Intelligent non-Cartesian magnetic resonance rapid imaging method

Abstract

The invention discloses an intelligent non-Cartesian magnetic resonance rapid imaging method, and relates to the technical field of reconstruction of magnetic resonance non-Cartesian sampling images. According to the invention, by designing the artifact suppression module, the sensitivity learning module, the data consistency module and the image reconstruction module, the network is allowed to alternately update and learn the high-frequency information component of the sensitivity graph and the reconstructed image, the sensitivity estimation accuracy is improved, and the method has the characteristics of high reconstructed image quality and fast reconstruction speed.

Description

Technical Field

[0001] The present invention relates to the technical field of magnetic resonance non-Cartesian sampling image reconstruction, and in particular to an intelligent non-Cartesian magnetic resonance rapid imaging method. Background Art

[0002] The statements in this section merely provide background information related to the present disclosure and may not constitute prior art.

[0003] Magnetic Resonance Imaging (MRI) is a technology widely used in medical diagnosis. Its biggest advantage is that it is non-radioactive. However, current MRI technology generally faces the problems of slow scanning speed and long imaging time. Therefore, how to accelerate MRI has become a key issue that needs to be solved urgently. Non-Cartesian imaging technology shows excellent robustness in processing motion, especially in applications such as dynamic contrast-enhanced imaging of the liver, and can achieve a higher acceleration than traditional Cartesian methods. However, due to the networked processing of non-uniform Fourier transforms and inaccurate morbidity and sensitivity estimation of non-Cartesian MRI, non-Cartesian MRI faces the dilemma of long reconstruction time and the need to improve the quality of reconstructed images.

[0004] In the past, many magnetic resonance image reconstruction methods have been proposed. Reconstruction methods for estimating coil sensitivity based on the self-calibration signal ACS region have been proposed, such as sensitivity encoding (KPPruessmann, M.Weiger, MBScheidegger, P.Boesiger,"SENSE:Sensitivity encoding for fast MRI,"Magnetic Resonance inMedicine, 42, 952-962, 1999;Ying L, Sheng J:Joint image reconstruction and sensitivity estimation in SENSE(JSENSE).Magn Reson Med57(6):1196-1202, 2007), compressed sensing sparsity (Y.Liu, Z.Zhan, J.-F.Cai, D.Guo, Z.Chen, X.Qu,"Projected iterative soft-thresholding algorithm for tight frames in compressed sensing magnetic resonance imaging,"IEEE Transactions on Medical Imaging, 35, 2130-2140, 2016.;X.Zhang et al.,"A guaranteed convergence analysis for the projected fast iterative soft-thresholding algorithmin parallel MRI,"Medical Image Analysis,69,101987,2021;ET,Shin H,Jun Y,Kim T,Hwang D,"Accelerating Cartesian MRI bydomain-transform manifold learning in phase-encoding direction",Medical Image Analysis,63:101689,2020), these methods operate on the image under a manually designed sparse representation to remove image artifacts. However, the sparse expression ability of the manually designed sparse representation is limited. The sensitivity estimated based on ACS loses the high-frequency information of sensitivity, resulting in the need to improve the quality of the reconstructed image.To solve the above problems, deep learning has brought opportunities to magnetic resonance imaging reconstruction, which has advantages in reconstruction time and image quality (Wang Z, Qian C, Guo D, Sun H, Li R, Zhao B, Qu X, "One-dimensional Deep Low-rank and Sparse Network for Accelerated MRI", IEEE Transactions on Medical Imaging, 1-1, 2022; Lu T, Zhang X, Huang Y, Guo D, Huang F, Xu Q, Hu Y, Ou-Yang L, Lin J, Yan Z, "pFISTA-SENSE-ResNet for parallel MRI reconstruction", Journal of Magnetic Resonance, 318:106790, 2020.) However, these methods mainly focus on Cartesian MRI. Recently, deep learning has been introduced into non-Cartesian MRI (Malavé MO, Baron CA, Koundinyan SP, Sandino CM, Ong F, Cheng JY, Nishimura DG, "Reconstruction of undersampled 3D non-Cartesian image-based navigators for coronary MRA using an unrolled deep learning model", Magnetic resonance in medicine, 84(2): 800-812, 2020; Ramzi, Zaccharie, et al. "NC-PDNet: A density-compensated unrolled network for 2D and 3D non-Cartesian MRI reconstruction." IEEE Transactions on Medical Imaging 41(7), 1625-1638, 2022). Although improvements in imaging quality and reconstruction speed have been achieved, the sensitivity map based on ACS pre-estimation lacks high-frequency information and does not allow for updating during the reconstruction process, resulting in inaccurate sensitivity estimation and suboptimal reconstruction.

