Discrete Shearlets as a Sparsifying Transform in Low-Rank Plus Sparse Decomposition for Undersampled (k, t)-Space MR Data
Abstract
:1. Introduction
2. Theory
2.1. Focal Underdetermined System Solver (k-t FOCUSS)
2.2. Robust Principal Component Analysis (RPCA)
2.3. Sparsifying Transforms
2.4. Image Registration—Motility Metric
3. Materials and Methods
3.1. Small Bowel MR Acquisition
3.2. Simulated Abdominal DCE Data
3.3. Simulated Undersampled Acquisition
3.4. Quantitative Evaluation
3.5. Implementation Details
4. Results
4.1. Low-Rank Plus Sparse Image Decomposition
4.2. Low-Rank Plus Sparse Image Decomposition from Undersampled -Space Data
4.3. Quantification of Motility in Low-Rank Plus Sparse Decomposition Using Discrete Shearlets as Sparsifying Transforms
5. Discussion
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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decomposition and reconstruction algorithm |
---|
Input: -space samples y, decomposition parameters , |
Initialize: and , iteration k=1; |
while stopping criterion is not met, do |
Singular value thresholding |
Shrinkage operator |
Subtract aliasing artifacts from |
Stopping criterion |
or |
end while |
Output: , |
Unders. Factor 4 | Unders. Factor 8 | |
---|---|---|
k-t FOCUSS | 0.162 | 0.203 |
using I as sparsifying transform | 0.149 | 0.194 |
using TF as sparsifying transform | 0.147 | 0.189 |
using WT as sparsifying transform | 0.147 | 0.188 |
using DS as sparsifying transform | 0.144 | 0.187 |
Undersampling Factor 4 | Median | iQR |
k-t FOCUSS | 0.077 | 0.013 |
using I as sparsifying transform | 0.080 | 0.012 |
using TF as sparsifying transform | 0.079 | 0.012 |
using WT as sparsifying transform | 0.075 | 0.011 |
using DS as sparsifying transform | 0.064 * | 0.006 |
Undersampling Factor 8 | Median | iQR |
k-t FOCUSS | 0.120 | 0.025 |
using I as sparsifying transform | 0.119 | 0.018 |
using TF as sparsifying transform | 0.115 | 0.017 |
using WT as sparsifying transform | 0.112 | 0.021 |
using DS as sparsifying transform | 0.106 | 0.029 |
L | ||
---|---|---|
DCE images | 0.016 | 0.031 |
US4 | 0.021 | 0.025 |
US8 | 0.024 | 0.029 |
Scanner images | BH | FB | p-value |
S | 0.044 | 0.049 | 0.20 |
0.036 | 0.047 | 0.02 | |
Four-fold | BH | FB | p-value |
S | 0.039 | 0.045 | 0.08 |
0.034 | 0.043 | 0.02 | |
Eight-fold | BH | FB | p-value |
S | 0.039 | 0.047 | 0.04 |
0.035 | 0.043 | 0.01 |
L | S | ||
---|---|---|---|
Four-fold | 0.10 | 0.27 | 0.35 |
Eight-fold | 0.01 | 0.45 | 0.49 |
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Protonotarios, N.E.; Tzampazidou, E.; Kastis, G.A.; Dikaios, N. Discrete Shearlets as a Sparsifying Transform in Low-Rank Plus Sparse Decomposition for Undersampled (k, t)-Space MR Data. J. Imaging 2022, 8, 29. https://doi.org/10.3390/jimaging8020029
Protonotarios NE, Tzampazidou E, Kastis GA, Dikaios N. Discrete Shearlets as a Sparsifying Transform in Low-Rank Plus Sparse Decomposition for Undersampled (k, t)-Space MR Data. Journal of Imaging. 2022; 8(2):29. https://doi.org/10.3390/jimaging8020029
Chicago/Turabian StyleProtonotarios, Nicholas E., Evangelia Tzampazidou, George A. Kastis, and Nikolaos Dikaios. 2022. "Discrete Shearlets as a Sparsifying Transform in Low-Rank Plus Sparse Decomposition for Undersampled (k, t)-Space MR Data" Journal of Imaging 8, no. 2: 29. https://doi.org/10.3390/jimaging8020029