging,Jun 2018.37(6):1394 1406]提出了一种无参数贪婪轨迹选择方法(PFGMS)，通过逐步地更新降采样轨迹，作用于k空间数据，搜索出能获得较高图像质量的降采样轨迹。然而，由于学习降采样轨迹的过程中没有可调节的参数(非神经网络结构)，PFGMS方法只依靠贪婪迭代的方式去扩增降采样轨迹，需要消耗大量的时间来迭代获得最终的降采样轨迹，不能适用于大规模数据的训练。另外，PFGMS方法中降采样轨迹优化和CNN模型的训练被分离处理，然后交替进行更新来得到近似最优解，无法实现跨域联合训练的机制。
Huijben等人[Iris A.M.Huijben,Bastiaan S.Veeling,Ruud J.G.van Sloun.Deep probabilistic subsampling for task-adaptive compressed sensing[C]//International Conference for Learning Representations,2020:1 16]提出了一种概率表示的采样方式(DPS)，并引入二层的全连接网络、三层的卷积网络或生成网络，实现了端到端的联合训练机制。然而，Huijben等人只在MNIST和CIFAR-10小规模的图像集上进行训练和验证，未在特定的MR图像集上进行测试。为了突破采样点分布不可微的限制，DPS中引入了Gumbel-softmax作为一种连续可微的近似松弛法，但这并不等价于真实的离散采样值，且只选择了概率值最大的前k个采样点，却忽略了大部分的高频信息，更无法对采样点的选择给出通用的理论分析。
Aggarwal等人[Hemant Kumar Aggarwal,Mathews Jacob.J-MoDL:joint model-based deep learning for optimized sampling and reconstruction[J].arXiv Preprint,2019.1911.02945:1 10]提出了一种基于深度学习的联合优化降采样轨迹和重建模型的方法(J-MoDL)，其中提出了2D降采样轨迹优化的概念，训练的模型包括k空间数据一致性操作(需已知降采样轨迹)和U-Net[Olaf Ronneberger,Philipp Fischer,Thomas Brox.U-Net:convolutional networks for biomedical image segmentation[C]//Nassir Navab,Joachim Hornegger,William M Wells,Alejandro F Frangi.International Conference on Medical Image Computing and Computer-Assisted Intervention.Cham:Springer International  Publishing,2015:234–241]结构。但是，Aggarwal等人采用较复杂的训练机制：1)单独训练U-Net模型；2)单独训练降采样轨迹；3)同时训练降采样轨迹和U-Net网络。这导致了训练的效率不高，且存在大量重复的计算。J-MoDL为了使得降采样轨迹可以参与梯度更新，直接使用了连续值的参数代替离散的采样值，导致它与真实的降采样轨迹差异太大，所以训练的结果对离散的降采样过程的借鉴意义不足。另外，降采样轨迹对低频、高频部分的采样比例分配过于平均，没有利用k空间数据重要性的分布规律，也缺少对获得的降采样轨迹进行理论分析。
最近，Weiss等人[Tomer Weiss,Sanketh Vedula,Ortal Senouf,Oleg Michailovich,Michael Zibulevsky,Alex Bronstein.Joint learning of Cartesian under sampling and reconstruction for accelerated MRI[C]//IEEE International Conference on Acoustics,Speech and Signal Processing(ICASSP).IEEE,May 2020:8653 8657]提出了一种降采样轨迹和重建网络U-Net联合训练的方法(J-UCR)，用于学习1D Cartesian降采样轨迹，以加速磁共振成像过程。Weiss等人[9]设计了二值化mask向量Φ和连续值mask向量Φ c。在训练阶段的每一次迭代后，通过硬阈值(τ)方法由Φ c更新Φ。Weiss等人使用单一阈值法导致了降采样轨迹不能灵活变化。另外，J-UCR中采用的向量Φ和Φ c的初始化步骤过于复杂，需要手动设计将低频、高频部分按特定的采样比例分配。由于降采样轨迹严重依赖于特定的初始化值，其在联合训练的过程中并无显著的改变，其中连续值向量Φ c也没有作为概率分布进行理论分析。J-UCR的训练过程也只采用了一个l 1损失函数，导致其对降采样过程的监督信息不足，因而训练的降采样轨迹不能重建获得最佳质量的MR图像。
