Evolutionary Signal Enhancement Based on Hölder Regularity Analysis

Abstract

We present an approach for signal enhancement based on the analysis of the local Hölder regularity. The method does not make explicit assumptions on the type of noise or on the global smoothness of the original data, but rather supposes that signal enhancement is equivalent to increasing the Hölder regularity at each point. The problem of finding a signal with prescribed regularity that is as near as possible to the original signal does not admit a closed form solution in general. Attempts have been done previously on an analytical basis for simplified cases [1]. We address here the general problem with the help of an evolutionary algorithm. Our method is well adapted to the case where the signal to be recovered is itself very irregular, e.g. nowhere differentiable with rapidly varying local regularity. In particular, we show an application to SAR image denoising where this technique yields good results compared to other algorithms. The implementation of the evolutionary algorithm has been done using the EASEA (EAsy specification of Evolutionary Algorithms) language.