CN114998458A - Undersampled magnetic resonance image reconstruction method based on reference image and data correction - Google Patents

Undersampled magnetic resonance image reconstruction method based on reference image and data correction Download PDF

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CN114998458A
CN114998458A CN202111434806.8A CN202111434806A CN114998458A CN 114998458 A CN114998458 A CN 114998458A CN 202111434806 A CN202111434806 A CN 202111434806A CN 114998458 A CN114998458 A CN 114998458A
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杜晓凤
何一凡
满旺
李白云
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Xiamen University of Technology
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
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    • G06N3/00—Computing arrangements based on biological models
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    • G06N3/08—Learning methods
    • G06N3/084—Backpropagation, e.g. using gradient descent
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    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T3/00—Geometric image transformation in the plane of the image
    • G06T3/40—Scaling the whole image or part thereof
    • G06T3/4053—Super resolution, i.e. output image resolution higher than sensor resolution
    • G—PHYSICS
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    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
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    • G06T2207/10088—Magnetic resonance imaging [MRI]

Abstract

The invention provides an undersampled magnetic resonance image reconstruction method based on a reference image and data correction, which comprises the following steps: acquiring a fully sampled T1 weighted image as a reference image I ref (ii) a Obtaining a fully sampled T2 weighted image I T2 And converted into undersampled k-space data y; initializing a sequence of images I s And initializing a sequence of mutual information valuesMI s (ii) a Building reference image based I using residual module based convolutional neural network ref And an undersampled magnetic resonance image reconstruction model of the undersampled k-space data y; training an undersampled magnetic resonance image reconstruction model; recording a reconstructed image and a mutual information value between the reconstructed image and a reference image in the reconstruction process; selecting an optimal reconstructed image based on the mutual information values; and carrying out iterative k-space data correction on the optimal reconstructed image to obtain a final reconstructed image. The invention can improve the accuracy of the reconstructed image.

Description

Undersampled magnetic resonance image reconstruction method based on reference image and data correction
Technical Field
The invention relates to a method for realizing unsupervised undersampled magnetic resonance image reconstruction, in particular to a method for improving reconstruction quality based on unsupervised learning of a reference image, which introduces a k-space data correction module to accelerate the convergence speed of a convolutional neural network and improves reconstruction precision through iterative k-space data correction in post-processing.
Background
Magnetic Resonance Imaging (MRI) has been a very significant development in the fields and research of life science and medicine for the last 30 years and has become an important tool for clinical diagnosis and basic research [1 ]. In clinical diagnosis and later image analysis, fully sampled MRI images can provide abundant auxiliary information, but the fully sampled MRI scan time is long and the imaging process is often more than 30 minutes. Therefore, in practical imaging, the resolution of the magnetic resonance image is limited by various factors, such as hardware conditions, scan time, and patient tolerance. An undersampling technique is generally used, i.e. information of partial frequencies is sampled to reduce the time of magnetic resonance imaging, the fewer the partial frequencies are sampled, the faster the imaging time is; however, the undersampled magnetic resonance image often has the problems of artifact, blurred details and the like, so that the undersampled magnetic resonance image cannot be applied to clinical diagnosis.
Under the condition of not changing hardware, how to reduce the MRI scanning time is a problem to be solved urgently, and the problem of reconstructing an image meeting the required resolution is solved urgently. The common methods for accelerating imaging based on software algorithm are mainly divided into two categories:
(1) based on supervised machine learning algorithms. The algorithm designs a machine learning model, and a mapping function [2] - [7] between an undersampled image and a corresponding full sampling image is learned through a large-scale image training set; therefore, during prediction, the fully sampled image can be reconstructed from the under-sampled images of the same type by directly utilizing the learned mapping function. The algorithm needs to prepare a large amount of paired under/full sampling image data in advance, which is difficult to do in clinical scenes, and currently, most of algorithms use simulation data for training, so that the application is limited.
(2) Based on unsupervised machine learning algorithms. The algorithm only utilizes one or a plurality of reference images and undersampled magnetic resonance data to reconstruct the images and does not need a large-scale training set [8] - [11 ]. At present, the algorithm has the problems that the reference image information is not fully utilized, and the undersampled original data is not fully utilized.
