The quality of dynamic magnetic resonance imaging reconstruction has heavy impact on clinical diagnosis. In this paper, we propose a new reconstructive algorithm based on the
Image reconstruction is widely applied in the medical field, and most clinical diagnoses depend on computer hardware equipment; thus the improvement on image reconstruction algorithm has great significance. At present, among all kinds of detection methods, magnetic resonance imaging (MRI) and computed tomography (CT) are the most common and important ways for clinical diagnosis. When checking organs by MR, the final image is affected in varying degrees by artifacts, which results in degrading in quality and affects the diagnoses. Therefore, reconstruction algorithms with high quality and fast calculation have become one of the research focuses in this field.
In recent years, in order to ensure image quality and to speed up the pace of reconstruction, there emerge many improved methods, such as multicoil parallel imaging [
Since the development of robust principal component analysis (RPCA) theory [
Recently, a lot of researchers focused on the problem of
Inspired by the above discussion, combining RPCA theory with a nonconvex idea, we propose a new MR image reconstruction model. The contributions of this paper are as follows:
Framework of the proposed dynamic MRI reconstruction.
The rest of this paper is organized as follows: in Section
According to the theory of RPCA [
Since (
Let the data of an image correspond to the data of the
Singular Value Thresholding (SVT) algorithm [
Although the above methods have good theoretical guarantee and have made major breakthroughs in dynamic MR image reconstruction,
Defining the
Combining the properties of supergradient for nonsmooth points with Taylor expansion [
Therefore, the new model can be further expressed as
By introducing a Lagrangian multiplier, (
When
In the iteration process, after
Finally, the parameters
While not convergence do
End while
According to [
Let
In order to evaluate the performance of the proposed model, we compare our algorithm with the
The iteration stop indicator for all algorithms of this paper is linked to the relative error (Err), which is defined as
There are nine sets of test data in this paper, three of them are open-data which come from [
One of the three sets of open-data is the dynamic cardiac perfusion data, which consists of 40 images with size
For
The relationship between the function values and the parameter
The 5th frame of each data set. (a)–(f) are named as image 1 to image 6.
In this section, we compare our method with the
Comparison on object indexes.
Image |
|
XD-GRASP | LplusS | Ours | |
---|---|---|---|---|---|
Cardiac perfusion | |
|
|
|
|
|
0.8124 | 0.8013 | 0.8009 |
|
|
Time (s) | 220.4 | 202.4 |
|
84.2 | |
|
|||||
Abdomen images | |
|
|
|
|
|
12.4521 | 11.7607 | 9.2530 |
|
|
Time (s) | 336.2 | 310.3 |
|
293.8 | |
|
|||||
Cardiac cine | |
|
|
|
|
|
0.5233 | 0.5147 | 0.5063 |
|
|
Time (s) | 156.0 | 159.0 | 141.7 |
|
Comparison on object indexes.
Image |
|
XD-GRASP | LplusS | Ours | |
---|---|---|---|---|---|
Image 1 | |
|
|
|
|
|
9.7235 | 9.3785 | 8.2500 |
|
|
Time (s) | 202.0 | 185.3 |
|
171.6 | |
|
|||||
Image 2 | |
|
|
|
|
|
12.7820 | 10.2324 | 9.4725 |
|
|
Time (s) | 196.1 | 188.4 |
|
185.2 | |
|
|||||
Image 3 | |
|
|
|
|
|
5.2474 | 3.2596 | 2.9487 |
|
|
Time (s) | 153.0 | 147.8 |
|
110.8 | |
|
|||||
Image 4 | |
|
|
|
|
|
12.2844 | 11.5627 | 9.0751 |
|
|
Time (s) | 214.3 | 193.1 |
|
169.0 | |
|
|||||
Image 5 | |
|
|
|
|
|
10.7704 | 9.8403 | 8.7709 |
|
|
Time (s) | 189.7 | 163.2 |
|
144.3 | |
|
|||||
Image 6 | |
|
|
|
|
|
8.5527 | 8.2764 | 7.3008 |
|
|
Time (s) | 157.5 | 140.6 |
|
135.7 |
Reconstruction comparisons on the first frame of dynamic cardiac perfusion. (a)
Reconstruction comparisons on the 3rd frame of dynamic cardiac perfusion. (a)
Reconstruction comparisons on the 2nd frame of dynamic abdomen. (a)
Reconstruction comparisons on the 5th frame of dynamic abdomen. (a)
Reconstruction comparisons on the 20th frame of dynamic cardiac cine. (a)
Reconstruction comparisons on four images. From top to bottom are images 1, 2, 4, and 6, respectively. From left to right are
Figures
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Figure
Tables
In this paper, we propose a nonconvex model for reconstructing high-quality dynamic MR images. In the new model, based on the RPCA theory, the
The authors declare that they have no conflicts of interest.
This project is partially supported by the National Natural Science Foundation of China (61362021, 61661017, 61272216, and 61572147), Guangxi Natural Science Foundation (2013GXNSFDA019030, 2014GXNSFAA118003, and 2016GXNSFAA380043), Guangxi Colleges and Universities Key Laboratory of Intelligent Processing of Computer Images and Graphics (GIIP201408, GIIP201503), Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation (LDAC201704), Basic Research Capacity Promotion Project for Youth and Middle-Aged Teachers in Colleges and Universities of Guangxi (ky2016YB162), and Project of Education Innovation Project of Guilin University of Electronic Science and Technology (2017YJCX84).