Efficient Gaussian Sampling for Solving Large-Scale Inverse Problems Using MCMC

Clement Gilavert, Said Moussaoui, Jerome Idier
2015 IEEE Transactions on Signal Processing  
The resolution of many large-scale inverse problems using MCMC methods requires a step of drawing samples from a high dimensional Gaussian distribution. While direct Gaussian sampling techniques, such as those based on Cholesky factorization, induce an excessive numerical complexity and memory requirement, sequential coordinate sampling methods present a low rate of convergence. Based on the reversible jump Markov chain framework, this paper proposes an efficient Gaussian sampling algorithm
more » ... ng a reduced computation cost and memory usage. The main feature of the algorithm is to perform an approximate resolution of a linear system with a truncation level adjusted using a self-tuning adaptive scheme allowing to achieve the minimal computation cost. The connection between this algorithm and some existing strategies is discussed and its efficiency is illustrated on a linear inverse problem of image resolution enhancement.
doi:10.1109/tsp.2014.2367457 fatcat:5jfle26wjzdxtigssf4ou6y6bi