Time-Scale Similarities for Robust Image De-noising

This paper presents a novel image denoising algorithm, namely Atomic Non Local Means (ANL-means), that looks for similarities in the time-scale domain. To this aim, wavelet details are approximated by linear combinations of predefined atoms, whose centers of mass trace trajectories in the time-scale plane (from fine to coarse scales). These trajectories depend on the mutual distance between not isolated singularities, their different decay along scales and their amplitude ratio. These three parameters have proved to be useful in catching image self-similarities and in the implementation of a robust NL-means based denoising algorithm. ANL-means is able to reach and often outperform the most powerful and recent NL-means based de-noising schemes in terms of both mean square error and visual quality.