发明内容
本发明的目的在于提供基于跨域网络的磁共振成像降采样和重建方法，可以有效提升磁共振成像的重建效果。
本发明采取以下技术方案：
基于跨域网络的磁共振成像降采样和重建方法，所述方法包括：
(1)获取头部MR图像，经过预处理后，通过傅里叶变换得到仿真全采样k空间数据；
(2)将步骤(1)中获得的仿真全采样k空间数据的实部和虚部进行分离，独立保存在两个同维度的矩阵中，然后合并为两个通道作为跨域网络的输入；
(3)构建跨域网络，所述跨域网络包括降采样层、逆傅里叶变换层和空间域重建层；将步骤(2)中数据作为输入进行训练，降采样层模拟降采样轨迹对仿真全采样k空间数据进行降采样、逆傅里叶变换层将降采样后的k空间数据重建得到降采样MR图像、空间域重建网络将降采样MR图像重建恢复出细节内容，得到训练完成后的跨域网络；
(4)使用步骤(3)训练完成后的跨域网络对头部MR图像进行降采样和重建：
(4-1)设置步骤(3)中降采样层的采样比例，通过优化跨域网络，得到不同采样比例下的概率矩阵以及相应的空间域重建网络，基于概率矩阵和采样间隔约束生成最优降采样轨迹；
(4-2)根据不同采样比例下的概率矩阵，定量分析不同采样比例约束下的概率矩阵与采样比例的关系，数据拟合得到不同采样比例下的概率矩阵的三位曲面图P face，经过中心点的行/列方向的截面概率曲线P center和行/列方向的边缘概率曲线P margin的函数表达式；
(4-3)根据P face、P center、P margin的函数表达式和采样间隔约束可以生成不同采样比例的概率矩阵和降采样轨迹；
(4-4)使用步骤(4-3)中的降采样轨迹对MR图像获取k空间数据，逆傅里叶变换层将k空间数据重建得到降采样MR图像，空间域重建网络将降采样MR图像重建恢复出细节内容。
在步骤(1)中，每一组数据的空间分辨率为256×256×(240～320)(维度256×256，240～320张扫描切片不等)，在数据预处理阶段，以组为基本单位对数据进行归一化，并对每个切片进行8次随机角度旋转，尽可能削弱边缘突变效应对降采样轨迹的优化和分析带来的干扰，同时考虑到真实扫描过程中数据多样性，提高方法的泛化能力。
在步骤(1)中，本发明采用了复数分离快速计算的策略。傅里叶变换采用的Fourier 矩阵表示为：
Figure PCTCN2022138662-appb-000003
其中，F n表示Fourier矩阵，(·) H表示共轭转置Hermitian；
将矩阵F n的实部和虚部分离，借助欧拉Euler公式，得到如下矩阵：
Figure PCTCN2022138662-appb-000004
Figure PCTCN2022138662-appb-000005
由于矩阵的维度可提前确定，Fourier矩阵F m和F n可以提前计算并保存，不需要作为学习参数加入训练过程。本发明已经将k空间数据(复数)的实部和虚部分离，同理在训练前把Fourier矩阵F n(F m)的实部和虚部分离，以避免复数的格式并且加速训练。
在步骤(3)中，所述降采样层用矩阵元素乘积的方式实现降采样层：
Figure PCTCN2022138662-appb-000006
M u表示降采样矩阵/轨迹，维度和k空间数据的行列维度保持一致，但取值范围仅为离散值{0，1}，“0”表示不采样的部分，“1”表示采样部分；
Figure PCTCN2022138662-appb-000007
表示输入的全采样k空间数据，
Figure PCTCN2022138662-appb-000008
表示降采样后的k空间数据。
在步骤(3)中，构建降采样层的方法为：
(3-1)设计概率矩阵P u，并将所有元素值都初始化为降采样比例，并在训练过程中对概率矩阵进行两点约束：概率矩阵的平均值与降采样比例之间的差值保持在一定的误差范围内
Figure PCTCN2022138662-appb-000009
概率矩阵中每个点的概率值满足p∈(0，1]；
(3-2)基于概率矩阵P u，根据伯努利分布生成采样矩阵M u；
