Stable sparse approximations via nonconvex optimization

We present theoretical results pertaining to the ability of ℓp minimization to recover sparse and compressible signals from incomplete and noisy measurements. In particular, we extend the results of Cand`es, Romberg and Tao [1] to the p < 1 case. Our results indicate that depending on the restricted isometry constants (see, e.g., [2] and [3]) and the noise level, ℓp minimization with certain values of p < 1 provides better theoretical guarantees in terms of stability and robustness than ℓ1 minimization does. This is especially true when the restricted isometry constants are relatively large.

• Type: Conference
• Year: 2008
• Where: ICASSP
• Authors: Rayan Saab, Rick Chartrand, Özgür Yilmaz
• Keywords: ICASSP 2008, Isometry Constants, Restricted Isometry, Signal Processing, ℓp Minimization