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Sparse approximation property and stable recovery of sparse signals from noisy measurements
Sparse approximation property noisy measurements Information Theory
2011/9/21
Abstract: In this paper, we introduce a sparse approximation property of order $s$ for a measurement matrix ${\bf A}$: $$\|{\bf x}_s\|_2\le D \|{\bf A}{\bf x}\|_2+ \beta \frac{\sigma_s({\bf x})}{\sqrt...
Measurement Design for Detecting Sparse Signals
Sparse Signals Information Theory Measurement Design
2011/8/31
Abstract: We consider the problem of testing for the presence (or detection) of an unknown sparse signal in additive white noise. Given a fixed measurement budget, much smaller than the dimension of t...
Stable Restoration and Separation of Approximately Sparse Signals
Sparse signal recovery signal restoration signal separation deterministic recovery guarantee,
2011/8/23
Abstract: This paper develops new theory and algorithms to recover signals that are approximately sparse in some general (i.e., basis, frame, over-complete, or in-complete) dictionary but corrupted by...