Non-local means (NLM) filtering has been shown to outperform alternative denoising methodologies under the model of additive white Gaussian noise contamination. Recently, several theoretical frameworks have been developed to extend this class of algorithms to more general types of noise statistics. However, many of these frameworks are specifically designed for a single noise contamination model, and are far from optimal across varying noise statistics. The NLM filtering techniques rely on the definition of a similarity measure, which quantifies the similarity of two neighbourhoods along with their respective centroids. The key to the unification of the NLM filter for different noise statistics lies in the definition of a universal similarity measure which is guaranteed to provide favourable performance irrespective of the statistics of the noise. Accordingly, the main contribution of this work is to provide a rigorous statistical framework to derive such a universal similarity measure, while highlighting some of its theoretical and practical favourable characteristics. Additionally, the closed form expressions of the proposed similarity measure are provided for a number of important noise scenarios and the practical utility of the proposed similarity measure is demonstrated through numerical experiments.

Date Published: 25 February 2014
PDF: 10 pages
Proc. SPIE 9019, Image Processing: Algorithms and Systems XII, 90190B (25 February 2014); doi: 10.1117/12.2042396

Published in SPIE Proceedings Vol. 9019:
Image Processing: Algorithms and Systems XII
Karen O. Egiazarian; Sos S. Agaian; Atanas P. Gotchev, Editor(s)