CN108335339B - Magnetic resonance reconstruction method based on deep learning and convex set projection - Google Patents

Magnetic resonance reconstruction method based on deep learning and convex set projection Download PDF

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CN108335339B
CN108335339B CN201810306848.5A CN201810306848A CN108335339B CN 108335339 B CN108335339 B CN 108335339B CN 201810306848 A CN201810306848 A CN 201810306848A CN 108335339 B CN108335339 B CN 108335339B
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Abstract

The invention discloses a magnetic resonance reconstruction method based on deep learning and convex set projection, which relates to the technical field of magnetic resonance and comprises the following steps: s1: constructing a network according to an overlapping structure of a plurality of convolutional neural network modules and a plurality of convex set projection layers and shared data, wherein the shared data comprises acquired K space data and coil sensitivity information, and the convex projection layers are obtained based on the shared data; s2: after the network is constructed, training all network parameters through a back propagation process, and verifying the network parameters; s3: and determining the structure and the operational characteristics of the network according to the inspected network parameters, inputting known test set data, performing forward propagation of the network to obtain unknown mapping data, and completing reconstruction of magnetic resonance. The method solves the problem that the existing magnetic resonance reconstruction technology based on deep learning can only support single-channel magnetic resonance data and can not process multi-channel magnetic resonance data.

Description

Magnetic resonance reconstruction method based on deep learning and convex set projection
Technical Field
The invention relates to the technical field of magnetic resonance, in particular to a magnetic resonance reconstruction method based on deep learning and convex set projection.
Background
The magnetic resonance imaging technique is a technique for performing imaging by utilizing a nuclear magnetic resonance phenomenon of hydrogen protons. Nuclei in the human body containing a single proton, such as the ubiquitous hydrogen nucleus, have a spin motion. The spin motion of the charged nuclei is physically similar to that of the individual small magnets, and the directional distribution of these small magnets is random without the influence of external conditions. When a human body is placed in an external magnetic field, the small magnets are rearranged according to the magnetic lines of the external magnetic field, specifically, the small magnets are arranged in two directions which are parallel or antiparallel to the magnetic lines of the external magnetic field, the direction which is parallel to the magnetic lines of the external magnetic field is called as a positive longitudinal axis, the direction which is antiparallel to the magnetic lines of the external magnetic field is called as a negative longitudinal axis, and the atomic nucleus only has a longitudinal magnetization component which has both a direction and an amplitude.
The magnetic resonance phenomenon is that nuclei in an external magnetic field are excited by Radio Frequency (RF) pulses of a specific Frequency, so that the spin axes of the nuclei deviate from the positive longitudinal axis or the negative longitudinal axis to generate resonance. After the spin axes of the excited nuclei are offset from the positive or negative longitudinal axis, the nuclei have a transverse magnetization component.
After the emission of the radio frequency pulse is stopped, the excited atomic nucleus emits an echo signal, absorbed energy is gradually released in the form of electromagnetic waves, the phase and the energy level of the electromagnetic waves are restored to the state before the excitation, and the image can be reconstructed by further processing the echo signal emitted by the atomic nucleus through space coding and the like.
Due to the physical characteristics of magnetic resonance and the limitation of the scanned human body, the magnetic resonance imaging scan needs a long time to acquire enough signals (K-space data) for image reconstruction. The long scanning time results in low efficiency of hospital scanning diagnosis and is easy to cause discomfort to patients during scanning. In addition, the long scan time makes it difficult for magnetic resonance scanning to deal with imaging of moving tissues of the human body, such as the abdomen, the heart, and the like. Therefore, how to shorten the scanning time based on ensuring the image quality required by clinical diagnosis becomes one of the core researches in the magnetic resonance imaging and reconstruction field. The parallel imaging technology relies on a plurality of phased array receiving coils, and an effective parallel imaging processing algorithm is used for restoring an undersampled signal or unlocking image aliasing caused by undersampling, so that the shorter image acquisition time is finally realized.
In 1999, K.P.Pruessmann et al proposed the SENSE (SENSE: sensing Encoding for Fast MRI) technique. The technology relies on a multi-channel phased array coil, and combines the space coding capacity of coil sensitivity with the coding capacity of gradient pulses, so that the data acquisition is reduced, and the scanning time is shortened. The SENSE technique first requires the calculation of the coil sensitivity profiles of all the receive channels, this information can be achieved by a pre-scan independent of the main scan; and then, the undersampled K space data is acquired in the formal scanning, so that the scanning time is effectively shortened. These undersampled K-space data correspond to the image in the image domain as the image is warped. Finally, through the coil sensitivity and the deconvolution algorithm, the image with the convolution can be effectively unwrapped, and the image without the convolution can be obtained. From a technical principle point of view, the SENSE algorithm based on known coil sensitivities can yield optimal results with the goal of minimizing the mean square error. Meanwhile, the SENSE technology has wide applicability, can be suitable for various K space scanning tracks and can easily fuse various known information in the reconstruction process to improve the reconstruction quality. However, it is not easy to stably obtain an accurate coil sensitivity distribution, and even a very small coil sensitivity error may introduce very noticeable artifacts on the image.
