Local Strong Homogeneity of a Regularized Estimator

This paper deals with regularized pointwise estimation of discrete signals which contain large strongly homogeneous zones, where typically they are constant, or linear, or more generally satisfy a linear equation. The estimate is defined as the minimizer of an objective function combining a quadratic data-fidelity term and a regularization prior term. The latter term is the sum of the values obtained by applying a potential function (PF) to each component, called a difference, of a linear transform of the signal. Minimizers of functions of this form arise in various settings in statistics and optimization.The features exhibited by such an estimate are closely related to the shape of the PF. Our goal is to determine estimators providing solutions which involve large strongly homogeneous zones--where more precisely the differences are null--in spite of the noise corrupting the data. To this end, we require that the strongly homogeneous zones, recovered by the estimator, be insensitive to any variation of th...

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