Efficient Gaussian Sampling for Solving Large-Scale Inverse Problems using MCMC Methods

TL;DR

This paper introduces an efficient Gaussian sampling algorithm for large-scale inverse problems using MCMC, reducing computational costs and memory requirements through an adaptive linear system approximation.

Contribution

It proposes a novel, self-tuning Gaussian sampling method based on the reversible jump MCMC framework, improving efficiency over traditional techniques.

Findings

Reduces computation time compared to direct methods

Uses adaptive truncation for linear system solving

Demonstrates effectiveness on image resolution enhancement

Abstract

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 having 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.