GRAPPA (Generalized Auto-calibrating Parallel responses) technology was proposed in 2002 by m.a. griswold et al. GRAPPA techniques also utilize multi-channel phased array coils, but do not require additional computation of the spatial sensitivity profiles of the coils, but rather recover undersampled data using correlations of the K-space data. While the GRAPPA technique undersamples the K space, the data in the center of the K space is kept as full samples, and the data is called an ACS (auto-calibration signal); then, calculating a convolution kernel (GRAPPA kernel) representing the correlation between the K space data according to the ACS signal; and finally, reconstructing undersampled data by using the estimated convolution kernel and the acquired data so as to obtain complete K space data, wherein the corresponding K space data is an image without a convolution. The GRAPPA technique avoids the spatial distribution of the coil sensitivity from being accurately estimated, the reconstruction quality is stable, but the effect is obviously reduced under the condition of higher acceleration factor.
In 2004, samonov et al proposed a SENSE (POCSENSE) technique based on projection of convex sets. Unlike classical SENSE, this technique treats the problem of convolution image recovery from a subspace perspective, indicating that the reconstruction problem of undersampled magnetic resonance can be equivalently defined as the problem of seeking non-convolution images of all individual channels. The non-convolved image of a single channel is constrained by the coil sensitivity and the overall image, i.e. the single channel image is from a subspace defined by the coil sensitivity. The convex set projection SENSE technique still requires first obtaining the coil sensitivity profiles of the individual channels and then obtaining the non-convolved images of all the individual channels by the convex set projection process and the consistency constraints of the acquired data. The POCSENSE technique further simplifies the SENSE reconstruction process and more easily incorporates linear or non-linear constraints.
In 2014, Martin Uecker, Peng Lai et al proposed a mixed-domain ESPIRiT (An Eigenvalue Approach to Autocalizing Parallel MRI: Where SENSE Meets GRAPPA) technique. This technique attempts to fuse the two methods SENSE and GRAPPA from a subspace perspective. The authors note that the SENSE technique limits the undersampled data to a particular subspace by knowing the coil sensitivity profile, whereas the GRAPPA technique recovers the undersampled data by the null space defined by the autocorrelation matrix. Based on the above relationship, the ESPIRiT technique constructs a specific K-space correlation matrix from the ACS signal, and then generates a stable and accurate spatial distribution of coil sensitivities by a eigenvalue decomposition method of an image domain. Meanwhile, in the reconstruction stage, soft constraint conditions of multiple groups of coil sensitivities are introduced to replace the hard constraint of the traditional SENSE, and the hierarchy of coil sensitivity distribution is avoided. The method combines the advantages of the respective SENSE technology and GRAPPA technology, and can obtain more stable and accurate reconstruction effect.
To further shorten the scan time on the basis of parallel imaging, in 2007, michael lustig et al proposed magnetic resonance imaging based on a compressed sensing technique. The theory of compressed sensing holds that if the processed signal has sparsity in a certain domain, discrete samples of the signal can be obtained by randomly sampling the signal under the condition of far less than the nyquist sampling rate, and then the original signal is restored by a nonlinear reconstruction algorithm. In the clinic, especially for dynamic scanning (such as heart) or space sparse structures (such as blood vessel imaging), the compressed sensing technology has good effect by extremely fast scanning speed and good reconstruction capability.
The compressed sensing technology has specific requirements on the acquisition and reconstruction process of signals, and mainly comprises four aspects. First, K-space signal acquisition must be done in a random or non-cartesian manner to ensure that image artifacts due to undersampling are uncorrelated in the transform domain. However, in clinical practice, particularly in the most widely used magnetic resonance two-dimensional scans, the scan trajectory is difficult to randomize or to non-cartesian. Second, the compressed sensing technique requires that the image to be reconstructed has a sparse representation in a particular transform domain. Commonly used sparse representations include wavelet transforms or total variabilities. In these transform domains, sparsity is often expressed approximately using the L1 norm. However, the above approximate transformation is difficult to describe a complicated microscopic biological structure, which leads to a blurred reconstructed image or a mosaic effect. Third, the compressed sensing technique defines the magnetic resonance reconstruction as a nonlinear optimization problem, thus resulting in long reconstruction times. Finally, a plurality of hyper-parameters having great influence on the reconstruction result exist in the compressive sensing algorithm, the definition and debugging of the hyper-parameters are often dependent on experience, and the generalized and stable hyper-parameter definition is difficult to obtain.
In recent years, deep learning represented by a convolutional neural network has been significantly advanced in the fields of computer vision, language understanding, and the like. In recent two years, in order to obtain a higher acceleration ratio and a better reconstruction effect, a technology of using a deep learning idea for magnetic resonance sparse reconstruction and further shortening the scanning time is continuously emerging. According to the network construction method of deep learning, the related technologies can be divided into two categories: deep learning-based reconstruction techniques and discriminant learning-based reconstruction techniques. The reconstruction technology based on deep learning adopts an end-to-end learning method and various network construction methods, can extract, identify and recover images and data, and has flexible network structure. Discriminant learning-based reconstruction techniques are intermediate between model-based and deep learning-based reconstruction techniques, which, on the one hand, have defined the magnetic resonance reconstruction problem in accordance with model-based methods, and, on the other hand, attempt to solve the problems encountered by model-based methods, such as more accurate hyper-parameter definition, faster reconstruction times, etc., by convolutional neural networks.
