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Szirmay-Kalos, László Budapest Uni of Tech

GPU-based Image Processing Methods in Higher Dimensions and their Application to Tomography Reconstruction  . Szirmay-Kalos, László Budapest Uni of Tech. Sapporo, 2010. Positron Emission Tomography. Intensity: x. e -. e +. Line Of Response : y.

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Szirmay-Kalos, László Budapest Uni of Tech

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  1. GPU-based Image Processing Methods in Higher Dimensions and their Application to Tomography Reconstruction   Szirmay-Kalos, László Budapest Uni of Tech Sapporo, 2010

  2. Positron Emission Tomography Intensity: x e- e+ Line Of Response: y

  3. Iterative Maximum Likelihood Reconstruction Source estimation Compute expected detector response Expected detector response Source intensity as a 3D voxel array Source correction Measured detector response

  4. Ill-posed reconstruction error Maximum likelihood estimate Iteration number

  5. Regularization • Additional information • Penalty term added to the likelihood • Prevents overfitting • TV norm (L1 optimization) • No smoothness condition • Preserves edges

  6. TV minimalization • In steepest descent search the derivative of the TV term is needed: • Function |x|cannot be differentiated: • Add a small term (blurring) • Primal-dual methods • Only local values are needed: parallelization xV

  7. Detector scattering compensation photon crystals absorption intercrystal scattering Electronics number of hits Path probability inside the detector can be pre-computed or measured

  8. Pre-computation q

  9. Quasi-Monte Carlo filtering L L w =

  10. Random sampling undersampling oversampling Random sampling

  11. Delta-Sigma modulator pixels Filter kernel

  12. Delta-Sigma modulator Filter kernel

  13. Delta-Sigma modulator Filter kernel Floyd-Steinberg halftoning!

  14. Sampling with Sigma-Delta modulation

  15. GPU Implementation high dim. integrals • Simulation step: • GPU: Quasi-SIMD massively parallel machine • Gathering = threads to equations (outputs) • “No” conditional statements or variable length loops • Reconstruction algorithm • Geometric LOR marching: threads to LORs (adjoint problem) • LOR filtering: threads to output LORs • TV regularization: threads to voxels 108 LORs 108 voxels

  16. TV regularization results No TV =0.005 =0.05 =0.008

  17. TV results =0.001 =0.0005 =0.0001 =0.005

  18. Scatteringinthedetector 2D reconstruction: SSRB + OSEM 3D reconstruction, no detectorscatteringcompensation Detectorscatteringcompensation

  19. F18 mouse

  20. Conclusions • Image processing algorithms can be and are worth being generalized to higher dimensions, but • beware the curse of dimensions and use Monte Carlo methods. • GPUs are good platforms for image processing, but adopt the gathering view and refrain from conditionals.

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