Resolution Limits of Sparse Coding in High Dimensions

This paper addresses the problem of sparsity pattern detection for unknown ksparse n-dimensional signals observed through m noisy, random linear measurements. Sparsity pattern recovery arises in a number of settings including statistical model selection, pattern detection, and image acquisition. The main results in this paper are necessary and sufficient conditions for asymptotically-reliable sparsity pattern recovery in terms of the dimensions m, n and k as well as the signal-tonoise ratio (SNR) and the minimum-to-average ratio (MAR) of the nonzero entries of the signal. We show that m > 2k log(n - k)/(SNR

• Type: Conference
• Year: 2008
• Where: NIPS
• Authors: Alyson K. Fletcher, Sundeep Rangan, Vivek K. Goyal
• Keywords: Information Technology, NIPS 2008, Sparsity Pattern, Sparsity Pattern Recovery, Sufficient Condition