[0005] In summary, the existing image reconstruction sensitivity estimates for MRI under non-Cartesian sampling are inaccurate and lack high-frequency sensitivity prior information to guide network reconstruction. Summary of the Invention

[0006] The purpose of the present invention is to provide an intelligent non-Cartesian magnetic resonance rapid imaging method to address the problems existing in the prior art, propose a sensitivity learning unfolding network, allow the sensitivity map and the reconstructed image to be alternately learned and updated in the network, improve the accuracy of sensitivity estimation, and have the characteristics of high reconstructed image quality and fast reconstruction speed.

[0007] The technical solutions of the present invention are as follows:

[0008] An intelligent non-Cartesian magnetic resonance rapid imaging method, comprising:

[0009] Step S1: training data generation; non-Cartesian fully sampled k-space data is acquired from a scanner, an undersampling operator is used to perform an undersampling operation on the fully sampled k-space data to obtain undersampled k-space data, and a fully sampled sensitivity map, a fully sampled composite map, and a fully sampled multi-coil map are obtained using the fully sampled k-space data. The undersampled k-space data, the fully sampled sensitivity map, the fully sampled composite map, and the fully sampled multi-coil image together constitute a training set;

[0010] Step S2: Network design: Design a deep sensitivity learning unfolding network model for non-Cartesian sampling magnetic resonance intelligent imaging network, network reasoning capability and loss function;

[0011] Step S3: training the network; using the training set obtained in step S1, solving the optimal parameters of the magnetic resonance intelligent imaging network;

[0012] Step S4: reconstructing the network; inputting the magnetic resonance non-Cartesian under-sampled k-space data to be reconstructed into the trained magnetic resonance intelligent imaging network to reconstruct the magnetic resonance image.

[0013] Furthermore, the step S1 includes:

[0014] Step S11: Acquire non-Cartesian full-sampling multi-channel magnetic resonance data, i.e., non-Cartesian full-sampling k-space data, from a magnetic resonance scanner;

[0015] Step S12: using an undersampling operator to undersample the non-Cartesian fully sampled multi-channel magnetic resonance data to obtain undersampled k-space data;

[0016] Step S13: Calculate the non-Cartesian fully sampled k-space data using non-uniform Fourier transform to obtain a fully sampled sensitivity map, a fully sampled composite map, and a fully sampled multi-coil map, which together with the undersampled k-space data form a training set.

[0017] Furthermore, the magnetic resonance intelligent imaging network is composed of an initialization module IC and multiple iteration blocks as the core, and is constructed by cascading K network iteration modules;

[0018] Among them, the initialization module IC includes: calculation of multi-channel zero-filling map, initialization sensitivity map and initialization synthesis map; the network iteration module includes: artifact suppression module DAS, sensitivity learning module DSE, data consistency module DC and image reconstruction module IR.

[0019] Furthermore, the workflow of the initialization module IC is as follows:

[0020] The undersampled k-space data k is converted into a multi-channel zero-filling map through density compensation and non-uniform Fourier transform.

[0021] Fill multi-channel zero map Divide by the composite graph after the SOS operation to obtain the initialized sensitivity graph

[0022] Fill multi-channel zero map Multiply by the initialized sensitivity map The complex conjugate transpose of gets the initialized synthetic graph m (0) .

[0023] Furthermore, the artifact suppression module DAS uses a multi-channel zero-filling map As input, the consistency of k-space data is verified, the encoder and decoder are used to output the multi-coil zero-filling map after artifact suppression.

[0024] The encoder and decoder are composed of M filters, each filter is composed of a convolution layer, a normalization function, a nonlinear activation function and a convolution layer cascade; the encoder is based on the k-space data after consistency check. As input, the encoded features are used as output; the decoder uses the encoded features of the encoder and the features after Relu nonlinear mapping as input and the features after artifact suppression as output. as output.

[0025] Furthermore, the sensitivity learning module DSE initializes the sensitivity map As input, it uses two submodules, DSE1 and DSE2, to learn sensitivity and output a sensitivity map with high-frequency details.

[0026] The sensitivity learning submodules DSE1 and DSE1 are composed of J filters, each of which is composed of a convolution layer, a normalization function, a nonlinear activation function and a convolution layer cascade; the sensitivity learning submodule DSE1 is used to initialize the sensitivity map As input, the encoded features are output; the sensitivity learning submodule DSE2 takes the features learned by DSE1 as input and the sensitivity map of high-frequency details after learning as output.

[0027] Furthermore, the data consistency module DC initializes the composite graph m (k-1) As input, after calculating the consistency prior formula, the updated composite image is output

[0028] Furthermore, the image reconstruction module IR uses the updated synthetic image As input, through the forward sparse representation N1, ReLu non-activation function and reverse sparse reconstruction N2, the output artifact-suppressed reconstructed image m (k) ;

[0029] Both the forward sparse representation N1 and the reverse sparse reconstruction N2 are composed of N convolution units, each of which is composed of a convolution layer, a normalization function, a nonlinear activation function and a convolution layer cascade; the forward sparse representation N1 is used to synthesize the image As input, the sparsely represented feature δ n As output; reverse sparse reconstruction N2 is the feature δ after forward sparse representation n After ReLu nonlinear mapping, it is used as input to reconstruct the image m (k) as output.

