Unsupervised bayesian convex deconvolution based on a field with an explicit partition function

TL;DR

This paper introduces a novel unsupervised Bayesian convex deconvolution method utilizing a non-Gaussian Markov field with an explicit partition function, enabling effective edge-preserving image restoration.

Contribution

It presents the first non-Gaussian Markov field with an explicit partition function and develops a fully Bayesian deconvolution approach based on this model.

Findings

Method effectively preserves edges in deconvolution tasks.

Computational feasibility demonstrated on simulated data.

Provides a new probabilistic model with explicit partition function.

Abstract

This paper proposes a non-Gaussian Markov field with a special feature: an explicit partition function. To the best of our knowledge, this is an original contribution. Moreover, the explicit expression of the partition function enables the development of an unsupervised edge-preserving convex deconvolution method. The method is fully Bayesian, and produces an estimate in the sense of the posterior mean, numerically calculated by means of a Monte-Carlo Markov Chain technique. The approach is particularly effective and the computational practicability of the method is shown on a simple simulated example.