In 2017, Kerstin Hammernik et al used a variational network (variable network) for magnetic resonance fast reconstruction. The method comprises the steps of firstly, defining a magnetic resonance sparse reconstruction problem as a variational model solved by using a gradient descent algorithm by adopting a model-based method; then, the iterative process of the gradient descent algorithm is networked, and parameters in the algorithm are guaranteed not to be set manually but generated through training. Each iteration stage in the network thus produced corresponds to an iterative calculation in a conventional model-based reconstruction. In 2017, Yan Yang et al proposed an ADMM network (ADMM-Net: A Deep Learning Approach for Compressive Sensing MRI) for magnetic resonance sparse reconstruction. The method also adopts a model-based method, firstly, the magnetic resonance sparse reconstruction problem is defined as an iterative process solved by adopting an ADMM algorithm; then, defining a data flow based on the iterative process; finally, the data flow structure is generalized through the network structure, and parameters in the network are guaranteed to be trainable. Both methods belong to discriminant learning-based reconstruction techniques and achieve higher reconstruction quality compared to parallel imaging and compressed sensing reconstruction techniques.
In 2016, Wang et al proposed a technique for deep learning for sparse reconstruction of magnetic resonance. The technology firstly constructs a convolutional neural network, then uses an end-to-end training mode to enable the network to convert input undersampled data into full-sampling data, and finally uses an output result of the network as an initial value of compressed sensing reconstruction or as a regularization term newly introduced in an equation of the compressed sensing reconstruction. In 2017, Jo Schlemper et al proposed a series deep learning network mode for magnetic resonance sparse reconstruction. The technology defines magnetic resonance sparse reconstruction as a learning process for eliminating artifacts in an image domain, and a constructed convolutional neural network can learn how to eliminate the image artifacts caused by undersampling through a training process. The technology firstly constructs a shallow convolutional neural network, and then a specially arranged data consistency layer (data consistency layer) is added behind the network and is used for providing information of sampled data; and finally, connecting the two basic structure repetitions in series to construct a deeper convolutional network. The technology is characterized in that a more stable and efficient network structure is constructed by combining two independent factors of reconstruction based on a convolutional neural network and the consistency of sampled data. Experiments show that compared with a reconstruction method based on dictionary learning, the method is faster and more accurate. However, the technology only supports single-channel magnetic resonance data at present and cannot process multi-channel magnetic resonance data.
Disclosure of Invention
The invention aims to: the invention provides a magnetic resonance reconstruction method based on deep learning and convex set projection, and solves the problems that the existing magnetic resonance reconstruction technology based on deep learning can only support single-channel magnetic resonance data and cannot process multi-channel magnetic resonance data.
A magnetic resonance reconstruction method based on deep learning and convex set projection comprises the following steps:
s1: and constructing a reconstruction network according to the overlapping structure of the plurality of convolutional neural network modules and the plurality of convex set projection layers and shared data, wherein the shared data comprises acquired K-space data and coil sensitivity information, and the convex set projection layers are obtained based on the shared data.
S2: after the network is constructed, training all network parameters through a back propagation process, and verifying the network parameters;
s3: and determining the structure and the operational characteristics of the network according to the inspected network parameters, inputting known test set data, performing forward propagation of the network to obtain unknown mapping data, and completing reconstruction of magnetic resonance.
Further, the S1 includes the following steps:
s1.1: the method comprises the steps of collecting under-sampled multichannel data and self-calibration data in K space, taking a central area in the K space multichannel data as the self-calibration data, and taking the part except the self-calibration data as the under-sampled multichannel data.
S1.2, generating a multi-channel convolution image corresponding to the under-sampled multi-channel data through inverse Fourier transform, and taking the multi-channel convolution image as the input of a reconstruction network.
S1.3: multichannel coil sensitivity distribution information is obtained from the self-calibration data.
S1.4: synthesizing the multichannel convolution images into an image I through a channel synthesis operator based on the multichannel coil sensitivity distribution informationcomb；
S1.5: image I is passed through convolutional neural network module CNN1combMapping to an output image I without or with reduced wrap-around artifactscnn1；
S1.6: will output image Icnn1Transmitting into a convex set projection layer POCS, and dividing in the convex set projection layer POCS according to coil sensitivityThe information distribution and the collected K space multichannel data complete the projection process of the convex set to obtain an image Ipocs1；
S1.7: image Ipocs1Inputting into convolutional neural network module CNN2 to obtain image Ipocs1Mapping to an output image I without or with reduced wrap-around artifactscnn2(ii) a Then the image I is processedcnn2Transmitting the signal into a convex set projection layer POCS, and completing the convex set projection process in the convex set projection layer POCS according to the coil sensitivity distribution information and the acquired K-space multi-channel data to obtain an image Ipocs2；
S1.8: repeating S1.7 to construct a deep network structure which comprises N in totalcCNN layers and NcAnd a POCS layer, so far, the network construction is completed.
