CN114119791A - MRI (magnetic resonance imaging) undersampled image reconstruction method based on cross-domain iterative network - Google Patents

MRI (magnetic resonance imaging) undersampled image reconstruction method based on cross-domain iterative network Download PDF

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CN114119791A
CN114119791A CN202010881742.5A CN202010881742A CN114119791A CN 114119791 A CN114119791 A CN 114119791A CN 202010881742 A CN202010881742 A CN 202010881742A CN 114119791 A CN114119791 A CN 114119791A
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杨春升
李钊
宋长明
郑利敏
张雪华
李利平
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Zhongyuan University of Technology
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Abstract

The invention provides an MRI (magnetic resonance imaging) under-sampling image reconstruction method based on a cross-domain iterative network, which is characterized by preparing fully-sampled and under-sampled MRI k-space data and image data sets to form training set and verification set data; constructing a CNN dense connection network with a crossed k space domain and an image domain, and predefining a loss function; inputting training set data into a network for training; testing the performance and generalization capability of the network by using a verification set, and determining a network model and parameters; and inputting the undersampled k-space data into an image reconstruction network obtained by training to reconstruct an image. The loss function considers the loss of an image domain and the loss of a k space domain, and multiple supervision training is used, so that supervision information loss during gradient return is effectively avoided. The invention can recover the detail information of the image while eliminating the high-frequency oscillation artifact caused by undersampling, thereby realizing the acquisition of high-quality images while accelerating the MRI sampling.

Description

MRI (magnetic resonance imaging) undersampled image reconstruction method based on cross-domain iterative network
Technical Field
The invention relates to the technical fields of Magnetic Resonance Imaging (MRI), deep learning, undersampled reconstruction and the like, in particular to an MRI undersampled image reconstruction method based on a K space domain and image domain cross iterative network.
Background
MRI is a non-invasive, non-ionizing radiation, multi-parameter imaging technique with arbitrary section direction, high soft tissue resolution, and can provide high-resolution structural and functional information for clinical diagnosis. In the conventional MRI, a 2D or 3D data matrix, i.e., k-space domain data, needs to be acquired in a cartesian coordinate system, and corresponding image domain information can be obtained after inverse Fourier (Fourier) transform. Each line of k-space data corresponds to one step of phase encoding, the acquisition of different phase encoded data requires waiting for the recovery of longitudinal magnetization, i.e. waiting for TR, which varies from hundreds of milliseconds to several seconds according to different MRI imaging methods, so MRI is a relatively time-consuming imaging technique. In conventional MRI, the theoretical premise is that the imaging part is still, otherwise motion artifacts are introduced, so that the examinee needs to keep a body position and stay still for one to several minutes during MRI examination. Abdominal examination, which requires multiple breath-holding acquisitions; the development of special imaging methods is required for parts with natural physiological motion, such as the heart; meanwhile, for MRI data acquisition, a patient needs to be in a semi-closed magnet space, which is a challenge for long-time matching of most patients, so that the development of a rapid imaging technology is urgently needed for MRI.
At present, the imaging speed is increased by combining a method of multi-coil unit parallel imaging, the acceleration factor is above or below 2, but the methods rely on special hardware or sequences, and the space for further increasing the sampling speed is limited. Compressed Sensing-based MRI (CS-MRI) is a technique that can undersample k-space data well below the nyquist sampling law, thereby speeding up imaging without specific hardware and sequences. However, there are some limitations to the CS-MRI technique, such as the CS-MRI sampling trajectory needs to satisfy the irrelevance criterion, and the typical acceleration factor is between 2.5 and 3; the CS-MRI uses less sparse coefficients in the global coefficient transformation, has the risk of latent hidden image detail structure and even introduction of fuzzy artifacts, and cannot accurately describe complex biological tissue structure.
The Convolutional Neural Network (CNN) combines three ideas of local receptive field, weight sharing and time or space sub-sampling, can obtain certain displacement, scale and deformation invariance, is more similar to a biological neural network, reduces the complexity of a network model and reduces the number of weights. In recent years, the method is used in the field of MRI undersampled reconstruction, a nonlinear relation between an undersampled image and a reference image (a fully sampled image) is obtained through a training network, the acquired k-space data information is not fully utilized basically, and the detailed information of the image cannot be reconstructed when the acceleration factor is high.
