A Stochastically Evolving Non-local Search and Solutions to Inverse Problems with Sparse Data

TL;DR

This paper introduces a stochastic global optimization method based on measure changes and Bayesian game concepts, demonstrating superior performance in benchmark and medical imaging inverse problems.

Contribution

It presents a novel stochastic search scheme for inverse problems, extending previous martingale-based optimization with measure changes and state-space splitting.

Findings

Outperforms existing optimization schemes on NP-hard benchmarks

Achieves better reconstruction in medical imaging inverse problems

Demonstrates robustness with simulated and experimental data

Abstract

Building upon our earlier work of a martingale approach to global optimization, a powerful stochastic search scheme for the global optimum of cost functions is proposed on the basis of change of measures on the states that evolve as diffusion processes and splitting of the state-space along the lines of a Bayesian game. To begin with, the efficacy of the optimizer, when contrasted with one of the most efficient existing schemes, is assessed against a family of Np-hard benchmark problems. Then, using both simulated- and experimental data, potentialities of the new proposal are further explored in the context of an inverse problem of significance in medical imaging, wherein the superior reconstruction features of a global search vis-\`a-vis the commonly adopted local or quasi-local schemes are brought into relief.