Specifically, in S1.1, S1.3 includes the following steps:
s1.3.1: generating a correction matrix A according to self-calibration data in the K space multichannel data;
s1.3.2: performing singular value decomposition on the correction matrix A to obtain a right singular matrix V, wherein the decomposition formula is as follows: a ═ U ∑ VHWherein, U is a left singular matrix, V is a right singular matrix, and singular values are arranged on a main diagonal line of the matrix sigma from large to small;
s1.3.3: constructing a sensitivity matrix at each spatial position of an image domain according to all column vectors of the right singular matrix V;
s1.3.4: and carrying out eigenvalue decomposition on each sensitivity matrix to obtain multi-channel coil sensitivity distribution information corresponding to the spatial position.
Specifically, the formula adopted for the synthesis of S1.4 is:
Figure GDA0003181158870000061
Figure GDA0003181158870000062
wherein N iscAs to the number of the channels,Cifor the coil sensitivity of the ith channel,
Figure GDA0003181158870000063
is CiThe conjugate matrix of (a) is determined,
Figure GDA0003181158870000064
representing the normalized coil sensitivity of the ith channel,
Figure GDA0003181158870000065
is composed of
Figure GDA0003181158870000066
The conjugate matrix of (a) is determined,
Figure GDA0003181158870000067
for the input image of the ith channel with convolution, IcombIs the synthesized image.
Preferably, the convolutional neural network module in S1.5 includes a plurality of CBR units, each unit including at least 1 convolutional layer, 1 normalization layer, and 1 nonlinear activation layer.
Further, the convolutional neural network further comprises a convergence layer and an anti-convergence layer.
Furthermore, residual connection is also introduced into the convolutional neural network module, and input data I of the convolutional neural network is inputcombOr IpocsThe residual error connection is overlapped with the output of the CBR unit to form the final output I of the convolutional neural network modulecnn。
Specifically, the projection process of the convex set of S1.6 specifically includes:
fcsm(i)＝CiIcnn |1≤i≤Nc (5-1)
Scsm(i)＝Ffcsm(i) |1≤i≤Nc (5-2)
Figure GDA0003181158870000071
Idp＝F-1fdp(Scsm，Sacq，k) (5-4)
Figure GDA0003181158870000072
Nci is the number of channels, i is the serial number of the channel,
Figure GDA0003181158870000073
is composed of
Figure GDA0003181158870000074
The conjugate matrix of (1), equation (5-1), IcnnComposite image input for CNN Module, CiFor coil sensitivity, the step is to generate a plurality of single-channel images f based on the synthesized image and the coil sensitivitycsm(i) (ii) a Equation (5-2) where F is Fourier transform, converts the images of a plurality of single channels into a K space signal Scsm(i) (ii) a Equation (5-3) is a data projection process, and Ω represents the acquired data set, i.e., if data at a certain K-space position has been acquired, the acquired data S is filled inacqOtherwise, filling the data S calculated according to the above processcsmFurther construct new complete K space data fdp(ii) a Equation [5-4 ]]Middle F-1For inverse Fourier transformation, new K space data fdpMulti-channel image I converted into image domaindp(ii) a Equation [5-5 ]]Performing multi-channel synthesis based on coil sensitivity, combining images of multiple channels together to obtain Ipocs。
Specifically, the loss function takes the L2 norm of the image domain:
Figure GDA0003181158870000075
wherein the input data is a known convolution image X and the marker data is a complete image Y synthesized based on the coil sensitivities.
After the scheme is adopted, the invention has the following beneficial effects:
(1) the invention provides a brand-new convolutional neural network structure, which not only integrates the prior knowledge of magnetic resonance, but also utilizes the learning capability of a deep convolutional network. With respect to the creativity of the deep convolutional network portion. Firstly, the method comprises the following steps: in the field of convolutional neural network structure design based on deep learning, no network is designed aiming at multi-channel magnetic resonance data at present, and the newly added convex set projection layer proposed by the network is an unprecedented result. In the field of deep learning, generally speaking, a new network structure is creative in itself; secondly, the method comprises the following steps: the traditional convolutional neural network structure only needs to calculate in an image domain, and the network structure provided by the invention needs to alternately perform in the image domain and a K space signal domain, which is also the core creation of the invention. The creativity of fusing the magnetic resonance prior knowledge lies in that the algorithm of convex set projection does exist in the past, but the invention constructs a convex set projection layer which needs to be fused with a convolutional neural network, so that the technical problem that the convolutional neural network works (including forward propagation and backward propagation) in an image domain and a K space signal domain (a POCS process needs to be transformed into the K space signal domain) is solved creatively.
(2) The "multi-channel processing capability" of the present invention enables the present invention to use fewer signals and to more efficiently utilize redundant information between multiple channels than a single-channel algorithm or network. The invention uses less magnetic resonance signals to generate a complete image, thereby further shortening the scanning time, improving the clinical scanning efficiency, better lightening or avoiding artifacts introduced by moving organs, and using the same magnetic resonance signals, the invention can generate more accurate images and improve the effectiveness of clinical diagnosis; compared with the traditional method, the reconstruction time of the invention is greatly shortened, which is beneficial to clinical real-time imaging and diagnosis.
