Naive mean field approximation for image restoration

TL;DR

This paper analyzes the naive mean field approximation for image restoration within Bayesian inference, comparing theoretical predictions with simulations to assess its effectiveness and potential advantages over other methods.

Contribution

It provides a statistical-mechanical analysis of the naive mean field approximation in image restoration, highlighting its theoretical basis and practical potential.

Findings

Theoretical results align with computer simulations.

Naive mean field approximation offers a computationally efficient alternative.

Potential for improved image restoration performance.

Abstract

We attempt image restoration in the framework of the Baysian inference. Recently, it has been shown that under a certain criterion the MAP (Maximum A Posterior) estimate, which corresponds to the minimization of energy, can be outperformed by the MPM (Maximizer of the Posterior Marginals) estimate, which is equivalent to a finite-temperature decoding method. Since a lot of computational time is needed for the MPM estimate to calculate the thermal averages, the mean field method, which is a deterministic algorithm, is often utilized to avoid this difficulty. We present a statistical-mechanical analysis of naive mean field approximation in the framework of image restoration. We compare our theoretical results with those of computer simulation, and investigate the potential of naive mean field approximation.