Linear-Time Algorithm in Bayesian Image Denoising based on Gaussian Markov Random Field

TL;DR

This paper introduces a novel linear-time algorithm for Bayesian image denoising using Gaussian Markov Random Fields, enabling efficient hyperparameter estimation and demonstrating practical effectiveness.

Contribution

The paper presents the first linear-time algorithm for Bayesian image denoising with GMRF, significantly improving computational efficiency over existing methods.

Findings

Algorithm operates in O(n) time, where n is the number of pixels.

Numerical experiments confirm the method's practical effectiveness.

State-of-the-art computational speed achieved for Bayesian denoising.

Abstract

In this paper, we consider Bayesian image denoising based on a Gaussian Markov random field (GMRF) model, for which we propose an new algorithm. Our method can solve Bayesian image denoising problems, including hyperparameter estimation, in $O(n)$-time, where $n$ is the number of pixels in a given image. From the perspective of the order of the computational time, this is a state-of-the-art algorithm for the present problem setting. Moreover, the results of our numerical experiments we show our method is in fact effective in practice.