(3) The invention has no special requirements on the sampling track of the magnetic resonance scanning, can sample randomly or regularly, and therefore, has wide applicability to various clinical sequences.
(4) The invention is followed by a channel synthesis operator based on coil sensitivity after the input layer to ensure the multi-channel processing capability of the network.
(5) All hyper-parameters in the convolutional neural network are not set manually, but are obtained through a large amount of data training, so that more stable image reconstruction quality can be provided for clinically complex structures including scanning parts, image signal-to-noise ratios and the like.
(6) Compared with the references Schlemper, Jo, Caballero, Jose, Hajnal, Joseph v., Price, antitony, Rueckert, daniel.a Deep case of a volumetric Neural network for MR Image reconstruction. arxiv:1703.00555v1 preprint 2017, the present invention adds a convex projection Layer in the Convolutional stem network, and the use of the convex projection Layer (POCS Layer) enables the network structure to process magnetic resonance data from multiple channels, whereas this reference can only process data from a single channel; the multi-channel processing capability brought by the convex set projection Layer (POCS Layer) can more effectively utilize the redundancy characteristic of magnetic resonance data, help the convolutional neural network based on deep learning to establish a more stable and accurate end-to-end mapping relation, fundamentally improve the quality of magnetic resonance reconstruction and more obviously shorten the magnetic resonance scanning time; compared with a single convex set projection Layer (POCS Layer), the convolutional neural network structure fusing the convex set projection Layer (POCS Layer) into a sequential model in a series connection mode can improve the generalization capability of the network structure and improve the stability of network training and testing. The convex set projection layers proposed by the method are fused into the whole network structure in a sequential mode, but the convex set projection layers share the same coil sensitivity calculated based on magnetic resonance priori knowledge and acquired K-space data. The coil sensitivity is obtained through accurate calculation, and the method has wide applicability.
(7) According to the invention, the convergence/inverse convergence layer is added in the convolutional neural network module, so that the receptive field of the convolutional neural network can be increased, the learning capability of the network structure is improved, and better reconstruction performance is brought, and the inverse convergence layer is used for ensuring the consistency of the size of output data.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without creative efforts. The above and other objects, features and advantages of the present invention will become more apparent from the accompanying drawings. Like reference numerals refer to like parts throughout the drawings. The drawings are not necessarily to scale, emphasis instead being placed upon illustrating the principles of the invention.
FIG. 1 is a schematic diagram of a process of constructing a correction matrix A from K-space self-calibration data;
FIG. 2 is a diagram illustrating a singular value decomposition process for the correction matrix A;
FIG. 3 is a diagram of a matrix G constructed according to the matrix V and corresponding to each pixelqA process schematic of (a);
FIG. 4 is a pass-pair matrix GqAnd (5) performing characteristic value decomposition on the calculated coil sensitivity distribution information graph.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In order to solve the problem that the existing magnetic resonance reconstruction technology based on deep learning can only support single-channel magnetic resonance data and can not process multi-channel magnetic resonance data, the invention provides a magnetic resonance reconstruction method based on deep learning and convex set projection. The deep learning convolutional neural network provided by the method firstly uses training sample data to train and check through a back propagation process to determine all parameters in a network structure; the test data (undersampled magnetic resonance data) is then reconstructed by a forward propagation process. As with all deep learning based convolutional neural networks, in the training and verification phase, the network needs to be provided with paired input data and labeled data to train the network to establish an "end-to-end" mapping relationship, i.e., the training network can automatically and accurately map the input data to the labeled data. In the field of magnetic resonance reconstruction, the marker data represent the known K-space fully sampled image (target of the network learning), while the training data represent the corresponding K-space artificially undersampled image (input of the network learning). In the testing stage, only the test data is needed to be provided to the network as input, and the convolutional neural network which has been learned through training will complete the next data mapping process. From the image domain, the convolution network can map the input convolution image into an output complete image; viewed from K space, the convolutional network is equivalent to mapping the input undersampled K space into complete K space data; in actual data processing, the convolutional network operates in the image domain and the K space in a staggered mode, and therefore the convolutional network is generally called a reconstruction process.
In 2017, when a serial deep learning network mode is proposed by Jo Schlemper et al for sparse reconstruction of magnetic resonance, a scheme for effectively processing multi-channel data in a neural network is not proposed or disclosed, so that a single-channel method is adopted by the Jo Schlemper et al at first. Only a single channel can be processed because the relationship between the data of multiple channels requires proper processing and application.
Projection of a convex set is an algorithm that is believed to be effective in dealing with relationships between multiple channel data. The key point of the invention is that the traditional convex set projection algorithm is transformed into a convex set projection layer in the convolutional neural network, and the convex set projection layer is fused into the deep convolutional neural network in a sequential mode, thereby creatively providing a novel convolutional neural network structure. The structure can effectively utilize redundant information among a plurality of channels, inherits the advantages of a convex set projection algorithm and a deep convolutional neural network on a network structure, and therefore can bring better reconstruction effect and wider clinical application (because the receiving channels in clinic are generally multi-channel at present).