(3-3)基于概率矩阵P u和采样矩阵M u，设计降采样概率层，每次训练迭代过程中，基于采样矩阵M u进行前向计算，得到降采样的k空间数据，基于概率矩阵P u进行梯度传播，实现参数更新。
优选的，步骤(3-1)中，概率化降采样层中的概率矩阵P u的所有元素值都初始化 为将采样比例，并且在训练过程中一直保持约束
Figure PCTCN2022138662-appb-000010
采样矩阵M u的初始状态是由概率矩阵P u通过伯努利分布得到。同时在训练过程中概率矩阵的取值范围是p∈(0，1]，当p＝0时，其采样分布就无意义，而且会导致采样矩阵中对应的元素无法参与更新，使得训练过早陷入局部的极小值，当p>1时，梯度更新过程中出现越界值，导致生成的采样矩阵M u的步骤出现异常。
优选的，步骤(3-2)中降采样矩阵M u的元素均为{0，1}离散值，能进行前向计算，但是离散值是不可微的，不存在梯度，无法实现反向传播的更新过程。因此，本发明提出了网络结构自动训练的策略：M u定义为结构参数，P u定义为控制参数。即每一次训练迭代之前，前向计算的过程中使用的结构参数M u，其值由控制参数P u通过伯努利分布生成离散值；接着，反向传播时使用控制参数进行梯度更新；如此循环，直至概率矩阵P u收敛：
Figure PCTCN2022138662-appb-000011
Figure PCTCN2022138662-appb-000012
Figure PCTCN2022138662-appb-000013
该策略既保留了采样矩阵M u的概率分布特性，也在训练过程中加入了随机性，使得概率矩阵P u经过不断的优化，可以趋于稳定且方便分析，容易发现其中的普遍规律。
优选的，步骤(3-2)中概率矩阵P u通过伯努利分布生成采样矩阵M u带有丰富的随机性，训练过程中随机性有助于概率矩阵P u进行充分地训练，训练结束后，该随机性使得每次由同样的P u生成的M u的采样点位置的大相迥异，导致重建网络的性能变化剧烈，不利于进一步分析概率矩阵P u的规律。
在步骤(3)中，所述逆傅里叶变换层(实现k空间数据转换为MR图像的功能)的输入是降采样后的部分k空间数据，在前向计算的过程中使用逆傅里叶变换就可以得到欠采样的MR图像；其中，正逆傅里叶变换、逆傅里叶变换的计算过程分别如下：
Figure PCTCN2022138662-appb-000014
Figure PCTCN2022138662-appb-000015
在步骤(3)中，所述空间域重建网络，选用普通的10层卷积网络结构，并加入全局的跳跃连接实现空间域重建网络，将降采样后的MR图像重建恢复出细节内容：
X rec＝X u+f cnn(X u|θ),
其中X u代表降采样后的MR图像，f cnn代表空间域重建网络，θ表示f cnn的待优化网络参数。
本发明提供的空间域重建网络使得图像的信噪比得到显著提升，同时保证了跨域网络的通用性。
所述空间域重建网络中前9层的卷积核大小为3×3，通道数为16，步长为1，每个卷积层后，都跟随一个ReLU激活函数；第十层卷积层进行特征融合，该层卷积核大小为3×3，通道数为1，步长为1。
在步骤(3)中，在训练过程中，训练的损失函数基于传统的Euclidean损失约束，由降采样损失和重建损失两部分组成：
L joint＝λ 1·L IFT+λ 2·L rec,λ 1,λ 2∈[0,1],
其中降采样损失
Figure PCTCN2022138662-appb-000016
重建损失
Figure PCTCN2022138662-appb-000017
Y rec表示真实的全采样MR图像。
为了避免深度网络带来的梯度消失，同时增强概率化降采样层的训练效果，损失函数不仅包括重建损失，还包括降采样层损失，为模型提供深度监督，其中超参数λ 1和λ 2都设置为1时效果最佳，这意味着两个损失函数在训练的过程中加入的监督信息同等的重要。
在步骤(4-1)中，基于概率矩阵P u生成采样矩阵M u的过程中进行采样间隔约束，等概率区域内所有采样点之间的距离尽可能平均分配，最小距离为r 0，最大距离为2r 0：
r 0＜‖M u(x i,y j)-M u(x k,y l)‖ 2＜2r 0
Figure PCTCN2022138662-appb-000018
在步骤(4-3)中，截面概率曲线P center、边缘概率曲线P margin和三维曲面图P face满足的函数表达式为：
Figure PCTCN2022138662-appb-000019
Figure PCTCN2022138662-appb-000020
Figure PCTCN2022138662-appb-000021