Disclosure of Invention
Based on the requirement of accelerated imaging and the prior technical problem, the invention provides an MRI undersampled image reconstruction method based on a k space domain and image domain cross iterative network.
The technical scheme of the invention is realized as follows: an MRI undersampled image reconstruction method based on a cross-domain iterative network comprises the following steps:
step 1: retrospectively preprocessing the k-space data of the full sampling to obtain a training set and a verification set;
step 2: constructing a cross-domain iterative neural network (KI network), wherein the KI network is formed by cascading N modules, each module consists of a k-space domain CNN network Kcnn and an image domain CNN network Icnn, and the two networks are connected through FT (Fourier transform) or IFT (inverse Fourier transform); predefining a loss function loss of the KI network;
and step 3: training a KI network, inputting a training set into the KI network for training, and taking the training set as a trained intermediate network if the loss function loss is minimum; if the loss function loss is not the minimum, the network parameters are propagated and updated in a reverse direction, and the KI network is returned for training;
and 4, step 4: detecting a KI network, inputting the verification set into the intermediate network trained in the step 3 to obtain a reconstructed image, detecting the generalization capability and overfitting condition of the neural network, and outputting the network and parameters thereof to be used as the image reconstruction network when the evaluation standard is met; if the evaluation standard is not met, adjusting network parameters and the number of layers, expanding the training set and returning to the step 2;
and 5: and (4) reconstructing an undersampled k-space image, inputting undersampled k-space data into the image reconstruction network obtained in the step (4), and reconstructing a high-quality image.
Further, in step 1, the fully sampled k-space data is randomly undersampled to obtain undersampled k-space data kuCarrying out Inverse Fourier Transform (IFT) on the fully sampled k-space data to obtain target image data x, wherein the training set consists of a plurality of groups of undersampled k-space data kuThe fully sampled k-space data and the target image data x; the verification set is composed of a plurality of sets of undersampled k-space data kuAnd target image data x.
Further, in step 2, both the Kcnn network and the Icnn network adopt residual neural networks, each of which is composed of an input layer, a plurality of hidden layers and an output layer, an activation function of a hidden layer is a Linear rectification function (ReLU), and an activation function of an output layer is a softmax function.
Further, the Icnn network hidden layer includes a channel-wise attention layer CA (channel-wise attention layer) for adjusting the weight of each channel; the Icnn network adds a Data fidelity layer DC layer before outputting.
Further, the target dataset of the Kcnn network is fully sampled k-space data, the target data of the Icnn network is target image data x; the input layer data of the first module Kcnn network is undersampled k-space data k in the training setuDividing the complex k-space data into a real part and an imaginary part, and respectively inputting the real part and the imaginary part into a network; the input layer data of the Kcnn network in the nth module is the image data x output by the Icnn network in the nth-1 modulen-1FT (x) data after FTn-1) And k-space data k from the output of the Kcnn network in all preceding modulesn-1，kn-2…k1。
Further, the n-thThe input data of the Icnn network in the module is k-space data k output by the Kcnn network in the nth modulenIFT (k) of IFT-passed datan) And image data x output by Icnn network in all the modules in frontn-1，xn-2…x1。
Further, in step 2, the loss function loss of the predefined KI network is:
Figure BDA0002654296210000031
wherein,
Figure BDA0002654296210000032
wherein, WkAnd WIIs a weight factor, K is the fully sampled K-space data in the training set,
Figure BDA0002654296210000033
is k-space data k output by the n-th module Kcnn networkn(ii) a I is the image x after the IFT of the fully sampled k-space data in the training set,
Figure BDA0002654296210000034
is the image data x output by the nth module Icnn networknAnd M is the total number of training set data sets.
Further, in step 3, undersampled k-space data k in the training set are processeduAnd inputting a KI network, and training the KI network by taking the fully sampled k-space data and the target image data x as target data.
Further, in step 4, a peak signal-to-noise ratio (PSNR) and a Structural Similarity (SSIM) between the reconstructed image and the target image are selected as criteria, and the criteria are that the PSNR is not less than 35dB and the structural similarity is not less than 0.95.