In this embodiment, a magnetic resonance reconstruction method based on deep learning and convex set projection includes the following steps:
s1: and constructing a reconstruction network according to a channel synthesis operator, an overlapping structure of a plurality of convolutional neural network modules and a plurality of convex set projection layers and shared data, wherein the shared data comprises acquired K space data and coil sensitivity information, the channel synthesis operator is obtained based on the coil sensitivity information, and the convex projection layers are obtained based on the shared data. S1 is the most critical step of the present invention, specifically, S1 comprises the following steps:
s1.1: as shown in fig. 1, it is known in the art to acquire under-sampled multi-channel data and self-calibration data in K-space, and to use a central region in the K-space multi-channel data as the self-calibration data for the central region of the K-space of the self-calibration data. In general, data of size 24X24 centered in the entire K space may be used, with the exception of the self-calibration data being the undersampled multi-channel data Su. The size of the K-space multi-channel data can be expressed as: n is a radical ofx*Ny*NcWherein N isxNumber of lines representing acquired data, NyNumber of columns representing data, NcRepresenting the number of receive channels.
S1.2 generating undersampled Multi-channel data S by inverse Fourier transform, as shown in FIG. 4uA corresponding multi-channel convolution image having a size of: n is a radical ofx*Ny*NcThe multi-channel convolved image is used as input for a reconstruction network. Due to undersampling of the K-space data, the image is wrinkled in the undersampling direction, creating artifacts. The role of the reconstruction network is to eliminate image wrap-around artifacts due to undersampling of the data, and is also equivalent to restoring the undersampled data in K-space.
S1.3: multichannel coil sensitivity distribution information is obtained from the self-calibration data.
S1.3 comprises the following specific steps:
s1.3.1: generating a correction matrix A from the self-calibration data in the K-space multi-channel data as shown at 103 in FIG. 1; firstly, selecting a local block data from the calibration data, as shown by the black box in the '103' in fig. 1; then, the partial data is placed in the row of the correction matrix A; then, the local data block in "103" is moved in the direction indicated by the arrow to obtain the data of the entire correction matrix a.
S1.3.2: performing singular value decomposition on the correction matrix A to obtain a right singular matrix V, wherein the decomposition formula is as follows:
A＝U∑VH, (1)
wherein, U is a left singular matrix, V is a right singular matrix, and singular values are arranged on a main diagonal line of the matrix sigma from large to small. The column vectors in matrix V are the basis of all the row vectors in matrix a and therefore also represent the basis of the local data blocks in self-calibration data "103". That is, any row vector in matrix a (equivalently, any block data of the same size in K-space) can be represented by the subspace represented by matrix V. Fig. 2 shows the whole process of singular value decomposition for the correction matrix a, where "201" is a module value image of the full-sampling correction data in K space, and "202" shows more clearly the meaning of the image domain of these data, i.e. the single-channel image corresponding to the full-sampling data; "203" indicates how to obtain singular values and singular matrices by singular value decomposition of the matrix a, and "204" and "205" respectively show the distribution of the singular values in practice and the right singular matrix V.
S1.3.3: constructing a sensitivity matrix G at each spatial position of an image domain according to all column vectors of the right singular matrix Vq. As shown in fig. 3. The basic process is as follows: firstly, taking out the column vector '302' in the right singular matrix '301', and dividing the column vector into NcChannel data, and convert the data from the column vector to block data "303" (the size of the block data, consistent with the size of the correction matrix a constructed in fig. 1); then, the block data is converted into an image domain "304" through inverse fourier transform; finally, corresponding multi-channel data are respectively taken out from the same spatial position of the data '304', and a sensitivity matrix G corresponding to the spatial position is constructedq“305”。
S1.3.4: for each sensitivity matrix GqAnd (3) carrying out characteristic value decomposition to obtain multi-channel coil sensitivity distribution information corresponding to the spatial position:
Gqk＝λk (2)
where λ is a scalar quantity, representing the matrix GqAnd k is the eigenvector corresponding to the eigenvalue λ. As shown in fig. 4, the eigenvalues are arranged on the left side "401" from top to bottom in order of small to large; the feature vector corresponding to the feature value of "1", namely "402", namely, the feature vector amplitude "403" and the feature vector phase "404" represent the multi-channel coil sensitivity of the spatial position point;
s1.4: as shown in fig. 4, S1.4: synthesizing the multichannel convolution images into an image I through a channel synthesis operator based on the multichannel coil sensitivity distribution informationcomb. The formula adopted for the synthesis of S1.3 is as follows:
Figure GDA0003181158870000121
Figure GDA0003181158870000122
wherein N iscIs the number of channels, CiFor the coil sensitivity of the ith channel,
Figure GDA0003181158870000123
is CiThe conjugate matrix of (a) is determined,
Figure GDA0003181158870000124
representing the normalized coil sensitivity of the ith channel,
Figure GDA0003181158870000125
is composed of
Figure GDA0003181158870000126
The conjugate matrix of (a) is determined,
Figure GDA0003181158870000127
for the input image of the ith channel with convolution, IcombIs the synthesized image.