Figure PCTCN2022138662-appb-000022
Figure PCTCN2022138662-appb-000023
Figure PCTCN2022138662-appb-000024
Figure PCTCN2022138662-appb-000025
其中，rate为总采样比例，
Figure PCTCN2022138662-appb-000026
为最小采样概率值的限制，z表示概率矩阵P u的坐标值，d表示概率矩阵P u中的像素点与矩阵中心的距离。
具体的：根据要求的采样比例rate可以计算出一系列参数σ、t 0、t 1、P min，那么根据这些参数，用公式P face就可以计算出概率矩阵P u中各个点的概率值，再根据概率矩阵结合采样间隔约束就可以生成采样矩阵。截面概率曲线P center和边缘概率曲线P margin是用于分析获得三维曲面图P face的表达式的，然后根据P face可以计算获得概率矩阵P u，再基于P u和采样间隔约束生成最终的降采样轨迹。
通过本发明得到的不同采样比例下的P face、P center、P margin的函数表达式，结合采样间隔约束就可以生成不同采样比例下的降采样轨迹，可以一种通用的二维降采样轨迹。降采样轨迹用于在获取k空间数据时，只对采样点进行降采样(也就是降采样矩阵中值为1的点)，逆傅里叶变换层将降采样后的k空间数据重建得到降采样MR图像、然后用训练好的空间域重建网络将降采样MR图像重建恢复出细节内容。
本发明提出的基于跨域网络的磁共振(MR)图像的降采样和重建方法，在这过程中 同时优化了磁共振(MR)图像的降采样轨迹及空间域重建网络，并且定量分析了跨域网络中的最佳降采样轨迹概率分布的函数表达式。本发明主要包括三个部分：概率化降采样层模拟降采样轨迹；逆傅里叶变换层将降采样后的k空间数据重建得到MR图像；空间域重建网络将模糊的MR图像重建恢复出细节内容。本发明提出的跨域重建网络使用基于真实MR数据经过傅里叶变换后获得的k空间数据，仅在传统的Euclidean损失约束下，充分训练2D概率化降采样层和重建网络模型，发现了最佳2D降采样轨迹的概率分布与采样比例(加速倍数)的关系。本发明提出的2D概率化降采样层和跨域联合训练机制的实用性更强、针对不同MR采集及重建场景的效果更优。本发明提供的方法学习到的最佳采样轨迹概率分布的函数表达式可为3D MR扫描磁共振成像(MRI)场景中的降采样轨迹提供理论依据。同时，本发明采用不同模态、不同健康状况的3D扫描的真实MR图像进行测试，证明了本发明的降采样轨迹的鲁棒性和普适性。对比现有的几种降采样策略，在同等的采样比例(加速倍数)条件下，本发明提出的概率化降采样轨迹的重建效果明显超过了已有几种降采样轨迹的重建效果。
附图说明
图1为跨域网络结构图。
图2为本发明优化得到的2D概率化降采样层的概率矩阵曲线的分析结果：三维曲面图P face、经过中心点的行(列)方向的截面概率曲线(实线)P center、和行(列)方向的边缘概率曲线(虚线)P margin，降采样比例分别为(a)10％，(b)20％，(c)30％，(d)40％。
图3为本发明提出的采样间隔约束性能展示，对降采样概率为10％并且均匀分布的采样结果如下：(a)为伯努利随机生成的采样矩阵；(b)为约束条件下生成的采样矩阵。
图4为本发明对比的几种降采样轨迹实例：(a)J-CUR；(b)PFGMS；(c)J-MoDL；(d)LOUPE；(e)Gaussian；(f)Poisson。
图5为本发明提出的2D概率化降采样层在无重建网络仅使用欠采样损失训练的结果，第一行表示概率矩阵，第二行表示在稳定性约束条件下生成的采样矩阵：降采样比例分别为：(a)10％；(b)20％；(c)30％；(d)40％。
图6为本发明优化得到的降采样轨迹和重建网络在MICCAI2013测试集和高级别胶质瘤患者的动态对比增强磁共振图像数据集中的测试样例。
具体实施方式
本发明采用公共数据集MICCAI 2013 Grand Challenge on Multi-Atlas Labeling中T1加权模态头部MR图像，经过傅里叶变换获得仿真全采样k空间数据。考虑到头部MR图像中除部分组织外、其余背景简单且无内容的情况，为了避免恢复的图像出现边缘突变效应，本发明采用将图像中组织部分平移至图像中心的预处理方式。另外，考虑到头部MR图像形态固定、方向不变化的特性，会导致图像特征的多样性不足，本发明采取如下的数据扩充策略：所有训练图像随机旋转0°–360°，重复8次，通过随机方向的旋转来丰富MR图像的形态特征，避免出现有偏收敛解和非预期的过拟合情况。
