Bayesian selection for the l2-Potts model regularization parameter: 1D piecewise constant signal denoising

TL;DR

This paper introduces a hybrid Bayesian-Potts approach for automatic regularization parameter tuning in 1D piecewise constant signal denoising, balancing accuracy and computational efficiency.

Contribution

It proposes a novel method combining hierarchical Bayesian and Potts models to automatically select the regularization parameter with reduced computational cost.

Findings

The method effectively tunes the regularization parameter automatically.

It achieves comparable accuracy to fully Bayesian methods.

It reduces computational load while maintaining denoising quality.

Abstract

Piecewise constant denoising can be solved either by deterministic optimization approaches, based on the Potts model, or by stochastic Bayesian procedures. The former lead to low computational time but require the selection of a regularization parameter, whose value significantly impacts the achieved solution, and whose automated selection remains an involved and challenging problem. Conversely, fully Bayesian formalisms encapsulate the regularization parameter selection into hierarchical models, at the price of high computational costs. This contribution proposes an operational strategy that combines hierarchical Bayesian and Potts model formulations, with the double aim of automatically tuning the regularization parameter and of maintaining computational effciency. The proposed procedure relies on formally connecting a Bayesian framework to a l2-Potts functional. Behaviors and performance for the proposed piecewise constant denoising and regularization parameter tuning techniques are studied qualitatively and assessed quantitatively, and shown to compare favorably against those of a fully Bayesian hierarchical procedure, both in accuracy and in computational load.