[0030] Furthermore, the network's inference function and loss function are designed, including:

[0031] The final reconstructed synthetic image m through the network and the fully sampled synthetic image m ref Constraints; The network finally outputs a multi-coil zero-filling diagram With full sampling multi-coil image Constraints; Sensitivity map of the network's final output Sensitivity plot with full sampling Constraints are formed to form three-constraint loss functions L1, L2 and L3, which realize the loss function construction of sensitivity learning:

[0032] The loss function L1 of the reconstructed synthetic image is defined as:

[0033]

[0034] The multi-coil zero-filling graph loss function L2 is defined as:

[0035]

[0036] The sensitivity loss function L3 is defined as:

[0037]

[0038] Among them, T represents the number of training samples, K represents the number of iterations, represents the fully sampled synthetic image of the t-th sample, represents the fully sampled multi-coil image of the t-th sample, represents the full sampling sensitivity map of the t-th sample, represents the reconstructed composite image of the t-th sample outputted by the k-th iteration network, represents the multi-coil zero-filled image output by the t-th sample in the k-th iteration network learning, Represents the sensitivity map of the t-th sample output by the k-th iteration network learning;

[0039] The total loss function of the magnetic resonance intelligent imaging network is expressed as:

[0040] L total =λ1L1+λ2L2+λ3L3

[0041] Among them, λ1, λ2, and λ3 are adjustable coefficients used to balance the attention paid to reconstructing the synthetic image, the multi-coil zero-filling map, and the sensitivity map learning.

[0042] Furthermore, in step S3, the Adam optimizer is used to solve the optimal parameters of the magnetic resonance intelligent imaging network, and the network is trained using the training set generated in step S1, by minimizing the loss function L in step S2. total Get the optimal target parameter set

[0043] Compared with the existing technology, the beneficial effects of the present invention are:

[0044] The present invention provides an intelligent non-Cartesian magnetic resonance fast imaging method based on an unfolded network for sensitivity learning. By designing an artifact suppression module, a sensitivity learning module, a data consistency module, and an image reconstruction module, the network is allowed to alternately update the high-frequency information components of the learned sensitivity map and reconstruct the image, thereby improving the accuracy of sensitivity estimation and achieving high-quality reconstructed images and fast reconstruction speed. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 Schematic diagram of the radial golden angel sampling trajectory (comprising 100 spokes) used in the embodiment;

[0046] Figure 2 Schematic diagram of the network structure of intelligent non-Cartesian magnetic resonance fast imaging based on the sensitivity learning deep expansion network; (a) is the overall network structure; (b) is the network structure diagram of the initialization module; (c) is the network structure diagram of the artifact suppression module; (d) is the network structure diagram of the sensitivity learning module; (e) is the formula of the data consistency module; (f) is the network structure diagram of the image reconstruction module;

[0047] Figure 3 : The fully sampled labeled image of the knee and the reconstructed image under 5 times acceleration; among them, (a) is the fully sampled labeled image, (b) is the undersampled image, (c) is the reconstructed image of the present invention, (d) is the error map corresponding to the fully sampled labeled image and itself, (e) is the error map corresponding to the fully sampled labeled image and the undersampled image, and (f) is the error map corresponding to the fully sampled labeled image and the reconstructed image of the present invention. DETAILED DESCRIPTION

[0048] It should be noted that relational terms such as "first" and "second" are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprises," "comprising," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or elements inherent to such process, method, article, or apparatus. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of additional identical elements in the process, method, article, or apparatus comprising the element.

[0049] The features and performance of the present invention are further described in detail below with reference to the embodiments.

[0050] Example 1

[0051] See also Figure 2 , an intelligent non-Cartesian magnetic resonance rapid imaging method, comprising:

[0052] Step S1: training data generation; non-Cartesian fully sampled k-space data is acquired from a scanner, an undersampling operator is used to perform an undersampling operation on the fully sampled k-space data to obtain undersampled k-space data, and a fully sampled sensitivity map, a fully sampled composite map, and a fully sampled multi-coil map are obtained using the fully sampled k-space data. The undersampled k-space data, the fully sampled sensitivity map, the fully sampled composite map, and the fully sampled multi-coil image together constitute a training set;

[0053] Step S2: Network design: Design a deep sensitivity learning unfolding network model for non-Cartesian sampling magnetic resonance intelligent imaging network, network reasoning capability and loss function;

[0054] Step S3: training the network; using the training set obtained in step S1, solving the optimal parameters of the magnetic resonance intelligent imaging network;

[0055] Step S4: Reconstructing the network; inputting the magnetic resonance non-Cartesian under-sampled k-space data to be reconstructed into the trained magnetic resonance intelligent imaging network to reconstruct the magnetic resonance image.

