Title :
Sampling bounds for sparse support recovery in the presence of noise
Author :
Reeves, Galen ; Gastpar, Michael
Author_Institution :
Dept. of Electr. Eng. & Comput. Sci., Univ. of California, Berkeley, CA
Abstract :
It is well known that the support of a sparse signal can be recovered from a small number of random projections. However, in the presence of noise all known sufficient conditions require that the per-sample signal-to-noise ratio (SNR) grows without bound with the dimension of the signal. If the noise is due to quantization of the samples, this means that an unbounded rate per sample is needed. In this paper, it is shown that an unbounded SNR is also a necessary condition for perfect recovery, but any fraction (less than one) of the support can be recovered with bounded SNP. This means that a finite rate per sample is sufficient for partial support recovery. Necessary and sufficient conditions are given for both stochastic and non-stochastic signal models. This problem arises in settings such as compressive sensing, model selection, and signal denoising.
Keywords :
quantisation (signal); signal denoising; stochastic processes; nonstochastic signal models; per-sample signal-to-noise ratio; quantization; signal denoising; sparse signal; sparse support recovery; stochastic signal; unbounded rate per sample; Graphical models; Quantization; Sampling methods; Signal analysis; Signal denoising; Signal to noise ratio; Statistics; Stochastic processes; Stochastic resonance; Sufficient conditions;
Conference_Titel :
Information Theory, 2008. ISIT 2008. IEEE International Symposium on
Conference_Location :
Toronto, ON
Print_ISBN :
978-1-4244-2256-2
Electronic_ISBN :
978-1-4244-2257-9
DOI :
10.1109/ISIT.2008.4595378