[1].Ma D,Gulani V,Seiberlich N,Liu KC,Sunshine JL,Duerk JL,Griswold MA.Magnetic Resonance Fingerprinting.Nature,495:187-192(2013).
[2].Yang G,Yu S,Dong H,et al.DAGAN:Deep De-Aliasing generative adversarial networks for fast compressed sensing MRI reconstruction[J].IEEE Transactions on Medical Imaging,2017.
[3].Lee D,Yoo J,Ye J C.Deep residual learning for compressed sensing MRI[C]//Biomedical Imaging(ISBI 2017),2017 IEEE 14th International Symposium on.IEEE,2017:15-18.
[4].Li R,Zhang W,Suk H I,et al.Deep learning based imaging data completion for improved brain disease diagnosis[C]//International Conference on Medical Image Computing and Computer-Assisted Intervention.Springer,Cham,2014:305-312.
[5].Huang Y,Shao L,Frangi A F.Simultaneous super-resolution and cross-modality synthesis of 3D medical images using weakly-supervised joint convolutional sparse coding[J].arXiv preprint arXiv:1705.02596,2017.
[6].Schlemper J,Caballero J,Hajnal J V,et al.A deep cascade of convolutional neural networks for dynamic MR image reconstruction[J].IEEE transactions on medical imaging,2018,37(2):491-503.
[7].X.Du and Y.He,“Gradient-guided convolutional neural network for mri image super-resolution,”Applied Sciences,vol.9,no.22,p.4874,2019.
[8].B.Yaman,S.A.H.Hosseini,and M.
Figure BDA0003381255660000021
“Zero-shot self-supervised learning for mri reconstruction,”arXiv preprint arXiv:2102.07737,2021.
[9].D.Ulyanov,A.Vedaldi,and V.Lempitsky,“Deep image prior,”in Proceedings of the IEEE conference on computer vision and pattern recognition,2018,pp.9446–9454.
[10].D.Zhao,F.Zhao,and Y.Gan,“Reference-driven compresse dsensing mr image reconstruction using deep convolutional neural networks without pre-training,”Sensors,vol.20,no.1,p.308,2020.
[11].F.Hashimoto,K.Ote,T.Oida,A.Teramoto,and Y.Ouchi,“Compressed-sensing magnetic resonance image reconstruction using an iterative convolutional neural network approach,”Applied Sciences,vol.10,no.6,p.1902,2020.
Disclosure of Invention
The invention aims to overcome the defects of the existing method and provides an undersampled magnetic resonance image reconstruction method based on reference images and data correction, which has the advantages of high convergence speed and high reconstruction precision.
In order to realize the purpose of the invention, the technical scheme is as follows:
an undersampled magnetic resonance image reconstruction method based on reference images and data correction comprises the following steps:
acquiring a fully-sampled T1 weighted image as a reference image I ref (ii) a Acquiring a fully sampled T2 weighted image I T2 And converted into undersampled k-space data y;
initializing a sequence of images I s And initializing a mutual information value sequence MI s ；
Building reference image based I using residual module based convolutional neural network ref And an undersampled magnetic resonance image reconstruction model of the undersampled k-space data y;
training an undersampled magnetic resonance image reconstruction model;
recording a reconstructed image and a mutual information value between the reconstructed image and a reference image in the reconstruction process;
selecting an optimal reconstructed image based on the mutual information values;
and carrying out iterative k-space data correction on the optimal reconstructed image to obtain a final reconstructed image.
Preferably, a fully sampled T2 weighted image I is acquired T2 And converting the k-space data into undersampled k-space data y, specifically comprising:
to weight the image I T2 Fourier transform is performed to k space, and then the k space data is point-multiplied by the undersampled mask M to obtain corresponding undersampled k space data y, which is as follows:
y＝M⊙FI T2
wherein F represents fourier transform.
Preferably, the undersampling mask M is a cartesian undersampling mask, and the sampling rate is 10%.
