Open Systems & Information Dynamics
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We present a class of nonlinear adaptive image restoration filters which may be steered to preserve sharp edges and contrasts in the restorations. From a theoretical point of view we discuss the associated variational problems and prove existence of solutions in certain Sobolev spaces W1,p or in a BV-space. The degree of regularity of the solution may be understood as a mathematical explanation of the heuristic properties of the designed filters.