The invention has the beneficial effects that:
the invention provides an MRI (magnetic resonance imaging) undersampled image reconstruction method based on a k-space domain and image domain cross iterative network, which is characterized by preparing fully sampled and undersampled MRI k-space data and image data sets to form training set and verification set data; constructing a CNN dense connection network with a crossed k-space domain and an image domain; inputting training set data into a network for training; testing the performance and generalization capability of the network by using a verification set, and determining a network model and parameters; and inputting the undersampled k-space data into an image reconstruction network obtained by training to reconstruct an image.
Dense connection is adopted in the network module iteration process, so that the information of the middle layer can be effectively utilized; considering the step-by-step distribution characteristics of MRI k-space data when constructing a k-space domain network, and adopting a residual error network; when an image domain network is constructed, a channel attention mechanism is introduced, the weight of each channel is effectively adjusted, the optimized extraction of the characteristics is realized, and the detail information of the image can be effectively recovered; the loss of the image domain and the loss of the k space domain are considered in the loss function, and the loss of the supervision information during gradient return is effectively avoided by using multi-supervision training. The k-space domain residual error network adopted by the invention can alleviate the characteristic that the data intensity distribution of k-space is not uniform, and can inhibit high-frequency oscillation artifacts in the image.
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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 used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a block diagram of a cross-domain iterative network;
FIG. 3 is a diagram of a k-space domain network Kcnn;
fig. 4 is a diagram of an image domain network Icnn;
fig. 5 is a k-space undersampled template and reconstructed image.
Detailed Description
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 only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without inventive effort based on the embodiments of the present invention, are within the scope of the present invention.
An MRI undersampled image reconstruction method based on a cross-domain iterative network is disclosed, the flow is shown in figure 1, and the specific steps are as follows:
step 1: and preprocessing the k-space data to obtain a training set and a verification set.
The fully sampled k-space data is randomly undersampled, and the sampling template is shown in fig. 5, so that undersampled k-space data k are obtainedu(ii) a The full-sampled k-space data is subjected to inverse fourier transform IFT to obtain an image x corresponding thereto, which is simply referred to as target image data x, and used as marker data.
The training set is composed of a plurality of sets of undersampled k-space data, fully sampled k-space data, and target image data x.
The validation set consists of sets of undersampled k-space data and target image data x.
Step 2: a cross-domain iterative neural network (KI network) is constructed as shown in fig. 2.
1) The KI network is formed by cascading N modules, each module consists of a k-space domain CNN network Kcnn and an image domain CNN network Icnn, the Kcnn network and the Icnn network are connected through inverse fourier transform IFT, the Icnn network and the Kcnn network are connected through fourier transform FT, and the Kcnn network in each module is connected with the Kcnn network in the previous module in a cascading manner; the Icnn network in each module is connected with the Icnn in the module at the front side in a cascade mode;
2) as shown in fig. 3 and 4, each of the Kcnn and Icnn networks is a residual neural network, and each of them is composed of an input layer, a plurality of hidden layers, and an output layer, the activation function of the hidden layers is a Linear rectification function (ReLU), and the activation function of the output layer is a softmax function.
3) As shown in fig. 4, the Icnn network hidden layer includes a channel-wise attention layer (CA) for adjusting the weight of each channel; the Icnn network adds a Data fidelity layer DC layer before outputting. The DC layer is calculated as follows:
Figure BDA0002654296210000051
Figure BDA0002654296210000052
wherein:
Figure BDA0002654296210000053
the k-space data of an image obtained by the Icnn network before the DC layer after FT, and k is the k-space data obtained by the Icnn network after the DC layer, corresponding to FT of the image data output by the Icnn network. c. Cx,cyIs a subscript of k-space data, and the random undersampled template Mask is a matrix consisting of 0 and 1, as shown in fig. 5; parameter lambda is taken to be 106。
4) The target datasets, i.e. the marker data, of the Kcnn, Icnn networks are the fully sampled k-space data and their IFT transformed image data x, respectively.
