An interpolation-fltering method for noise-corrupted images

We develop an interpolation method, that allows image filtering at the same time, for both additive and multiplicative noise. The noise-corrupted image is divided into several subimages, each of them is expanded into a series of uncorrelated coefficients. The basis functions are stochastic matched filters: they are obtained by solving an integral equation whose discrete form is similar to a generalized eigenvalues problem. Next, the Fourier coefficients of the interpolated-filtered subimages are determined according to the uncorrelated variables, and according to the Fourier coefficients of the stochastic matched filters. Finally, the interpolated-filtered image is obtained by reconstruction. In order not to have a blurred image as a result, each subimage is treated differently from the other. So that, this treatment is linear for the subimages and nonlinear for the entire image. Simulations on images containing 256×256 pixels are given for both an additive and a multiplicative noise case