Local Sorting for Adaptive Signal Regularization

This letter investigates the possibility of removing noise in correspondence to jump discontinuities using the sorted copy of the signal. It will be proved that sorting makes noise predictable so that it can be reproduced and subtracted from the sorted noisy signal. It will be also shown that the proposed method can substitute for the edge preserving term into an anisotropic diffusion scheme, gaining in terms of mean square error, edge preservation and computational effort.