Preferably, the convolution neural network based on the residual module is used for establishing the reference image I ref And an undersampled magnetic resonance image reconstruction model of the undersampled k-space data y, specifically comprising:
the convolution neural network is formed by stacking a plurality of residual error models and is input as a reference image I ref Output as reconstructed image I t (ii) a The mapping function from input to output is f (Θ | I) ref ) The mapping function has a parameter Θ ═ W 1 ,W 2 ,…W L ；B 1 ,B 2 ,…B L In which W is l Weight matrix representing the l-th layer, B l Representing the bias of the L layer, wherein L is the total layer number of the network model; given undersampled k-space data y and its corresponding reference image I ref As network input, the reconstructed image is taken as network output, and the loss function is defined as:
I′＝f(Θ|I ref )
I t ＝f dc (I′)＝|F -1 ((1-M)⊙FI′+y)|
E(Θ)＝‖y-M⊙Ff dc (I′)‖ 2
wherein F represents Fourier transform, FI 'represents Fourier transform of image I', F -1 Denotes inverse Fourier transform, 1 denotes matrices of all values equal to M, indicates dot product between matrices, f dc Representing data correction operations, | · | | non-conducting phosphor 2 Representing the square of the matrix norm.
Preferably, the training of the undersampled magnetic resonance image reconstruction model specifically includes:
estimating a mapping function f (Θ | I) by minimizing a loss function E (Θ) ref ) Optimal value of middle parameter theta
Figure BDA0003381255660000031
The minimization of the loss function is achieved by an adaptive gradient descent algorithm and a standard back-propagation algorithm.
Preferably, the recording of the reconstructed image and the mutual information value between the reconstructed image and the reference image in the reconstruction process specifically includes:
every n training times, storing the ith reconstructed image I i To a reconstructed image sequence I s ＝I s ∪I i In, calculate I i And a reference picture I ref And storing the mutual information value in MI s ＝MI s ∪MI i Wherein
Figure BDA0003381255660000041
Wherein p (x) is as shown in figure I i The probability density of the middle gray level x, p (y) is the graph I ref Probability density of middle gray level y, p (x, y) referring to image I i Gray level x and image I ref The gray level is the joint probability density of y.
Preferably, selecting the best reconstructed image based on the mutual information value specifically includes:
from I s Selecting an optimal reconstructed magnetic resonance image I 0 ∈I s And i is a subscript corresponding to a maximum value in the mutual information value set, and is as follows:
Figure BDA0003381255660000042
preferably, the iterative k-space data correction is performed on the optimal reconstructed image to obtain a final reconstructed image, and the method specifically includes:
to I 0 Correcting data K times to obtain the final reconstructed image i K ，
I k ＝f dc (I k-1 ) k＝1,2,3…K。
As can be seen from the above description of the present invention, compared with the prior art, the present invention has the following advantages:
the method utilizes unsupervised machine learning to realize the reconstruction of the undersampled image, the method introduces a reference image as input, designs a convolutional neural network model to extract the characteristics of the reference image to guide the whole reconstruction process, and utilizes a k-space data correction module to accelerate the convergence speed of the reconstruction in the reconstruction process; according to the method, the optimal output reconstructed image is selected according to the mutual information value of the network model output and the reference image, so that the accuracy of the reconstructed image is improved.
Drawings
Fig. 1 is a flowchart of an undersampled magnetic resonance image reconstruction method based on a reference image and data correction according to the present embodiment;
FIG. 2 is a block flow diagram of the present embodiment;
FIG. 3 is a diagram of Cartesian, Gaussian and Poisson undersampling masks at a sampling rate of 10%; wherein (a) represents a cartesian undersampling mask; (b) representing a gaussian undersampling mask; (c) representing a poisson undersampling mask;
FIG. 4 is a schematic diagram of a residual module;
FIG. 5 is a schematic diagram of a data correction module;
FIG. 6 is a curve of the mutual information value variation between the reconstructed image and the reference image during the training process, and a curve of the peak SNR variation between the reconstructed image and the real image;
FIG. 7 shows the under-sampled magnetic resonance data under Cartesian mask with a sampling rate of 10%, the MRI brain image super-resolution reconstruction result of the supervised method and the method; wherein (a) represents a true fully-sampled T2 weighted image; (b) a full sample T1 weighted image representing a reference; (c) represents an under-sampled zero-filled reconstructed T2 image; (e) representing a supervised convolutional neural network reconstructed T2 image; (g) a T2 image representing the reconstruction of the method; (d) representing a reconstruction error map in the (c) image; (f) representing (e) a reconstructed error map; (h) and (g) represents the error map.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
The embodiment of the invention is a specific process for multi-resolution reconstruction of multi-contrast MRI brain images by using a convolutional neural network, and is a detailed description of the method provided by the invention.