[0056] In this embodiment, specifically, step S1 includes:

[0057] Step S11: Acquire non-Cartesian full-sampling multi-channel magnetic resonance data, i.e., non-Cartesian full-sampling k-space data, from a magnetic resonance scanner;

[0058] Step S12: using an undersampling operator to undersample the non-Cartesian fully sampled multi-channel magnetic resonance data to obtain undersampled k-space data;

[0059] Step S13: Calculate the non-Cartesian fully sampled k-space data using non-uniform Fourier transform to obtain a fully sampled sensitivity map, a fully sampled composite map, and a fully sampled multi-coil map, which together with the undersampled k-space data form a training set.

[0060] In this embodiment, specifically, the magnetic resonance intelligent imaging network is composed of an initialization module IC and multiple iteration blocks as the core, and is formed by cascading K network iteration modules;

[0061] Among them, the initialization module IC includes: calculation of multi-channel zero-filling map, initialization sensitivity map and initialization synthesis map; the network iteration module includes: artifact suppression module DAS, sensitivity learning module DSE, data consistency module DC and image reconstruction module IR.

[0062] In this embodiment, specifically, the workflow of the initialization module IC is as follows:

[0063] The undersampled k-space data k is converted into a multi-channel zero-filling map through density compensation and non-uniform Fourier transform. (Multi-coil zero filling diagram);

[0064] Fill multi-channel zero map Divide the composite image after the SOS operation (Sum-of-Squares operation) to obtain the initialization sensitivity map

[0065] Fill multi-channel zero map Multiply by the initialized sensitivity map The complex conjugate transpose of gets the initialized synthetic graph m (0) .

[0066] In this embodiment, specifically, the artifact suppression module DAS uses a multi-channel zero-filling map As input, it verifies the consistency of k-space data, encoder (DAS1) and decoder (DAS2), and outputs the multi-coil zero-filling map after artifact suppression.

[0067] The encoder (DAS1) and decoder (DAS2) are composed of M filters, each of which is composed of a convolution layer, a normalization function, a nonlinear activation function and a convolution layer cascade; the encoder is based on the k-space data after consistency check. As input, the encoded features are used as output; the decoder uses the encoded features of the encoder and the features after Relu nonlinear mapping as input and the features after artifact suppression as output. as output.

[0068] In this embodiment, specifically, the sensitivity learning module DSE initializes the sensitivity map As input, it uses two submodules, DSE1 and DSE2, to learn sensitivity and output a sensitivity map with high-frequency details.

[0069] The sensitivity learning submodules DSE1 and DSE1 are composed of J filters, each of which is composed of a convolution layer, a normalization function, a nonlinear activation function and a convolution layer cascade; the sensitivity learning submodule DSE1 is used to initialize the sensitivity map As input, the encoded features are output; the sensitivity learning submodule DSE2 takes the features learned by DSE1 as input and the sensitivity map of high-frequency details after learning as output.

[0070] In this embodiment, specifically, the data consistency module DC initializes the composite graph m (k-1) As input, after calculating the consistency prior formula, the updated composite image is output

[0071] In this embodiment, specifically, the image reconstruction module IR uses the updated synthetic image As input, through the forward sparse representation N1, ReLu non-activation function and reverse sparse reconstruction N2, the output artifact-suppressed reconstructed image m (k) ;

[0072] Both the forward sparse representation N1 and the reverse sparse reconstruction N2 are composed of N convolution units, each of which is composed of a convolution layer, a normalization function, a nonlinear activation function and a convolution layer cascade; the forward sparse representation N1 is used to synthesize the image As input, the sparsely represented feature δ nAs output; reverse sparse reconstruction N2 is the feature δ after forward sparse representation n After ReLu nonlinear mapping, it is used as input to reconstruct the image m (k) as output.

[0073] In this embodiment, specifically, the artifact suppression module DAS, the sensitivity learning module DSE, the data consistency module DC and the image reconstruction module are cascaded in the iteration block, and the final reconstructed composite image m is input through iterative reconstruction of K iteration blocks. (K) .

[0074] In this embodiment, specifically, the magnetic resonance intelligent imaging network is represented as:

[0075] m=f overall (k|Θ)

[0076] Among them, Θ represents the learnable parameters of the entire reconstruction network, f overall (k|Θ) represents the network’s nonlinear mapping from the undersampled k-space data k input to the network’s final reconstructed synthetic image m.

