Robust signal analysis based on the L-statistic was introduced for signals disturbed with high additive impulse noise. The basic idea is that a certain, usually large number of arbitrary positioned signal samples is declared as heavily corrupted by noise. Then, these samples are removed. Thus, they can be considered as absent or unavailable. Hence, the L-statistics significantly reduces the number of available signal samples. Moreover these samples are randomly distributed, so an efficient analysis of such signals invokes the compressive sensing reconstruction algorithms. Also, it will be shown that the variance of noise, produced by missing samples, can be used as powerful tool for signal reconstruction. Additionally, in order to provide separation of stationary and nonstationary signals the L-statistic is combined with compressive sensing algorithms. The theoretical considerations are verified by various examples, where discrete forms of the Fourier transform and short-time Fourier transform are used to demonstrate the effective integration of the two techniques.

Date Published: 31 May 2013
PDF: 7 pages
Proc. SPIE 8717, Compressive Sensing II, 87170O (31 May 2013); doi: 10.1117/12.2015908

Published in SPIE Proceedings Vol. 8717:
Compressive Sensing II
Fauzia Ahmad, Editor(s)