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.
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