On piecewise-quadratic filter for Gaussian noisy image filtering

Image classification according to features or a statistical property relates often to a partition of the image domain space. Such a partition concept used in image filtering suggests that a nonlinear filter with a piecewise property is a suitable candidate. In this paper, we propose a novel kind of nonlinear filter, the piecewise-quadratic (PWQ) filter for Gaussian noisy image filtering, which utilizes the domain partition property in the filter function for various image features. We show that after a proper training of the filter function, such a filter has a good noise smoothing as well as an effective edge/detail-preserving property. Simulations are carried out for natural images and two examples are given for showing the performance of the proposed filter.