Impulse and Mixed Multichannel Denoising Using Statistical Halfspace Depth Functions

Abstract

Although the statistical depth functions have been studied in nonparametric inference for multivariate data for more than a decade, the results of these studies have thus far been mostly theoretical. Out of numerous statistical depth functions, the halfspace depth function behaves very well overall in comparison with various competitors, and is one of the few statistical depth functions for which a small number of algorithms for computation in real Euclidean spaces have been proposed. In this chapter a new approach for removal of impulse and mixed multichannel noise based on a modified version of the only proposed algorithm for higher dimensional computation of the deepest location, i.e. a set of points with maximal halfspace depth, is discussed. A survey of experimental results shows that even in its baseline nonlinear spatial domain form, this filtering method gives excellent results in comparison to currently used state-of-the-art filters in elimination of wide range of powers of impulse and mixed multichannel noise from various benchmark image datasets. Multivariate nature of the implemented algorithm ensures the preservation of spectral correlation between channels and consequently, fine image details. Also, since the presented filter is independent of the source or distribution of the noise, it can be potentially used for removal of other types of multichannel noise.