MAPEM.ppsx
- 2. Reconstruct an Image using Projection Maximum A Posteriori Expectation Maximization (MAPEM) Optimizing the Iteration Reducing the time Performance Analysis –Amdahl’s Law.
- 3. Mathematical Process Data obtained at various angles Medical imaging modalities ◦ CT scan ◦ PET ◦ MRI scan
- 4. Computed Tomography Scan Positron Emission Tomography Magnetic Resonance imaging
- 5. Analytical ◦ Filtered Back Projection (FBP) Iterative ◦ Algebraic Reconstruction Technique (ART) ◦ Statistical Reconstruction Technique Weighted Least Square Likelihood based iterative Expectation Maximization Maximum Likelihood Expectation Maximization Maximum A Posteriori Expectation Maximization
- 6. Projection is a line integral along the path: cos sin where y)ds f(x, ) ( y x s t p AB
- 7. Projections with different angles are stored in sinogram (raw data) Each horizontal line in sinogram is a projection with different angle ) (t p projection ) (t p
- 8. Y is constant posterior likelihood prior X: reconstruction Y: projection Bayes: MAP: maximize p(Y|X) p(X) or ln p(Y|X) + ln p(X)
- 9. Multi-core platform ◦ Thread level parallelism Simultaneous Multi-Threading (SMT) Chip Multi-Processor (CMP) Multi Core Many Core ◦ Two conclusions for applications running on multi- core platform Conclusion 1. When multiple applications are executed, the performance on multi-core platform is better than single-core platform with the same clock frequency. Conclusion 2. Applications without parallelization can’t make full use of computing power on multi-core platform. OpenMP (OMP) directives is implemented
- 10. Amdahl’s Law ◦ statement of the maximum theoretical speed-up you casn ever hope to achieve. time execution Parallel time execution Sequential Speedup f n f f p S 1 / ) 1 ( 1 ) (
- 11. Shepp Logan Phantom 64 x 64 128 x 128 256 x 256
- 12. Sinogram (Raw data) A B C D E 1 2 3
- 13. Iteration Optimized Projections/ Sizes 30 20 1 5 12 10 64x64 20 18 1 0 23 19 128x128 27 27 3 5 23 41 256x256 61 29 4 5 39 61
- 14. PSNR 10 12 15 20 30 64x64 53.43 72 53.37 98 53.09 74 53.26 82 53.36 85 128x1 28 61.67 12 61.23 3 62.13 11 62.09 66 62.15 82 256x2 56 69.58 12 69.70 39 70.25 1 70.31 48 71.01 51
- 15. Image Reconstructed A B C D E 1 2 3
- 16. Time Complexity 64 x 64 10 12 15 20 30 1 core 3.09129 4.27891 2.09782 5.43004 8.33448 2 Core 2.41019 2.99262 1.47404 4.17731 5.21191 4 Core 1.92379 2.53712 1.24897 2.96779 4.50192 8 Core 1.5557 1.60578 0.946761 2.04252 3.55317 0 1 2 3 4 5 6 7 8 9 Reconstruction Time (s) Time Complexity (64x64) 1 core 2 Core 4 Core 8 Core
- 17. Time Complexity 128 x 128 10 12 15 20 30 1 core 47.9322 26.299 66.0366 66.9674 98.2584 2 Core 36.5989 24.8049 41.1161 49.6748 72.4108 4 Core 25.3501 20.7042 40.2762 42.9248 53.6694 8 Core 10.3271 11.9932 30.9506 20.7319 30.8544 0 20 40 60 80 100 120 Reconstruction Time (s) Time complexity (128x128) 1 core 2 Core 4 Core 8 Core
- 18. Time Complexity 256 x 256 10 12 15 20 30 1 core 568.4280 394.722 630.297 552.071 1758.98 2 Core 464.261 337.362 483.439 453.559 1415.51 4 Core 273.036 250.089 340.672 323.802 1019.31 8 Core 185.939 164.266 225.58 193.718 646.457 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Reconstruction Time (s) Time complexity (256x256) 1 core 2 Core 4 Core 8 Core
- 19. Performance Analysis 0 2 4 6 8 10 10 12 15 20 30 1 2 4 8 0 2 4 6 8 10 10 12 15 20 30 1 2 4 8 0 2 4 6 8 10 10 12 15 20 30 1 2 4 8 64 x 64 128 x 128 256 x 256