الفهرس 
ContentsOnly 14 pages are availabe for public view
 |  | from | 76 |  |  |
| | | from | 76 | | |
Abstract
The thesis is mainly focused on the solution of Bayesian inverse problems under extreme non-Gaussian and nonlinear settings on parallel architecture with application to medical image retrieval. Specifically, we have developed parallel cluster sampling algorithms for solving large-scale Bayesian inverse problems. The algorithms discussed here are general, and can be applied in a wide range of fields such medical image reconstruction, atmospheric forecasting, sea surface modelling, and tomography. As a cornerstone of this work, we have introduced a detailed complexity analysis of parallel cluster sampling algorithms for mixture model representation of the prior knowledge, namely multi-chain CLHMC sampling algorithms. Generally speaking, aside from parallelization, the parallel versions of the cluster sampling algorithm result in higher acceptance rates, leading to massive saving of computations. Specifically, the parallel CLHMC increases the acceptance rate of the sampler from 44% to 83% with Gaussian proposal kernel. The parallel cluster sampling algorithm can run significantly faster than the serial sampler in ideal settings. Both serial and parallel versions of the C`HMC sampling algorithm have proven very useful in the context of medical image reconstruction from noisy observations, and uncertain prior. We have shown, using numerical experiments that the proposed sampling algorithms achieve an improvement of approximately 29% over the optimally-tuned Tikhonov-based solution for image retrieval. This can especially useful in various applications related to medical imaging and tomography. In future work, we will investigate the possibility of parallelizing other components.