[0077] In this embodiment, specifically, the inference function and loss function of the design network include:

[0078] The final reconstructed synthetic image m through the network and the fully sampled synthetic image m ref Constraints; The network finally outputs a multi-coil zero-filling diagram With full sampling multi-coil image Constraints; Sensitivity map of the network's final output Sensitivity plot with full sampling Constraints are formed to form three-constraint loss functions L1, L2 and L3, which realize the loss function construction of sensitivity learning:

[0079] The loss function L1 of the reconstructed synthetic image is defined as:

[0080]

[0081] The multi-coil zero-filling graph loss function L2 is defined as:

[0082]

[0083] The sensitivity loss function L3 is defined as:

[0084]

[0085] Among them, T represents the number of training samples, K represents the number of iterations, represents the fully sampled synthetic image of the t-th sample, represents the fully sampled multi-coil image of the t-th sample, represents the full sampling sensitivity map of the t-th sample, represents the reconstructed composite image of the t-th sample outputted by the k-th iteration network, represents the multi-coil zero-filled image output by the t-th sample in the k-th iteration network learning, Represents the sensitivity map of the t-th sample output by the k-th iteration network learning;

[0086] The total loss function of the magnetic resonance intelligent imaging network is expressed as:

[0087] L total =λ1L1+λ2L2+λ3L3

[0088] Among them, λ1, λ2, and λ3 are adjustable coefficients used to balance the attention paid to reconstructing the synthetic image, the multi-coil zero-filling map, and the sensitivity map learning.

[0089] In this embodiment, specifically, in step S3, the Adam optimizer is used to solve the optimal parameters of the magnetic resonance intelligent imaging network, and the network is trained using the training set generated in step S1, by minimizing the loss function L in step S2. total Get the optimal target parameter set

[0090] In this embodiment, specifically, in step S4, the magnetic resonance non-Cartesian under-sampled k-space data to be reconstructed is input into the trained network to reconstruct the magnetic resonance image, which is expressed as;

[0091]

[0092] Among them, m recom In order to reconstruct the final coil synthesis image, the undersampled k-space data k is input into the trained network.

[0093] Example 2

[0094] In this example, the knee joints of 100 volunteers were imaged using a 3T magnetic resonance imaging device. The specific MRI sequence parameters were set as follows: echo time (TE) of 27 milliseconds, repetition time (TR) of 2750 milliseconds, field of view of 320 × 320 mm, image size of 320 × 320, and number of coils of 4. Non-Cartesian, fully sampled, multi-coil MRI image data of the human brains of 100 volunteers were acquired.

[0095] This embodiment uses multi-coil knee data to construct a training set. Through multiple iterative training of a sensitivity-based deep unfolding network and loss function constraints, the optimal reconstructed image is obtained, thereby obtaining a reconstructed magnetic resonance image. The specific steps are as follows:

[0096] Step S1: training data generation; non-Cartesian fully sampled k-space data is acquired from a scanner, an undersampling operator is used to perform an undersampling operation on the fully sampled k-space data to obtain undersampled k-space data, and the fully sampled k-space data is used to obtain a fully sampled sensitivity map, a fully sampled composite map, and a fully sampled multi-coil map. The undersampled k-space data, the fully sampled sensitivity map, the fully sampled composite map, and the fully sampled multi-coil image together constitute a training set.

[0097] Step S11: Acquire non-Cartesian full-sampling multi-channel magnetic resonance data k from the magnetic resonance scanner full ∈C 640 ×500×4 , where C represents the complex domain, the number of radial line spokes of the fully sampled k-space data is 500, the number of sampling points of each radial line is 640, and the k-space data has 4 coils.

[0098] Step S12: Under-sampling the non-Cartesian fully sampled multi-channel magnetic resonance data using an under-sampling operator to obtain under-sampled k-space data k by:

[0099] k=Zk full

[0100] Where Z represents the undersampling operator, k∈C 640×100×4 is undersampled k-space data (the number of spokes is 100).

[0101] Step S13: Calculate the non-Cartesian fully sampled k-space data using non-uniform Fourier transform to obtain a fully sampled sensitivity map, a fully sampled composite map, and a fully sampled multi-coil image by:

[0102]

[0103] Where D is the density compensation, is the inverse non-uniform Fourier transform, SOS is the Sum-of-Squares operator, represents a fully sampled multi-coil image, represents the full-sample sensitivity map, represents the fully sampled synthetic image.

[0104] In summary, undersampled k-space data k, full sampling sensitivity map Fully sampled composite image and The fully sampled multi-coil images together constitute the training set.

[0105] Step S2: Network design; design the sensitivity learning deep unfolding network model for non-Cartesian sampling magnetic resonance intelligent imaging network, the network's reasoning ability and loss function.

[0106] In this example, specifically, the sensitivity learning deep unfolding network model for non-Cartesian magnetic resonance intelligent fast reconstruction network is based on the initialization module IC and multiple iteration blocks (blocks) as the core (Figure (a)), and is composed of K network iteration modules in cascade.

[0107] Among them, please refer to the initialization module IC Figure 2 (b) The multi-channel zero-filling map is obtained by density compensation and non-uniform Fourier transform of the undersampled k-space data k Fill multi-channel zero map Divide by the composite graph after the SOS operation (Sum-of-Squares operation) to obtain the initialization sensitivity map Fill multi-channel zero map Multiply by the initialized sensitivity map The complex conjugate transpose of gets the initialized synthetic image m (0) , the calculation process is expressed as:

[0108]

[0109] In this embodiment, specifically, the iteration module includes an artifact suppression module DAS, a sensitivity learning module DSE, a data consistency module DC and an image reconstruction module IR.

