A nonlinear gaussian filter applied to images with discontinuities
Fred Godtliebsen, E. Spj⊘tvoll, James Stephen Marron · Journal of nonparametric statistics · 1997
We focus on a simple nonlinear filter with Gaussian weights for recovering the true underlying scene from images distorted by independent and identically distributed Gaussian noise. In some applications, like magnetic resonance (MR) brain scans, this model for the distortion is re-asonable. Apart from the good performance of this filter, the main advantage is that it is nearly instantaneous in processing time, which allows convenient interactive use. In this paper, we give a statistical justification of the filter by means of a weighted least squares interpretation and a Bayesian motivation. Furthermore, we describe how a smoothing parameter, which controls the degree of smoothness in the image, can be estimated from the observed image. Successful applications to both artificial and MR images are presented.