Fast Compressed Sensing of 3D Radial T1 Mapping with Different Sparse and Low-Rank Models
<p>The simulated phantom.</p> "> Figure 2
<p>Convergence of Equation (3) with and without utilizing the preconditioner [<a href="#B13-jimaging-09-00151" class="html-bibr">13</a>] in the reconstruction. The preconditioned PDPS algorithm convergences significantly faster.</p> "> Figure 3
<p>The estimated T<sub>1</sub> (<b>a</b>) and S<sub>0</sub> (<b>b</b>) maps for the multiple tested acceleration factors (AF) for the simulated phantom. The lower left corner of each image shows the SSIM (<b>top</b>) and nRMSE (<b>bottom</b>) values of the respective reconstruction.</p> "> Figure 4
<p>The T<sub>1</sub> and S<sub>0</sub> map error metrics as a function of AF for the simulated phantom.</p> "> Figure 5
<p>The estimated T<sub>1</sub> (<b>a</b>) and S<sub>0</sub> (<b>b</b>) maps for the multiple tested acceleration factors (AF) for the ex vivo acquisition. The lower left corner of each image shows the SSIM (<b>top</b>) and nRMSE (<b>bottom</b>) values of the respective reconstruction.</p> "> Figure 6
<p>The T<sub>1</sub> and S<sub>0</sub> map error metrics as a function of AF for the ex vivo acquisition.</p> ">
Abstract
:1. Introduction
2. Theory
2.1. Total Variation Model (sTV + cTV)
2.2. Huber Model (sH + cH)
2.3. Locally Low-Rank Model (LLR)
2.4. Spatial Total Variation and Locally Low-Rank Model (sTV + LLR)
2.5. Primal-Dual Proximal Splitting Algorithm
Algorithm 1. Primal-dual proximal splitting. |
Choose and such that |
while not converged do |
end while |
Algorithm 2. Preconditioned primal-dual proximal splitting for least squares. |
Choose and such that |
while not converged do |
end while |
2.6. Variable Flip Angle Acquisition
3. Methods
3.1. Ex Vivo Multi-Band-SWIFT Acquisition
3.2. Simulated Phantom
3.3. Error Metrics
3.4. Computation
4. Results
5. Discussion
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A
Algorithm A1. Preconditioned primal-dual proximal splitting for the TV model of Equation (4). |
Choose and such that |
while not converged do |
end while |
Algorithm A2. Preconditioned primal-dual proximal splitting for the Huber model of Equation (6). |
Choose and such that |
while not converged do |
end while |
Algorithm A3. Preconditioned primal-dual proximal splitting for the locally low-rank model of Equation (7). |
while not converged do |
end while |
Algorithm A4. Preconditioned primal-dual proximal splitting for the spatial total variation combined with locally low-rank model of Equation (8). |
while not converged do |
end while |
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Paajanen, A.; Hanhela, M.; Hänninen, N.; Nykänen, O.; Kolehmainen, V.; Nissi, M.J. Fast Compressed Sensing of 3D Radial T1 Mapping with Different Sparse and Low-Rank Models. J. Imaging 2023, 9, 151. https://doi.org/10.3390/jimaging9080151
Paajanen A, Hanhela M, Hänninen N, Nykänen O, Kolehmainen V, Nissi MJ. Fast Compressed Sensing of 3D Radial T1 Mapping with Different Sparse and Low-Rank Models. Journal of Imaging. 2023; 9(8):151. https://doi.org/10.3390/jimaging9080151
Chicago/Turabian StylePaajanen, Antti, Matti Hanhela, Nina Hänninen, Olli Nykänen, Ville Kolehmainen, and Mikko J. Nissi. 2023. "Fast Compressed Sensing of 3D Radial T1 Mapping with Different Sparse and Low-Rank Models" Journal of Imaging 9, no. 8: 151. https://doi.org/10.3390/jimaging9080151