As shown in fig. 2 and 3, the input data of the first Kcnn network is undersampled k-space data in the training set, and the complex k-space data is divided into a real part and an imaginary part and is input into the network respectively; the input data of the Kcnn network in the nth module is the image data x output from the Icnn network in the nth-1 modulen-1FT (x) data after FTn-1) And k-space data k from the output of the Kcnn network in all preceding modulesn-1，kn-2…k1。
As shown in FIGS. 2 and 3, the input data of the Icnn network in the nth module is the image data k output from the Kcnn network in the nth modulenIFT (x) of IFT-passed datan) And image data x output by Icnn network in all the modules in frontn-1，xn-2…x1。
5) The loss function loss defined by the KI network is as follows:
Figure BDA0002654296210000061
wherein,
Figure BDA0002654296210000062
wherein, WkTake 0.1, WITaking 0.99, K is the fully sampled K-space data in the training set,
Figure BDA0002654296210000063
is k-space data k output by the n-th module Kcnn networkn(ii) a I is the image x after the IFT of the fully sampled k-space data in the training set,
Figure BDA0002654296210000064
is the image data x output by the nth module Icnn networknAnd M is the total number of training set data sets.
And step 3: and training the KI network.
As shown in fig. 1 and 2, undersampled k-space data k in the training setuAnd inputting a KI network, and training a neural network by taking the fully sampled k space and image data x obtained after IFT transformation as target image data.
And 4, step 4: a neural network (KI network) is detected.
As shown in fig. 1, under-sampled k-space data of the validation set and target image data x data corresponding to the under-sampled k-space data are input into a trained intermediate network, and a reconstructed image is obtained.
And selecting the peak signal-to-noise ratio (PSNR) and the Structural Similarity (SSIM) between the reconstructed image and the target image as judgment bases.
The judgment standard is that the PSNR is not less than 35dB and the structural similarity is not less than 0.95.
If the evaluation standard is met, the network and the parameters thereof are output to be used as an image reconstruction network;
if the evaluation criterion is not met, the network parameters and the layer number are adjusted, the training set is expanded and the second step is returned, so that the generalization capability and overfitting condition of the neural network are ensured, and the expansion of the training set refers to the increase of the number of the training set data groups.
The number of network modules finally used is 6.
And 5: an undersampled k-space image is reconstructed.
The undersampled k-space data is input into the image reconstruction network to reconstruct a high-quality image, as shown in fig. 5, which is a template Mask with undersampled k-space and a reconstructed image.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (9)

1. An MRI undersampled image reconstruction method based on a cross-domain iterative network is characterized by comprising the following steps:
step 1: preprocessing the fully sampled k-space data to obtain a training set and a verification set;
step 2: constructing a KI network, wherein the KI network is formed by cascading N modules, each module consists of a k-space domain CNN network Kcnn and an image domain CNN network Icnn, the two networks are connected through FT or IFT, and a loss function loss of the KI network is predefined;
and step 3: training a KI network, inputting a training set into the KI network for training, and taking the training set as a trained intermediate network if the loss function loss is minimum; if the loss function loss is not the minimum, the network parameters are propagated and updated in a reverse direction, and the KI network is returned for training;
and 4, step 4: detecting a KI network, inputting the verification set into the intermediate network trained in the step 3 to obtain a reconstructed image, detecting the generalization capability and overfitting condition of the neural network, and outputting the network and parameters thereof to be used as the image reconstruction network when the evaluation standard is met; if the evaluation standard is not met, adjusting network parameters and the number of layers, expanding the training set and returning to the step 2;
and 5: and (4) reconstructing an undersampled k-space image, inputting the undersampled k-space data into the image reconstruction network obtained in the step (4), and reconstructing a high-quality image.
2. The MRI undersampled image reconstruction method based on the cross-domain iterative network as claimed in claim 1, characterized in that: in step 1, the fully sampled k-space data is randomly undersampled to obtain undersampled k-space data kuIFT is carried out on the fully sampled k-space data to obtain target image data x, and the training set consists of a plurality of groups of undersampled k-space data kuThe fully sampled k-space data and the target image data x; the verification set is composed of a plurality of sets of undersampled k-space data kuAnd target image data x.
3. The MRI undersampled image reconstruction method based on the cross-domain iterative network as claimed in claim 2, characterized in that: in the step 2, both the Kcnn network and the Icnn network adopt residual error neural networks, and each residual error neural network consists of an input layer, a plurality of hidden layers and an output layer, wherein the activation function of the hidden layers is a linear rectification function, and the activation function of the output layer is a softmax function.