Referring to fig. 1 and 2, the method for reconstructing an undersampled magnetic resonance image based on a reference image and data correction of the present embodiment includes the following steps:
and S101, introducing full-sampling magnetic resonance images with different contrasts as reference images.
The data set used in this example is the MRI database derived from NAMIChttp://hdl.handle.net/ 1926/1687) The magnetic resonance image in (1) uses an image pixel size of 1 × 1 mm, a slice thickness of 1 mm, and a data size of 256 × 256 × 176.
Wherein the fully sampled high resolution T1 weights the image I ref 。
The undersampling process is as follows:
weighting fully sampled high resolution T2 image I T2 First, fourier transform is performed to k-space, and the k-space data is multiplied by undersampled mask points to obtain corresponding undersampled T2 weighted k-space data as y.
Referring to fig. 3, the undersampling mask includes a cartesian undersampling mask, a gaussian undersampling mask, and a poisson undersampling mask. In this embodiment, a cartesian undersampling mask M is used, and the sampling rate is 10%. The column with the M median value of 1 is a sampling column, and the column with the M median value of 0 is not sampled.
y＝M⊙FI T2
S102, initializing an image sequence and initializing a mutual information value sequence.
In particular, the image sequence I is initialized s Initializing a mutual information value sequence MI { } s ＝{}。
And S103, establishing an undersampled magnetic resonance image reconstruction model based on the reference image and the undersampled k-space data y by using the convolutional neural network based on the residual error module.
Specifically, the reconstruction model is composed of a convolution layer at the head and the tail and 8 residual modules in the middle. The first convolutional layer has 32 convolutional kernels of size 3 × 3; each residual module has two convolution layers, the first convolution layer of each layer has 32 convolution kernels with the size of 3 multiplied by 3, and the result of cross-over addition between the input of the residual module and the convolution output of the second layer is the output of the residual module; the last layer is 1 × 32 convolution kernels of size 3 × 3.
The residual block diagram is shown in fig. 4.
The mean square error of the output of the model with the corresponding undersampled T2 weighted data y as the loss function E (Θ) of the model:
I′＝f(Θ|I ref )
I t ＝f dc (I′)＝|F -1 ((1-M)⊙FI′+y)|
E(Θ)＝‖y-M⊙Ff dc (I′)‖ 2
wherein F represents Fourier transform, FI 'represents Fourier transform of image I', F -1 Denotes inverse Fourier transform, 1 denotes matrices of all values equal to M, indicates dot product between matrices, f dc Representing data correction operations, | · | | non-conducting phosphor 2 Representing the square of the matrix norm.
Specifically, fig. 5 is a schematic diagram of the data correction module of the present embodiment.
And S104, training an undersampled magnetic resonance image reconstruction model.
The training of the model is to estimate the mapping function f (Θ | I) by minimizing the loss function E (Θ) ref ) Middle parameter thetaIs optimally taken
Figure BDA0003381255660000062
The minimization of the loss function is achieved by an adaptive gradient descent algorithm and a standard back propagation algorithm.
And S105, recording the reconstructed image and the mutual information value between the reconstructed image and the reference image in the reconstruction process.