本发明提出的模型由Tensorflow与Keras高级接口共同实现。鉴于训练阶段所需的数据量、参数量和内存占用，本发明的实验都是在配备Intel Xeon(R)Platinum处理器(CPU)@2.50GHz，528GB内存，4个NVIDIA Tesla V100(32GB)GPU和Ubuntu Linux发行版的服务器上运行的。
本发明提供的跨域网络磁共振图像降采样轨迹和重建网络优化方法主要包括以下步骤：
(1)获取头部MR图像，并划随机分为训练集、验证集和测试集三个部分；以组为基本单位，对训练集中的数据进行归一化，并对每个切片进行随机角度旋转，提高数据多样性。对预处理后的图像经过傅里叶变换获得仿真全采样k空间数据。
具体为：采用公共数据集MICCAI 2013 Grand Challenge on Multi-Atlas Labeling中 T1加权模态头部MR图像，从训练样本中随机选取200组和10组分别作为本方法的训练集和验证集，从测试样本中随机选择10组作为本方法的测试集，经过预处理后，通过傅里叶变换得到仿真全采样k空间数据。
(2)将步骤(1)中获得的仿真全采样k空间数据的实部和虚部进行分离。独立保存在两个同维度的矩阵中，然后合并为两个通道，作为跨域网络的输入：
该过程记为：
Figure PCTCN2022138662-appb-000027
Figure PCTCN2022138662-appb-000028
表示复数形式的仿真全采样k空间数据，该方法可以避开频域的复数计算且无任何信息损失。
(3)构建跨域网络，如图1所示，跨域网络包括降采样层、逆傅里叶变换层和空间域重建层；将步骤(2)中数据作为输入进行训练，降采样层模拟降采样轨迹对仿真全采样k空间数据进行降采样、逆傅里叶变换层将降采样后的k空间数据重建得到降采样MR图像、空间域重建网络将降采样MR图像重建恢复出细节内容、得到训练完成后的跨域网络，具体过程为：
(3-1)设计概率矩阵P u，并将所有元素值都初始化为降采样比例，并在训练过程中对概率矩阵进行两点约束：概率矩阵的平均值与将采样比例之间的差值保持在一定的误差范围内
Figure PCTCN2022138662-appb-000029
概率矩阵中每个点的概率值满足p∈(0，1]。
(3-2)基于步骤(4-1)中设计的概率矩阵P u，根据伯努利分布生成采样矩阵M u。
(3-3)基于步骤(4)中设计的概率矩阵P u和步骤(4-2)中设计的采样矩阵M u，设计降采样概率层，每次训练迭代过程中，基于采样矩阵M u进行前向计算，得到降采样k空间数据，基于概率矩阵P u进行梯度传播，实现参数更新。
(3-4)设计逆傅里叶变换层，将步骤(4-3)中得到的降采样k空间数据变换到图像域，获得降采样MR图像。
在前向计算的过程中使用逆傅里叶变换就可以得到欠采样的MR图像；其中，正逆傅里叶变换、逆傅里叶变换的计算过程分别如下：
Figure PCTCN2022138662-appb-000030
Figure PCTCN2022138662-appb-000031
(3-5)设计空间域重建网络，提高步骤(4-4)中的降采样MR图像的信噪比，恢复出细节内容。
表示为：
X rec＝X u+f cnn(X u|θ),
其中X u代表降采样后的MR图像，f cnn代表空间域重建网络，θ表示f cnn的待优化网络参数。
具体的，空间域重建网络中前9层的卷积核大小为3×3，通道数为16，步长为1，每个卷积层后，都跟随一个ReLU激活函数；第十层卷积层进行特征融合，该层卷积核大小为3×3，通道数为1，步长为1。
(3-6)将步骤(3-3)-(3-5)中的三部分网络整合为跨域网络，基于步骤(1)-(2)中获得的数据对网络进行训练，直至网络收敛，得到优化后的降采样轨迹和重建网络。
在训练过程中，训练的损失函数基于传统的Euclidean损失约束，由降采样损失和重建损失两部分组成：
L joint＝λ 1·L IFT+λ 2·L rec,λ 1,λ 2∈[0,1],
其中降采样损失
Figure PCTCN2022138662-appb-000032
重建损失
Figure PCTCN2022138662-appb-000033
Y rec表示真实的全采样MR图像。
(3-7)基于步骤(3-6)中优化得到的降采样概率矩阵，在采样间隔约束的条件下生成采样矩阵，并将其固定为跨域网络中的概率矩阵和采样矩阵，对空间域重建网络进行微调，获得最终采样矩阵和空间域重建网络。
