Locally strongly homogeneous estimates

This Note concerns regularized estimation of signals comprising strongly homogeneous zones - e.g., locally constant, locally linear, etc. The estimate, defined in the MAP sense, is the minimizer of an energy which combines a quadratic data-fidelity term and a regularization prior term. Our main result is that strongly homogeneous zones are both recovered and locally conserved by the estimator, i.e. that they remain unchanged for data varying in a neighbourhood, if and only if the regularization function is nonsmooth over these zones.