Image Reconstruction with Reliability Assessment in Quantitative Photoacoustic Tomography
Abstract
:1. Introduction
2. Materials and Methods
2.1. Forward Model
2.2. Inverse Problem
2.3. Bayesian Approximation Error Modeling
2.4. Evaluating Credibility
3. Simulation Studies
3.1. Data Simulation
3.2. Inverse Problem
3.3. Prior Model
3.4. Approximation Error Statistics
3.5. Reliability of the Credibility Intervals
4. Results
4.1. Simulation I: Smooth Inclusions
4.2. Simulation II: Blood-Vessel-Mimicking Inclusions
4.3. Reliability of the Credibility Intervals
5. Discussion and Conclusions
Author Contributions
Funding
Conflicts of Interest
Abbreviations
PAT | Photoacoustic tomography |
QPAT | Quantitative photoacoustic tomography |
MAP | Maximum a posteriori |
RTE | Radiative transfer equation |
DA | Diffusion approximation |
FE | Finite element |
FEM | Finite element method |
BAE | Bayesian approximation error |
CEM | Conventional error model |
EEM | Enhanced error model |
2D | Two-dimensional |
SD | Standard deviation |
CDF | Cumulative distribution function |
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Mesh | |||
---|---|---|---|
Data simulation | 104,472 | 52,654 | |
Coarse mesh, basis for optical parameters | 2052 | 1085 | |
Fine mesh | 32,832 | 16,649 | |
Prior samples for evaluating the credibility | 1932 | 1024 |
Reconstructions | 1.25 | 0.2 (1) | 6 (1) | 0.2 (1) | 6 (1) |
Approximation error statistics | 1.25 | 0.2 | 6 | 0.067 | 2 |
Reliability of the credibility intervals | 1.25 | 0.2 | 6 | 0.067 | 2 |
MAP-REF | MAP-CEM | MAP-EEM | ||||
---|---|---|---|---|---|---|
(%) | (%) | (%) | (%) | (%) | (%) | |
Simulation I | 3.6 | 11.0 | 5.1 | 12.5 | 3.7 | 11.1 |
Simulation II | 6.7 | 15.2 | 9.5 | 16.5 | 7.6 | 15.7 |
MAP-REF | MAP-CEM | MAP-EEM | ||||
---|---|---|---|---|---|---|
Time (s) | Iteration | Time (s) | Iteration | Time (s) | Iteration | |
Simulation I | 18,081 | 9 | 445 | 11 | 296 | 10 |
Simulation II | 22,480 | 10 | 507 | 12 | 337 | 11 |
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Hänninen, N.; Pulkkinen, A.; Tarvainen, T. Image Reconstruction with Reliability Assessment in Quantitative Photoacoustic Tomography. J. Imaging 2018, 4, 148. https://doi.org/10.3390/jimaging4120148
Hänninen N, Pulkkinen A, Tarvainen T. Image Reconstruction with Reliability Assessment in Quantitative Photoacoustic Tomography. Journal of Imaging. 2018; 4(12):148. https://doi.org/10.3390/jimaging4120148
Chicago/Turabian StyleHänninen, Niko, Aki Pulkkinen, and Tanja Tarvainen. 2018. "Image Reconstruction with Reliability Assessment in Quantitative Photoacoustic Tomography" Journal of Imaging 4, no. 12: 148. https://doi.org/10.3390/jimaging4120148
APA StyleHänninen, N., Pulkkinen, A., & Tarvainen, T. (2018). Image Reconstruction with Reliability Assessment in Quantitative Photoacoustic Tomography. Journal of Imaging, 4(12), 148. https://doi.org/10.3390/jimaging4120148