And setting the whole training process as 5000 times of iteration, and storing the reconstructed image and the mutual information value of the reconstructed image and the reference image at an interval of 100 times of iteration. Storing the I x 100 th reconstructed image I i To a reconstructed image sequence I s ＝I s ∪I i In, calculate I i And a reference picture I ref And storing the mutual information value in MI s ＝MI s ∪MI i 。
Figure BDA0003381255660000061
Wherein p (x) is as shown in figure I i The probability density of the middle gray level x, p (y) is the graph I ref Probability density of middle gray level y, p (x, y) referring to image I i Gray level x and image I ref The gray level is the joint probability density of y.
Fig. 6 is a graph showing mutual information values of a reconstructed image and a reference image and a peak signal-to-noise ratio of the reconstructed image and a real image changing with a training process value in the training process of this embodiment. As can be seen from fig. 5, in the early stage of training, as the training times increase, the mutual information value between the reconstructed image and the reference image becomes larger and larger, and the quality of the reconstructed image also improves correspondingly, but in the later stage of training, the quality of the reconstructed image starts to decrease, which indicates that overfitting occurs in the training, and at this time, the mutual information value between the reconstructed image and the reference image also decreases. This shows that the mutual information value can be used as a judgment basis for judging whether the reconstructed image is optimal or not.
And S106, selecting the optimal reconstructed image as network output.
From I s Selecting an optimal reconstructed magnetic resonance image I 0 ∈I s I is a subscript corresponding to the maximum value in the mutual information value set,
Figure BDA0003381255660000071
and S107, carrying out iterative k-space data correction on the optimal reconstructed image to obtain a final reconstructed image.
Specifically, for I 0 Correcting data for 100 times to obtain final reconstructed image I 100 The following are:
I k ＝f dc (I k-1 ) k＝1,2,3…100。
specifically, a schematic diagram of the data correction module is shown in fig. 5.
Further, referring to fig. 7, the result of the MRI brain map super-resolution reconstruction with the supervised method and the present method is the undersampled magnetic resonance data under the cartesian mask with the sampling rate of 10%; wherein (a) represents a true fully-sampled T2 weighted image; (b) a fully sampled T1 weighted image representing a reference; (c) represents an under-sampled zero-filled reconstructed T2 image; (e) representing a supervised convolutional neural network reconstructed T2 image; (g) a T2 image representing the reconstruction of the method; (d) representing a reconstruction error map in the (c) image; (f) representing (e) a reconstructed error map; (h) and (g) represents the error map.
As can be seen from FIG. 7, the method of the present invention has the advantages of small reconstruction error and high reconstruction accuracy.
The above description is only an embodiment of the present invention, but the design concept of the present invention is not limited thereto, and any insubstantial modifications made by using this concept shall fall within the scope of the present invention.

Claims (8)

1. An undersampled magnetic resonance image reconstruction method based on a reference image and data correction is characterized by comprising the following steps:
acquiring a fully sampled T1 weighted image as a reference image I ref (ii) a Acquiring a fully sampled T2 weighted image I T2 And converted into undersampled k-space data y;
initializing a sequence of images I s And initializing a mutual information value sequence MI s ；
Building reference image based I using residual module based convolutional neural network ref And an undersampled magnetic resonance image reconstruction model of the undersampled k-space data y;
training an undersampled magnetic resonance image reconstruction model;
recording a reconstructed image and a mutual information value between the reconstructed image and a reference image in the reconstruction process;
selecting an optimal reconstructed image based on the mutual information values;
and carrying out iterative k-space data correction on the optimal reconstructed image to obtain a final reconstructed image.
2. Method for undersampled magnetic resonance image reconstruction based on reference images and data correction according to claim 1, characterized in that a fully sampled T2 weighted image I is acquired T2 And converting the k-space data into undersampled k-space data y, specifically comprising:
to weight the image I T2 Fourier transform is performed to k space, and then the k space data is point-multiplied by the undersampled mask M to obtain corresponding undersampled k space data y, which is as follows:
y＝M⊙FI T2
wherein F represents fourier transform.
3. An undersampled magnetic resonance image reconstruction method based on a reference image and data correction as claimed in claim 2, characterized in that the undersampled mask M is a cartesian undersampled mask with a sampling rate of 10%.
