Why Sparse? Fuzzy Techniques Explain Empirical Efficiency of Sparsity-Based Data- and Image-Processing Algorithms

Authors

Fernando Cervantes, The University of Texas at El PasoFollow
Bryan E. Usevitch, The University of Texas at El PasoFollow
Leobardo Valera, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

4-2016

Comments

Technical Report: UTEP-CS-16-11a

To appear in Proceedings of the 2016 World Conference on Soft Computing, Berkeley, California, May 22-25, 2016.

Abstract

In many practical applications, it turned out to be efficient to assume that the signal or an image is sparse, i.e., that when we decompose it into appropriate basic functions (e.g., sinusoids or wavelets), most of the coefficients in this decomposition will be zeros. At present, the empirical efficiency of sparsity-based techniques remains somewhat a mystery. In this paper, we show that fuzzy-related techniques can explain this empirical efficiency. A similar explanation can be obtained by using probabilistic techniques; this fact increases our confidence that our explanation is correct.