Finding needles in noisy haystacks

13 years 4 months ago
Finding needles in noisy haystacks
The theory of compressed sensing shows that samples in the form of random projections are optimal for recovering sparse signals in high-dimensional spaces (i.e., finding needles in haystacks), provided the measurements are noiseless. However, noise is almost always present in applications, and compressed sensing suffers from it. The signal to noise ratio per dimension using random projections is very poor, since sensing energy is equally distributed over all dimensions. Consequently, the ability of compressed sensing to locate sparse components degrades significantly as noise increases. It is possible, in principle, to improve performance by “shaping” the projections to focus sensing energy in proper dimensions. The main question addressed here is, can projections be adaptively shaped to achieve this focusing effect? The answer is yes, and we demonstrate a simple, computationally efficient procedure that does so.
Rui M. Castro, Jarvis Haupt, Robert Nowak, Gil M.
Added 30 May 2010
Updated 30 May 2010
Type Conference
Year 2008
Authors Rui M. Castro, Jarvis Haupt, Robert Nowak, Gil M. Raz
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