如图3所示。因此除了总采样比例约束外，本发明提出采样间隔约束，等概率区 域内所有采样点之间的距离尽可能平均分配，最小距离为r 0，最大距离为2r 0。
r 0＜‖M u(x i,y j)-M u(x k,y l)‖ 2＜2r 0
Figure PCTCN2022138662-appb-000034
(4)分别将采样比例设置为10％、20％、30％、40％和50％，重复步骤(3-6)-(3-7)训练得到不同采样比例下优化的降采样轨迹和重建网络。
(5)定量分析不同采样比例和其对应的概率矩阵之间的数量关系，数据拟合得到截面概率曲线P center、边缘概率曲线P margin和三维曲面图P face满足的函数表达式，根据该函数表达式和采样间隔约束可以生成不同采样比例的概率矩阵和降采样轨迹，该过程中需要手动配置的参数只有总采样比例rate和最小采样概率值的限制
Figure PCTCN2022138662-appb-000035
Figure PCTCN2022138662-appb-000036
并不需要大量的超参数调整。
步截面概率曲线P center、边缘概率曲线P margin和三维曲面图P face满足的函数表达式为：
Figure PCTCN2022138662-appb-000037
Figure PCTCN2022138662-appb-000038
Figure PCTCN2022138662-appb-000039
Figure PCTCN2022138662-appb-000040
Figure PCTCN2022138662-appb-000041
Figure PCTCN2022138662-appb-000042
Figure PCTCN2022138662-appb-000043
其中，rate为总采样比例，
Figure PCTCN2022138662-appb-000044
为最小采样概率值的限制，z表示概率矩阵P u的坐标值，d表示概率矩阵P u中的像素点与矩阵中心的距离。
步骤(5)中获得的不同采样比例下的概率矩阵具有高度规律性，继续进行定量分析，本发明探索了不同采样比例下的概率矩阵的三维曲面图P face、经过中心点的行(列)方向的截面概率曲线(实线)P center、和行(列)方向的边缘概率曲线(虚线)P margin，如图2所示，随着采样比例的上升，中心区域的采样比例逐渐增加，高频区域的最低采样比例P min也逐渐提高。另外，由于概率矩阵是高度中心对称的，截面概率曲线P center的行、列方向的结果是完全重合的，且边缘概率曲线P margin的行、列方向的结果也是完全重合的。因此，本发明只需关注任意一个方向进行曲线分析。截面概率曲线P center的最大值为1，最小值为预设的P min；随着采样比例的增加，曲线的形状变得越来越“宽”。边缘概率曲线P margin的最大值随着采样比例的增加而变大，最小值为预设的P min；随着采样比例的增加，曲线的形状变得越来越“高”且“宽”。经过曲线数据拟合，本发明提出了上述几个概率分布的具体表达式。
(6)使用步骤(5)中的降采样轨迹对MR图像获取k空间数据，逆傅里叶变换层将k空间数据重建得到降采样MR图像，空间域重建网络将降采样MR图像重建恢复出细节内容。
其中，当步骤(6)中采样比例与步骤(4)相同时，采用步骤(4)中的空间域重建网络；当两者不同时，需要重新训练得到此采样比例下的空间域重建网络。
为了测试本发明提出的概率化降采样的策略，本发明选择一些现有的降采样方法，在10％–50％采样比例条件下，对应10倍–2倍加速，进行结果比较。对比方法包括JCUR、PFGMS、J-MoDL、LOUPE、Gaussian、Poisson。本发明使用上述(一部分固定、另一部分可训练)的降采样轨迹代替本发明提出的概率化降采样层中的采样矩阵，并且训练重建网络，最后进行定量比较MR重建图像的信噪比。由于不同的采样比例的模型参数不能共享，本发明针对不同采样比例的条件，分别训练出多个模型用 于测试。
定量分析不同采样比例以及对应的概率矩阵，数据拟合得到截面概率曲线P center、边缘概率曲线P margin和三维曲面图P face满足的函数表达式，并且根据该函数表达式和采样间隔约束可以生成不同采样比例的概率矩阵和降采样轨迹，该过程中需要手动配置的参数只有总采样比例rate和最小采样概率值的限制
Figure PCTCN2022138662-appb-000045
并不需要大量的超参数调整；并且采样概率函数和最佳的降采样轨迹可作为真实的降采样策略部署于MRI扫描仪，实现了有限采样比例下高信噪比的MR图像采集和重建的目标。