4. The MRI undersampled image reconstruction method based on the cross-domain iterative network as claimed in claim 3, characterized in that: the Icnn network hiding layer comprises a channel attention layer CA for adjusting the weight of each channel; and a data fidelity layer DC layer is added before the output of the Icnn network.
5. The MRI undersampled image reconstruction method based on the cross-domain iterative network as claimed in claim 3, characterized in that: the target dataset of Kcnn is fully sampled k-space data, the target dataset of Icnn network is target image data x; the input layer data of the first module Kcnn network is the undersampled k-space number in the training setAccording to kuDividing the complex k-space data into a real part and an imaginary part, and respectively inputting the real part and the imaginary part into a network; the input layer data of the Kcnn network in the nth module is the image data x output by the Icnn network in the nth-1 modulen-1FT (x) data after FTn-1) And k-space data k output by Kcnn network in all modules in frontn-1，kn-2…k1。
6. The MRI undersampled image reconstruction method based on the cross-domain iterative network as claimed in claim 5, characterized in that: the input layer data of the Icnn network in the nth module is k-space data k output by the Kcnn network in the nth modulenIFT (k) of IFT-passed datan) And image data x output by Icnn network in all the modules in frontn-1，xn-2…x1。
7. The MRI undersampled image reconstruction method based on the cross-domain iterative network as claimed in claim 6, characterized in that: in step 2, the loss function loss of the predefined KI network is:
Figure FDA0002654296200000021
wherein,
Figure FDA0002654296200000022
wherein, WkAnd WIIs a weight factor, K is the fully sampled K-space data in the training set,
Figure FDA0002654296200000023
is k-space data k output by the n-th module Kcnn networkn(ii) a I is the target image data x after the fully sampled k-space data IFT in the training set,
Figure FDA0002654296200000024
is the image data x output by the nth module Icnn networknAnd M is the total number of training set data sets.
8. The MRI undersampled image reconstruction method based on the cross-domain iterative network as claimed in claim 2, characterized in that: in step 3, undersampled k-space data k in the training set are processeduAnd inputting a KI network, and training the KI network by taking the fully sampled k-space data and the target image data x as target data.
9. The MRI undersampled image reconstruction method based on the cross-domain iterative network as claimed in claim 1, characterized in that: in step 4, the PSNR and the structural similarity between the reconstructed image and the target image are selected as judgment criteria, wherein the judgment criteria are that the PSNR is not less than 35dB and the structural similarity is not less than 0.95.
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CN114693823A (en) * 2022-03-09 2022-07-01 天津大学 Magnetic resonance image reconstruction method based on space-frequency double-domain parallel reconstruction
US11751825B2 (en) 2019-03-27 2023-09-12 Siemens Healthcare Gmbh Devices, systems, and methods for controlling acquisition parameters when carrying out a medical x-ray examination
CN117576250A (en) * 2024-01-19 2024-02-20 中国科学技术大学先进技术研究院 Rapid reconstruction method and system for prospective undersampled MRI Dixon data
WO2024052814A1 (en) * 2022-09-05 2024-03-14 B. G. Negev Technologies And Applications Ltd., At Ben-Gurion University System and method for compressed sensing using partial ensemble measurements

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US11751825B2 (en) 2019-03-27 2023-09-12 Siemens Healthcare Gmbh Devices, systems, and methods for controlling acquisition parameters when carrying out a medical x-ray examination
CN114693823A (en) * 2022-03-09 2022-07-01 天津大学 Magnetic resonance image reconstruction method based on space-frequency double-domain parallel reconstruction
CN114693823B (en) * 2022-03-09 2024-06-04 天津大学 Magnetic resonance image reconstruction method based on space-frequency double-domain parallel reconstruction
WO2024052814A1 (en) * 2022-09-05 2024-03-14 B. G. Negev Technologies And Applications Ltd., At Ben-Gurion University System and method for compressed sensing using partial ensemble measurements
CN117576250A (en) * 2024-01-19 2024-02-20 中国科学技术大学先进技术研究院 Rapid reconstruction method and system for prospective undersampled MRI Dixon data
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