S1.5: image I is passed through convolutional neural network module CNN1combMapping to an output image I without or with reduced wrap-around artifactscnn1. As can be seen in fig. 4, the specific structure of the convolutional neural network, the Convolutional Neural Network (CNN) module "505" includes a plurality of CBR Units, each of which includes at least one convolutional layer (convolution layer), one Normalization layer (BN), and one nonlinear activation layer (RELU); further, in order to obtain a larger receptive field of the network structure and ensure that the sizes of the input and output images are consistent, a convergence Layer (Pooling Layer) or an inverse convergence Layer (Un-focusing Layer) needs to be added in the CBR unit in the module "505", and the convergence Layer and the inverse convergence Layer are to appear in pairs, that is, if a convergence Layer is applied in one CBR unit, the inverse convergence Layer should be correspondingly used in a unit behind the CBR unit. To ensure that the output of the Convolutional Neural Network (CNN) module is compatible with the following POCS layer, CBRndThe number of convolutions in (a) should be equal to 1. Meanwhile, the Convolutional Neural Network (CNN) module introduces residual connection in the network, namely input data I of the CNN modulecombOr IpocsLinked by residual errors with CBRndThe outputs of the units are superposed to form the final output I of the CNN modulecnn. The residual error linkage not only can effectively avoid network degradation caused by depth increase, but also can obviously improve learning ability under the condition of unchanged depth.
S1.6: will output image Icnn1Transmitting the signal into a convex set projection layer POCS, and completing the convex set projection process in the convex set projection layer POCS according to the coil sensitivity distribution information and the acquired K-space multi-channel data to obtain an image Ipocs1；
The projection process of the convex set of S1.6 specifically comprises the following steps:
fcsm(i)＝CiIcnn |1≤i≤Nc (5-1)
Scsm(i)＝Ffcsm(i) |1≤i≤Nc (5-2)
Figure GDA0003181158870000131
Idp＝F-1fdp(Scsm，Sacq，k) (5-4)
Figure GDA0003181158870000132
wherein N iscI is the number of channels, i is the serial number of the channel,
Figure GDA0003181158870000133
is composed of
Figure GDA0003181158870000134
The conjugate matrix of (1), equation (5-1)cnnComposite image input for CNN Module, CiFor coil sensitivity, the step is to generate a plurality of single-channel images f based on the synthesized image and the coil sensitivitycsm(i) (ii) a Equation (5-2) where F is Fourier transform, converts the images of a plurality of single channels into a K space signal Scsm(i) (ii) a Equation (5-3) is a data projection process, and Ω represents the acquired data set, i.e., if data at a certain K-space position has been acquired, the acquired data S is filled inacqOtherwise, filling the data S calculated according to the above processcsmFurther construct new complete K space data fdp(ii) a Equation [5-4 ]]Middle F-1For inverse Fourier transformation, new K space data fdpMulti-channel image I converted into image domaindp(ii) a Equation [5-5 ]]Performing multi-channel synthesis based on coil sensitivity, combining images of multiple channels together to obtain Ipocs。
S1.7: as shown in fig. 4, image Ipocs1Inputting into convolutional neural network module CNN2 to obtain imageIpocs1Mapping to an output image I without or with reduced wrap-around artifactscnn2(ii) a Then the image I is processedcnn2Transmitting the signal into a convex set projection layer POCS, and completing the convex set projection process in the convex set projection layer POCS according to the coil sensitivity distribution information and the acquired K-space multi-channel data to obtain an image Ipocs2. Specifically, each neural network module is a set of convolutional neural networks to be trained, all parameters of which are unknown, so that even though the structures of a plurality of CNN modules are similar, their roles in the whole network are different, and the parameters after training are different, so that they can be said to be different. The data manipulation and parameters of the POCS in the projection layer of the convex set are the same.
Repeating S1.7 to construct a deep network structure which comprises N in totalcCNN layers and NcThe POCS layer, so far, the network construction is completed, and in the concrete implementation, the parameter N can be setcAnd (6) carrying out optimization and adjustment.
S2: after the network is constructed, training all network parameters through a back propagation process, and verifying the network parameters;
the loss function takes the L2 norm of the image domain:
Figure GDA0003181158870000141
wherein the input data is a known convolution image X and the marker data is a complete image Y synthesized based on the coil sensitivities.
S3: and determining the structure and the operational characteristics of the network according to the inspected network parameters, inputting known test set data, performing forward propagation of the network to obtain unknown mapping data, and completing reconstruction of magnetic resonance.
The above description is only an embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention.