为了比较同样以数据驱动方式、学习到的降采样策略的方法和传统降采样策略方法，本发明对比了J-CUR降采样(图4中(a))，PFGMS降采样(图4中(b))，J-MoDL降采样(图4中(c))，LOUPE降采样(图4中(d))，Gaussian降采样(图4中(e))，Poisson降采样(图4中(f))。可以发现J-CUR方法和PFGMS方法的降采样轨迹对高频部分的信息采集太少，而J-MoDL方法的降采样轨迹把低频、高频部分的信息按同等的比例采集，这都导致了重建的MR图像信噪比相对不高。而本发明获得的概率化降采样轨迹(如图5所示：2D概率化降采样层在无重建网络仅使用欠采样损失训练的结果，第一行表示概率矩阵，第二行表示在稳定性约束条件下生成的采样矩阵：降采样比例分别为：(a)10％；(b)20％；(c)30％；(d)40％)能把采样点合理地分配到k空间中的低频、高频区域，概率矩阵中心的低频区域的概率值最大且高度对称，以同心圆向外，概率值迅速降低，使其可以适用于不同类型的MR数据。同时本发明训练得到的概率矩阵同样被认为是k空间采样点的重要性分布：中心低频部分的能量很高，对恢复MR图像的整体结构很重要；高频部分的能量很低，但对提升MR图像的复杂细节很关键。
如图6所示，我们在两个不同的数据集上对本发明进行性能测试，其中一个测试集是与训练集独立同分布，另一个测试集是高级别胶质瘤患者的动态对比增强磁共振图像，从结果上看，本发明提出的端到端的降采样轨迹和重建网络优化能够提高图像的 降采样质量以及重建质量，同时相比其他方法，本发明对于分布不同的数据也能够表现出较好的性能，证明了本发明具有一定的普适性。

Claims (10)

  1. 基于跨域网络的磁共振成像降采样和重建方法，其特征在于，所述方法包括：
    (1)获取头部MR图像，经过预处理后，通过傅里叶变换得到仿真全采样k空间数据；
    (2)将步骤(1)中获得的仿真全采样k空间数据的实部和虚部进行分离，独立保存在两个同维度的矩阵中，然后合并为两个通道作为跨域网络的输入；
    (3)构建跨域网络，所述跨域网络包括降采样层、逆傅里叶变换层和空间域重建层；将步骤(2)中数据作为输入进行训练，降采样层模拟降采样轨迹对仿真全采样k空间数据进行降采样、逆傅里叶变换层将降采样后的k空间数据重建得到降采样MR图像、空间域重建网络将降采样MR图像重建恢复出细节内容，得到训练完成后的跨域网络；
    (4)使用步骤(3)训练完成后的跨域网络对头部MR图像进行降采样和重建：
    (4-1)设置步骤(3)中降采样层的采样比例，通过优化跨域网络，得到不同采样比例下的概率矩阵以及相应的空间域重建网络，基于概率矩阵和采样间隔约束生成最优降采样轨迹；
    (4-2)根据不同采样比例下的概率矩阵，定量分析不同采样比例约束下的概率矩阵与采样比例的关系，数据拟合得到不同采样比例下的概率矩阵的三位曲面图P face，经过中心点的行/列方向的截面概率曲线P center和行/列方向的边缘概率曲线P margin的函数表达式；
    (4-3)根据P face、P center、P margin的函数表达式和采样间隔约束可以生成不同采样比例的概率矩阵和降采样轨迹；
    (4-4)使用步骤(4-3)中的降采样轨迹对MR图像获取k空间数据，逆傅里叶变换层将k空间数据重建得到降采样MR图像，空间域重建网络将降采样MR图像重建恢复出细节内容。
  2. 根据权利要求1所述的基于跨域网络的磁共振成像降采样轨迹及重建网络方法，其特征在于，在步骤(1)中，傅里叶变换采用的Fourier矩阵表示为：
    Figure PCTCN2022138662-appb-100001
    其中，F n表示Fourier矩阵，(·) H表示共轭转置Hermitian；
    将矩阵F n的实部和虚部分离，借助欧拉Euler公式，得到如下矩阵：
    Figure PCTCN2022138662-appb-100002
    Figure PCTCN2022138662-appb-100003
  3. 根据权利要求1所述的基于跨域网络的磁共振成像降采样轨迹及重建网络方法，其特征在于，在步骤(3)中，所述降采样层用矩阵元素乘积的方式实现降采样层：
    Figure PCTCN2022138662-appb-100004
    M u表示降采样矩阵/轨迹，维度和k空间数据的行列维度保持一致，但取值范围仅为离散值{0，1}，“0”表示不采样的部分，“1”表示采样部分；
    Figure PCTCN2022138662-appb-100005
