Adaptive filtering of multiplicative noise by a new differential method

In this paper, we present a new and original mathematical statement of the filtering problem. We only consider adaptive filtering of an image degraded by a multiplicative noise. The proposed method is stated with an evolution equation of the problem of interest. It achieves an improvement of the efficiency of the well-known iterated Kuan filter. Mainly, it incorporates the local determination of the extent used to estimate the different local statistics, we consider in the differential equation. This estimation is carried out differently according to the nature of the processed pixel. An adapted criteria decides if the pixel belongs either to an edge or to an homogeneous zones, following the idea used in the classical anisotropic methods. Then, the existence and the uniqueness of the solution of our proposed differential equation are shown. Its efficiency is assessed in simulation. The results are compared to the well-known filters in order to confirm the theoretical waitings.