Bayesian selection for the l2-Potts model regularization parameter: 1D piecewise constant signal denoising
This addresses a challenging parameter selection issue in signal processing for denoising applications, though it is incremental as it builds on existing Bayesian and optimization methods.
The paper tackles the problem of automatically selecting the regularization parameter for piecewise constant signal denoising using the l2-Potts model, proposing a hybrid Bayesian-Potts method that achieves favorable accuracy and computational efficiency compared to fully Bayesian approaches.
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.