Claims (8)

1. A magnetic resonance reconstruction method based on deep learning and convex set projection is characterized by comprising the following steps:
s1: constructing a network according to an overlapping structure of a plurality of convolutional neural network modules and a plurality of convex set projection layers and shared data, wherein the shared data comprises acquired K-space data and coil sensitivity information, and the convex set projection layers are obtained based on the shared data;
s2: after the network is constructed, training all network parameters through a back propagation process, and verifying the network parameters;
s3: determining the structure and the operational characteristics of the network according to the inspected network parameters, inputting known test set data, carrying out forward propagation on the network to obtain unknown mapping data, and completing reconstruction of magnetic resonance;
the S1 includes the following steps:
s1.1: acquiring undersampled multichannel data and self-calibration data in K space, taking a central region in the K space multichannel data as self-calibration data, and taking the part except the self-calibration data as the undersampled multichannel data;
s1.2: generating a multi-channel convolution image corresponding to the under-sampled multi-channel data through inverse Fourier transform, and taking the multi-channel convolution image as the input of a reconstruction network;
s1.3: acquiring multi-channel coil sensitivity distribution information from self-calibration data;
s1.4: synthesizing the multichannel convolution images into an image I through a channel synthesis operator based on the multichannel coil sensitivity distribution informationcomb；
S1.5: image I is passed through convolutional neural network module CNN1combMapping to an output image I without or with reduced wrap-around artifactscnn 1；
S1.6: will output image Icnn 1Transmitting the signal into a convex set projection layer POCS, and completing the convex set projection process in the convex set projection layer POCS according to the coil sensitivity distribution information and the acquired K-space multi-channel data to obtain an image Ipocs 1；
S1.7: drawing(s)Like Ipocs 1Inputting into convolutional neural network module CNN2 to obtain image Ipocs 1Mapping to an output image I without or with reduced wrap-around artifactscnn 2(ii) a Then the image I is processedcnn 2Transmitting the signal into a convex set projection layer POCS, and completing the convex set projection process in the convex set projection layer POCS according to the coil sensitivity distribution information and the acquired K-space multi-channel data to obtain an image Ipocs 2；
S1.8: repeating S1.7 to construct a deep network structure which comprises N in totalcCNN layers and NcAnd a POCS layer, so far, the network construction is completed.
2. The method of claim 1, wherein in S1.1, S1.3 includes the following steps:
s1.3.1: generating a correction matrix A according to self-calibration data in the K space multichannel data;
s1.3.2: and (3) carrying out singular value decomposition on the correction proof A to obtain a right singular matrix V, wherein the decomposition formula is as follows:
A＝U∑VH， (1)
the matrix sigma is a left singular matrix, the matrix sigma is a right singular matrix, and singular values are arranged on a main diagonal line of the matrix sigma from large to small;
s1.3.3: constructing a sensitivity matrix at each spatial position of an image domain according to all column vectors of the right singular matrix V;
s1.3.4: and carrying out eigenvalue decomposition on each sensitivity matrix to obtain multi-channel coil sensitivity distribution information corresponding to the spatial position.
3. The method of claim 1, wherein the synthesis of S1.4 is performed by the following formula:
Figure FDA0003121155590000021
Figure FDA0003121155590000022
wherein N iscIs the number of channels, CiCoil sensitivity for the ith channel, Cj HIs CiThe conjugate matrix of (a) is determined,
Figure FDA0003121155590000023
representing the normalized coil sensitivity of the ith channel,
Figure FDA0003121155590000024
is composed of
Figure FDA0003121155590000025
The conjugate matrix of (a) is determined,
Figure FDA0003121155590000026
for the input image of the ith channel with convolution, IcombIs the synthesized image.
4. The method of claim 1, wherein the convolutional neural network module in S1.5 comprises a plurality of CBR units, each unit comprising at least 1 convolutional layer, 1 normalization layer and 1 nonlinear activation layer.
5. The method of claim 4, wherein the convolutional neural network further comprises a convergence layer and a reverse convergence layer.
6. The method of claim 4 or 5, wherein residual connection is further introduced into the convolutional neural network module to connect input data I of the convolutional neural networkcombOrIpocsThe residual error connection is overlapped with the output of the CBR unit to form the final output I of the convolutional neural network modulecnn。
7. The magnetic resonance reconstruction method based on deep learning and convex set projection as claimed in claim 1, wherein the convex set projection process of S1.6 is specifically:
fcsm(i)＝CiIcnn |1≤i≤Nc (5-1)
Scsm(i)＝Ffcsm(i) |1≤i≤Nc (5-2)
Figure FDA0003121155590000031
Idp＝F-1fdp(Scsm，Sacq，k) (5-4)
Figure FDA0003121155590000032
wherein N iscI is the number of channels, i is the serial number of the channel,
Figure FDA0003121155590000033
is composed of
Figure FDA0003121155590000034
The conjugate matrix of (1), equation (5-1)cnnComposite image input for CNN Module, CiFor coil sensitivity, the step is to generate a plurality of single-channel images f based on the synthesized image and the coil sensitivitycsm(i) (ii) a Equation (5-2) where F is Fourier transform, converts the images of a plurality of single channels into a K space signal Scsm(i) (ii) a Equation (5-3) is a data projection process, and Ω represents the acquired data set, i.e., if data at a certain K-space position has been acquired, it is filled as acquiredData SacqOtherwise, filling the data S calculated according to the above processcsmFurther construct new complete K space data fdp(ii) a F in equation (5-4)-1For inverse Fourier transformation, new K space data fdpMulti-channel image I converted into image domaindp(ii) a Equation (5-5) performs multi-channel synthesis based on coil sensitivities, combining the images of multiple channels together to obtain Ipocs。
8. The method for magnetic resonance reconstruction based on deep learning and projection of convex set as claimed in claim 1, wherein said S2 is more specifically: after the network construction is finished, training all network parameters by taking a minimum loss function as a target through a back propagation process;
the loss function takes the L2 norm of the image domain:
Figure FDA0003121155590000035
wherein the input data is a known convolution image X and the marker data is a complete image Y synthesized based on the coil sensitivities.
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