4. Method for reference image and data correction based undersampled magnetic resonance image reconstruction as claimed in claim 1, characterized in that the reference image I based on is established using a convolutional neural network based on residual modules ref And an undersampled magnetic resonance image reconstruction model of the undersampled k-space data y, specifically comprising:
the convolution neural network is formed by stacking a plurality of residual error modelsInput as a reference image I ref Output as reconstructed image I t (ii) a The mapping function from input to output is f (Θ | I) ref ) The mapping function has a parameter Θ ═ W 1 ，W 2 ，...W L ；B 1 ，B 2 ，...B L In which W is l Weight matrix representing the l-th layer, B l Representing the bias of the L layer, wherein L is the total layer number of the network model; given undersampled k-space data y and its corresponding reference image I ref As a network input, the reconstructed image is taken as a network output, and the loss function is defined as:
I′＝f(Θ|I ref )
I t ＝f dc (I′)＝|F -1 ((1-M)⊙FI′+y)|
E(Θ)＝||y-M⊙Ff dc (I′)|| 2
wherein F represents Fourier transform, FI 'represents Fourier transform of image I', F -1 Denotes inverse Fourier transform, 1 denotes matrices of all values equal to M, indicates dot product between matrices, f dc Representing data correction operation, | · caly |, calving 2 Representing the square of the matrix norm.
5. The undersampled magnetic resonance image reconstruction method based on the reference image and the data correction according to claim 4, characterized in that training an undersampled magnetic resonance image reconstruction model specifically comprises:
estimating the mapping function f (Θ | I) by minimizing the loss function E (Θ) ref ) Optimal value of middle parameter theta
Figure FDA0003381255650000023
The minimization of the loss function is achieved by an adaptive gradient descent algorithm and a standard back propagation algorithm.
6. The undersampled magnetic resonance image reconstruction method based on reference image and data correction according to claim 1, characterized in that recording the reconstructed image and its mutual information value with the reference image during reconstruction process, specifically includes:
every n training times, storing the ith reconstructed image I i To a reconstructed image sequence I s ＝I s ∪I i In, calculate I i And a reference picture I ref And storing the mutual information value in MI s ＝MI s ∪MI i In which
Figure FDA0003381255650000021
Wherein p (x) is as shown in figure I i The probability density of the middle gray level x, p (y) is the graph I ref Probability density of medium gray level y, p (x, y) referring to image I i Gray level x and image I ref The gray level is the joint probability density of y.
7. The undersampled magnetic resonance image reconstruction method based on a reference image and data correction according to claim 6, characterized in that selecting an optimal reconstructed image based on the mutual information values specifically comprises:
from I s Selecting an optimal reconstructed magnetic resonance image I 0 ∈I s And i is a subscript corresponding to a maximum value in the mutual information value set, and is as follows:
Figure FDA0003381255650000022
8. the undersampled magnetic resonance image reconstruction method based on a reference image and data correction according to claim 7, characterized in that the optimal reconstructed image is subjected to iterative k-space data correction to obtain a final reconstructed image, specifically comprising:
to I 0 Correcting data for K times to obtain the final reconstructed image I K ，
I k ＝f dc (I k-1 ) k＝1，2，3...K。
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CN115830172A (en) * 2023-02-20 2023-03-21 泰山学院 Iterative refinement compressed sensing undersampled magnetic resonance image reconstruction method and reconstruction system
CN116993852A (en) * 2023-09-26 2023-11-03 阿尔玻科技有限公司 Training method of image reconstruction model, main control equipment and image reconstruction method
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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115830172A (en) * 2023-02-20 2023-03-21 泰山学院 Iterative refinement compressed sensing undersampled magnetic resonance image reconstruction method and reconstruction system
CN116993852A (en) * 2023-09-26 2023-11-03 阿尔玻科技有限公司 Training method of image reconstruction model, main control equipment and image reconstruction method
CN116993852B (en) * 2023-09-26 2024-01-30 阿尔玻科技有限公司 Training method of image reconstruction model, main control equipment and image reconstruction method
CN117333571A (en) * 2023-10-25 2024-01-02 烟台大学 Reconstruction method, system, equipment and medium of magnetic resonance image
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