Piecewise constant denoising can be solved either by deterministicoptimization approaches, based on the Potts model, or by stochastic Bayesianprocedures. The former lead to low computational time but require the selectionof a regularization parameter, whose value significantly impacts the achievedsolution, and whose automated selection remains an involved and challengingproblem. Conversely, fully Bayesian formalisms encapsulate the regularizationparameter selection into hierarchical models, at the price of highcomputational costs. This contribution proposes an operational strategy thatcombines hierarchical Bayesian and Potts model formulations, with the doubleaim of automatically tuning the regularization parameter and of maintainingcomputational effciency. The proposed procedure relies on formally connecting aBayesian framework to a l2-Potts functional. Behaviors and performance for theproposed piecewise constant denoising and regularization parameter tuningtechniques are studied qualitatively and assessed quantitatively, and shown tocompare favorably against those of a fully Bayesian hierarchical procedure,both in accuracy and in computational load.
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