A Survey of Stochastic Simulation and Optimization Methods in Signal Processing

TL;DR

This survey reviews stochastic simulation and optimization techniques in signal processing, highlighting their role in tackling complex models and Bayesian inference through methods like MCMC, variational Bayes, and message passing.

Contribution

It provides a comprehensive overview of recent stochastic simulation and optimization methods applied to high-dimensional signal processing problems, including their integration and overlap.

Findings

Coverage of high-dimensional MCMC methods

Discussion of surrogate deterministic methods

Analysis of stochastic optimization techniques

Abstract

Modern signal processing (SP) methods rely very heavily on probability and statistics to solve challenging SP problems. SP methods are now expected to deal with ever more complex models, requiring ever more sophisticated computational inference techniques. This has driven the development of statistical SP methods based on stochastic simulation and optimization. Stochastic simulation and optimization algorithms are computationally intensive tools for performing statistical inference in models that are analytically intractable and beyond the scope of deterministic inference methods. They have been recently successfully applied to many difficult problems involving complex statistical models and sophisticated (often Bayesian) statistical inference techniques. This survey paper offers an introduction to stochastic simulation and optimization methods in signal and image processing. The paper addresses a variety of high-dimensional Markov chain Monte Carlo (MCMC) methods as well as deterministic surrogate methods, such as variational Bayes, the Bethe approach, belief and expectation propagation and approximate message passing algorithms. It also discusses a range of optimization methods that have been adopted to solve stochastic problems, as well as stochastic methods for deterministic optimization. Subsequently, areas of overlap between simulation and optimization, in particular optimization-within-MCMC and MCMC-driven optimization are discussed.