Regularization of textured image decomposition via a geometric constraint

This paper describes a practical implementation of the decomposition of an image f into a sum of a cartoon component and an oscillating component consisting of texture and/or noise. Vese and Osher's decomposition is implemented in their paper with a semi-implicit fixed-point iterative finite difference scheme, and not a straight-forward non-iterative vectorisable scheme due to lack of stability of the latter. In this paper, we propose the addition of another term to their energy functional, which roughly speaking, penalizes cartoon boundaries which are situated within any given texture. Experiments with this new term indicate increased stability over Vese and Osher's model, as well as a modest increase in speed