[0110] Artifact Suppression Module DAS:

[0111] First, the module uses a multi-coil zero filling diagram As input, the consistency of k-space data is verified by the following formula:

[0112]

[0113] Among them, ν is the network learnable parameter, This is the output after consistency check.

[0114] Then, It is fed into the artifact suppression network learning module of the encoder (DAS1) and decoder (DAS2), and outputs the multi-coil zero-filling map after artifact suppression. The process is expressed as:

[0115]

[0116] Among them, the encoder (DAS1) consists of M filters, each filter consists of a convolution layer, a normalization function, a nonlinear activation function and a convolution layer cascade; the decoder (DAS2) consists of M filters, each filter consists of a convolution layer, a normalization function, a nonlinear activation function and a convolution layer cascade; Relu is a nonlinear mapping.

[0117] In summary, the artifact suppression module can be represented by the following nonlinear mapping:

[0118]

[0119] Among them, Θ DAS It is the set of network learnable parameters in the artifact suppression module DAS.

[0120] In this embodiment, specifically, the sensitivity learning module DSE learns full-sampled high-frequency information through a convolutional neural network to improve the accuracy of sensitivity estimation; the depth reconstruction module includes two sub-modules DSE1 and DSE2.

[0121] First, the sensitivity learning module suppresses the artifacts and fills the multi-coil zero image As input, the updated sensitivity map is calculated by SOS operation Through the following formula:

[0122]

[0123] Subsequently, the updated sensitivity map It is sent to the two sub-modules DSE1 and DSE2 for sensitivity learning, and then the sensitivity map is updated through the residual connection. The process is expressed as:

[0124]

[0125] in, represents the sensitivity map output by the sensitivity learning module, It is a network reference for DSE1 learning. are the network parameters learned by DSE2. Both DSE1 and DSE2 modules consist of J filters, each of which is composed of a convolutional layer, a normalization function, a nonlinear activation function, and a convolutional layer cascaded.

[0126] In summary, the sensitivity learning module can be represented by the following nonlinear mapping:

[0127]

[0128] Among them, Θ DSE It is the set of network learnable parameters in the artifact suppression module DSE.

[0129] In this embodiment, specifically, the data consistency module DC. This module synthesizes the graph As input, after the consistency calculation formula, the updated composite image is output The process is described as:

[0130]

[0131]

[0132] in, Updated k-space data for data verification, is the synthetic image output by the module, k represents the kth iteration, and η is the network learnable parameter.

[0133] In this embodiment, specifically, the image reconstruction module IR includes forward sparse representation N1, ReLu non-activation function and reverse sparse reconstruction N2 sub-modules.

[0134] The forward sparse representation N1 submodule consists of N convolution units, each of which consists of a convolution layer, a normalization function, a nonlinear activation function, and a convolution layer cascade. The convolution kernel size of the convolution layer is h×h.

[0135] Forward sparse representation N1 to synthesize the image As input, the sparse representation feature δ n As output; the process can be described as:

[0136]

[0137] in, are the learning parameters of the forward sparse representation network.

[0138] The reverse sparse reconstruction N2 submodule consists of N convolution units, each of which consists of a convolution layer, a normalization function, a nonlinear activation function, and a convolution layer cascade. The convolution kernel size of the convolution layer is h×h.

[0139] Reverse sparse reconstruction N2 to sparsely represent features δ n As input, the sparsely reconstructed image m (k+1) As output, the process can be described as:

[0140]

[0141] in, Learning parameters for the reverse sparse reconstruction network.

[0142] The module can be described as:

[0143]

[0144] In summary, the image reconstruction module IR can be represented by the following nonlinear mapping:

[0145]

[0146] Among them, Θ IR It is the set of network learnable parameters in the artifact suppression module DSE.

[0147] Therefore, a single iteration block can be represented as the following mapping form:

[0148]

[0149] in, represents the set of network training parameters for the kth iteration, Represents network training to synthesize reconstructed images To the next iteration output synthetic reconstructed image Nonlinear mapping.

[0150] In summary, the entire sensitivity learning depth expansion network is expressed as:

[0151] m=f overall (k|Θ)

[0152] Among them, Θ represents the learnable parameters of the entire reconstruction network, f overall (k|Θ) represents the nonlinear mapping from the undersampled k-space data k input to the network to the synthetic image m finally reconstructed by the network.

[0153] In this embodiment, the reasoning function and loss function of the design network are specifically designed, including:

[0154] The final reconstructed synthetic image m through the network and the fully sampled synthetic image m ref Constraints; The network finally outputs a multi-coil zero-filling diagram With full sampling multi-coil image Constraints; Sensitivity map of the network's final output Sensitivity plot with full sampling Constraints form three-constraint loss functions L1, L2 and L3.

