Families of Heron Digital Filters for Images Filtering

The basic idea behind this work is in extraction (estimation) of the uncorrupted image from the distorted or noised one. The idea is also referred to as the image denoising. Noise removal or noise reduction in an image can be done by linear or nonlinear filtering. The most popular linear technique is based on averaging (or meaning) linear operators. Usually, denoising via linear filters does not work sufficiently since both the noise and edges (in the image) contain high frequencies. Therefore, any practical denoising model has to be nonlinear. In this paper, we propose two new nonlinear data-dependent filters, namely, the generalized mean and median Heronian ones. These filters are based on the Heronian means and medians that are used for developing a new theoretical framework for image filtering. The main goal of the work is to show that new elaborated filters can be applied to solve problems of image filtering in a natural and effective manner.