Abstract
Cluster sampling algorithm is a scheme for sequential data assimilation developed to handle general non-Gaussian and nonlinear settings. The cluster sampling algorithm can be used to solve a wide spectrum of problems that requires data inversion such as image retrieval, tomography, weather prediction amongst others. This paper develops parallel cluster sampling algorithms, and show that a multi-chain version is embarrassingly parallel, and can be used efficiently for medical image retrieval amongst other applications. Moreover, it presents a detailed complexity analysis of the proposed parallel cluster samplings scheme and discuss their limitations. Numerical experiments are carried out using a synthetic one dimensional example, and a medical image retrieval problem. The experimental results show the accuracy of the cluster sampling algorithm to retrieve the original image from noisy measurements, and uncertain priors. Specifically, the proposed parallel algorithm increases the acceptance rate of the sampler from 45% to 81% with Gaussian proposal kernel, and achieves an improvement of 29% over the optimally-tuned Tikhonov-based solution for image retrieval. The parallel nature of the proposed algorithm makes the it a strong candidate for practical and large scale applications.
Highlights
Signal retrieval from noisy measurements involves solving an inverse problem
Inverse problems are essential in many fields such as image reconstruction or retrieval, tomography, weather prediction, and other predictions based on space-time models
data assimilation (DA) refers to the process of fusing information about a physical system obtained from different sources in order to produces more accurate conclusions about the physical system of concern
Summary
Signal retrieval from noisy measurements (observations) involves solving an inverse problem. HMC sampling filter [3] is an accelerated Markov chain Monte-Carlo (MCMC) algorithm for solving the non-Gaussian sequential DA “filtering problem”. This algorithm works by sampling the posterior distribution to produce description of the system state along with associated uncertainty. The main interest here is to develop highly accurate parallel Bayesian sampling algorithms that can be efficiently used for solving large-scale inverse problems, and show that they are suitable for a wide spectrum of applications including medical image retrieval. Following Tikhonov regularization approach (1), and assuming Gaussian noise, the likelihood function reads: P(y|x) ∝ exp 1 −
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