[0155] The loss function L1 of the reconstructed synthetic image is defined as:

[0156]

[0157] The multi-coil zero-filling graph loss function L2 is defined as:

[0158]

[0159] The sensitivity loss function L3 is defined as:

[0160]

[0161] Among them, T represents the number of training samples, K represents the number of iterations, represents the fully sampled synthetic image of the t-th sample, represents the fully sampled multi-coil image of the t-th sample, represents the full sampling sensitivity map of the t-th sample, represents the reconstructed composite image of the t-th sample outputted by the k-th iteration network, represents the multi-coil zero-filled image output by the t-th sample in the k-th iteration network learning, Represents the sensitivity map of the t-th sample output by the k-th iteration network learning;

[0162] The total loss function of the entire network is expressed as:

[0163] L total =λ1L1+λ2L2+λ3L3

[0164] Among them, λ1, λ2, and λ3 are adjustable coefficients used to balance the attention paid to reconstructing the synthetic image, the multi-coil zero-filling map, and the sensitivity map learning.

[0165] Step S3: training the network; using the training set obtained in step S1, solving the optimal parameters of the sensitivity-based learning depth expansion network;

[0166] In this embodiment, specifically, the optimal parameters of the sensitivity learning depth expansion network adopt the Adam optimizer with good performance, and the network training is performed using the training set generated in step S1. The network is trained for 200 rounds, and the three-constraint loss function L is minimized. total Get the optimal target parameter set

[0167] Step S4: reconstructing the image; inputting the non-Cartesian undersampled k-space data to be reconstructed into the trained deep learning network to reconstruct the magnetic resonance image; the reconstruction process can be expressed as:

[0168]

[0169] Among them, m recom In order to reconstruct the final coil synthesis image, the undersampled k-space data k is input into the trained network.

[0170] In the embodiment, the input of the network is a radial golden angle sampling trajectory with an acceleration factor of 5 (e.g. Figure 1 The fully sampled label image, undersampled zero-filled image and the image reconstructed by the present invention are shown in Figure 1. Figure 3 (a), Figure 3 (b) and Figure 3 (c) The difference diagrams between the undersampled zero-filled image and the fully sampled image, and the difference diagrams between the reconstructed image of the present invention and the fully sampled image are shown in FIG. Figure 3 (e) and Figure 3 (f).

[0171] The above-described embodiments merely represent specific implementation methods of the present application. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of protection of the present application. It should be noted that a person skilled in the art would be able to make numerous variations and improvements without departing from the technical concept of the present application, and all such variations and improvements fall within the scope of protection of the present application.

[0172] This background section is provided to generally present the context of the invention, and the work of the presently named inventors, the work to the extent described in this background section, and aspects of the description in this section that did not constitute prior art at the time of filing are neither explicitly nor implicitly admitted to be prior art to the present invention.

Claims

1. An intelligent non-Cartesian magnetic resonance rapid imaging method, characterized in that: include: Step S1: training data generation; Acquire non-Cartesian fully sampled k-space data from a scanner, use an undersampling operator to perform undersampling operation on the fully sampled k-space data to obtain undersampled k-space data, use the fully sampled k-space data to obtain a fully sampled sensitivity map, a fully sampled composite map, and a fully sampled multi-coil map, and the undersampled k-space data, the fully sampled sensitivity map, the fully sampled composite map, and the fully sampled multi-coil image together constitute a training set; Step S2: Network design: Design a deep sensitivity learning unfolding network model for non-Cartesian sampling magnetic resonance intelligent imaging network, network reasoning capability and loss function; Step S3: training the network; using the training set obtained in step S1, solving the optimal parameters of the magnetic resonance intelligent imaging network; Step S4: reconstructing the network; inputting the magnetic resonance non-Cartesian under-sampled k-space data to be reconstructed into the trained magnetic resonance intelligent imaging network to reconstruct the magnetic resonance image.

2. The intelligent non-Cartesian magnetic resonance rapid imaging method according to claim 1, characterized in that: The step S1 comprises: Step S11: Acquire non-Cartesian full-sampling multi-channel magnetic resonance data, i.e., non-Cartesian full-sampling k-space data, from a magnetic resonance scanner; Step S12: using an undersampling operator to undersample the non-Cartesian fully sampled multi-channel magnetic resonance data to obtain undersampled k-space data; Step S13: Calculate the non-Cartesian fully sampled k-space data using non-uniform Fourier transform to obtain a fully sampled sensitivity map, a fully sampled composite map, and a fully sampled multi-coil map, which together with the undersampled k-space data form a training set.

