Total variation based image restoration with free local constraints

Abstract

A new total variation based approach was developed by Rudin, Osher and Fatemi (see Physica D., vol.60, p.259, 1992) to overcome the basic limitations of all smooth regularization algorithms. The TV-based technique use the L/sup 1/ norm of the magnitude of a gradient, thus making discontinuous and nonsmooth solutions possible. In TV image restoration, the solution is obtained by solving a time-dependent, nonlinear PDE on a manifold that satisfies the degradation constraints. In practical applications, one assumes a space-varying blurring kernel and signal-dependent (e.g. multiplicative) noise. The evolution part of the TV-based PDE turned out to be related to the curve shortening equation, but scaled by an inverse.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>