An integro-differential method for adaptive filtering of additive or multiplicative noise

We present a new adaptive filtering method for either additive noise or multiplicative noise. The proposed method is stated with a differential equation of the temporal evolution of the problem of interest. It achieves an improvement in the efficiency of the well-known iterated Lee filter in the spatial domain. Mainly, it incorporates a local determination of the optimal regions which are subsequently used to estimate the different local statistics involved in the filtering method. This estimation is carried out differently according to the nature of the processed pixel. An adapted decisional criterion indicates if the pixel belongs either to a contour or to a homogeneous zone, following the idea used in classical anisotropic methods. Then, the efficiency of the proposed method, for which we can prove the existence and uniqueness of the solution, is assessed on several images degraded artificially. The results are compared to the main used filters in order to confirm the theoretical findings.