  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.
