Piecewise constant denoising can be solved either by deterministic optimization approaches, based on total variation (TV), or by stochastic Bayesian procedures. The former lead to low computational time but requires 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 large computational costs. This contribution proposes an operational strategy that combines hierarchical Bayesian and TVl0 formulations, with the double aim of automatically tuning the regularization parameter and of maintaining computational efficiency. The proposed procedure relies on formally connecting a Bayesian framework to a TVl0 minimization formulation. 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.
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