3. The intelligent non-Cartesian magnetic resonance rapid imaging method according to claim 1, characterized in that: The magnetic resonance intelligent imaging network is composed of an initialization module IC and multiple iteration blocks as the core, and is constructed by cascading K network iteration modules; Among them, the initialization module IC includes: calculation of multi-channel zero-filling map, initialization sensitivity map and initialization synthesis map; the network iteration module includes: artifact suppression module DAS, sensitivity learning module DSE, data consistency module DC and image reconstruction module IR.

4. The intelligent non-Cartesian magnetic resonance rapid imaging method according to claim 3, characterized in that: The workflow of the initialization module IC is as follows: The undersampled k-space data k is converted into a multi-channel zero-filling map through density compensation and non-uniform Fourier transform. Fill multi-channel zero map Divide by the composite graph after the SOS operation to obtain the initialized sensitivity graph Fill multi-channel zero map Multiply by the initialized sensitivity map The complex conjugate transpose of gets the initialized synthetic graph m (0) .

5. The intelligent non-Cartesian magnetic resonance rapid imaging method according to claim 4, characterized in that: The artifact suppression module DAS uses a multi-channel zero-filling map As input, the consistency of k-space data is verified, the encoder and decoder are used to output the multi-coil zero-filling map after artifact suppression. The encoder and decoder are composed of M filters, each filter is composed of a convolution layer, a normalization function, a nonlinear activation function and a convolution layer cascade; the encoder is based on the k-space data after consistency check. As input, the encoded features are output; The decoder takes the encoded features of the encoder and the features after Relu nonlinear mapping as input, and takes the features after artifact suppression as as output.

6. The intelligent non-Cartesian magnetic resonance rapid imaging method according to claim 5, characterized in that: The sensitivity learning module DSE is used to initialize the sensitivity map As input, it uses two submodules, DSE1 and DSE2, to learn sensitivity and output a sensitivity map with high-frequency details. The sensitivity learning submodules DSE1 and DSE1 are composed of J filters, each of which is composed of a convolution layer, a normalization function, a nonlinear activation function and a convolution layer cascade; the sensitivity learning submodule DSE1 is used to initialize the sensitivity map As input, the encoded features are output; The sensitivity learning submodule DSE2 takes the features learned by DSE1 as input and uses the sensitivity map of the learned high-frequency details as the input. as output.

7. The intelligent non-Cartesian magnetic resonance rapid imaging method according to claim 6, characterized in that: The data consistency module DC initializes the composite graph m (k-1) As input, after calculating the consistency prior formula, the updated composite image is output 8. The intelligent non-Cartesian magnetic resonance rapid imaging method according to claim 7, characterized in that: The image reconstruction module IR uses the updated synthetic image As input, through the forward sparse representation N1, ReLu non-activation function and reverse sparse reconstruction N2, the output artifact-suppressed reconstructed image m (k) ; Both the forward sparse representation N1 and the reverse sparse reconstruction N2 are composed of N convolution units, each of which is composed of a convolution layer, a normalization function, a nonlinear activation function and a convolution layer cascade; the forward sparse representation N1 is used to synthesize the image As input, the sparsely represented feature δ n As output; reverse sparse reconstruction N2 is the feature δ after forward sparse representation n After ReLu nonlinear mapping, it is used as input to reconstruct the image m (k) as output.

9. The intelligent non-Cartesian magnetic resonance rapid imaging method according to claim 8, characterized in that: Design the network's inference capabilities and loss function, including: The final reconstructed synthetic image m through the network and the fully sampled synthetic image m ref Constraints; The network finally outputs a multi-coil zero-filling diagram With full sampling multi-coil image Constraints; Sensitivity map of the network's final output Sensitivity plot with full sampling Constraints are formed to form three-constraint loss functions L1, L2 and L3, which realize the loss function construction of sensitivity learning: The loss function L1 of the reconstructed synthetic image is defined as: The multi-coil zero-filling graph loss function L2 is defined as: The sensitivity loss function L3 is defined as: Among them, T represents the number of training samples, K represents the number of iterations, represents the fully sampled synthetic image of the t-th sample, represents the fully sampled multi-coil image of the t-th sample, represents the full sampling sensitivity map of the t-th sample, represents the reconstructed composite image of the t-th sample outputted by the k-th iteration network, represents the multi-coil zero-filled image output by the t-th sample in the k-th iteration network learning, Represents the sensitivity map of the t-th sample output by the k-th iteration network learning; The total loss function of the magnetic resonance intelligent imaging network is expressed as: L total =λ1L1+λ2L2+λ3L3 Among them, λ1, λ2, and λ3 are adjustable coefficients used to balance the attention paid to reconstructing the synthetic image, the multi-coil zero-filling map, and the sensitivity map learning.

10. The intelligent non-Cartesian magnetic resonance rapid imaging method according to claim 9, characterized in that: In step S3, the Adam optimizer is used to solve the optimal parameters of the magnetic resonance intelligent imaging network, and the network is trained using the training set generated in step S1, by minimizing the loss function L in step S2. total Get the optimal target parameter set

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