    表示输入的全采样k空间数据，
    Figure PCTCN2022138662-appb-100006
    表示降采样后的k空间数据。
  4. 根据权利要求3所述的基于跨域网络的磁共振成像降采样轨迹及重建网络方法，其特征在于，在步骤(3)中，构建降采样层的方法为：
    (3-1)设计概率矩阵P u，并将所有元素值都初始化为降采样比例，并在训练过程中对概率矩阵进行两点约束：概率矩阵的平均值与降采样比例之间的差值保持在一定的误差范围内
    Figure PCTCN2022138662-appb-100007
    概率矩阵中每个点的概率值满足p∈(0，1]；
    (3-2)基于概率矩阵P u，根据伯努利分布生成采样矩阵M u；
    (3-3)基于概率矩阵P u和采样矩阵M u，设计降采样概率层，每次训练迭代过程中，基于采样矩阵M u进行前向计算，得到降采样的k空间数据，基于概率矩阵P u进行梯度传播，实现参数更新。
  5. 根据权利要求1所述的基于跨域网络的磁共振成像降采样轨迹及重建网络方法，其特征在于，在步骤(3)中，所述逆傅里叶变换层的输入是降采样后的部分k空间数据，在前向计算的过程中使用逆傅里叶变换就可以得到欠采样的MR图像；其中，正逆傅里叶变换、逆傅里叶变换的计算过程分别如下：
    Figure PCTCN2022138662-appb-100008
    Figure PCTCN2022138662-appb-100009
  6. 根据权利要求1所述的基于跨域网络的磁共振成像降采样轨迹及重建网络方法，其特征在于，在步骤(3)中，所述空间域重建网络，选用普通的10层卷积网络结构，并加入全局的跳跃连接实现空间域重建网络，将降采样后的MR图像重建恢复出细节内容：
    X rec＝X u+f cnn(X u|θ),
    其中X u代表降采样后的MR图像，f cnn代表空间域重建网络，θ表示f cnn的待优化网络参数。
  7. 根据权利要求6所述的基于跨域网络的磁共振成像降采样轨迹及重建网络方法，其特征在于，所述空间域重建网络中前9层的卷积核大小为3×3，通道数为16，步长为1，每个卷积层后，都跟随一个ReLU激活函数；第十层卷积层进行特征融合，该层卷积核大小为3×3，通道数为1，步长为1。
  8. 根据权利要求1所述的基于跨域网络的磁共振成像降采样轨迹及重建网络方法，其特征在于，在步骤(3)中，在训练过程中，训练的损失函数基于传统的Euclidean损失约束，由降采样损失和重建损失两部分组成：
    L joint＝λ 1·L IFT+λ 2·L rec,λ 1,λ 2∈[0,1],
    其中降采样损失
    Figure PCTCN2022138662-appb-100010
    重建损失
    Figure PCTCN2022138662-appb-100011
    Y rec表示真实的全采样MR图像。
  9. 根据权利要求1所述的基于跨域网络的磁共振成像降采样轨迹及重建网络方法，其特征在于，在步骤(4-1)中，基于概率矩阵P u生成采样矩阵M u的过程中进行采样间隔约束，等概率区域内所有采样点之间的距离尽可能平均分配，最小距离为r 0，最大距离为2r 0：
    Figure PCTCN2022138662-appb-100012
  10. 根据权利要求1所述的基于跨域网络的磁共振成像降采样轨迹及重建网络方法，其特征在于，在步骤(4-3)中，截面概率曲线P center、边缘概率曲线P margin和三维曲面图P face满足的函数表达式为：
    Figure PCTCN2022138662-appb-100013
    Figure PCTCN2022138662-appb-100014
    Figure PCTCN2022138662-appb-100015
    Figure PCTCN2022138662-appb-100016
    Figure PCTCN2022138662-appb-100017
    Figure PCTCN2022138662-appb-100018
    其中，rate为总采样比例，
    Figure PCTCN2022138662-appb-100019
    为最小采样概率值的限制，z表示概率矩阵P的坐标值，d表示矩阵P中的像素点与矩阵中心的距离。
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