Error-Correction for Sparse Support Recovery Algorithms

Consider the compressed sensing setup where support $\mathbf {s}^{\ast}$ of an notation="LaTeX">$m$ -sparse notation="LaTeX">$d$ -dimensional signal {x}$ is to be recovered from notation="LaTeX">$n$ linear measurements with a given algorithm. Suppose that are such algorithm does not guarantee perfect recovery and true features may missed. Can they efficiently retrieved? We address this question through simple error-correction module referred as LiRE. LiRE takes input estimate {s}_{\text {in}}$ , outputs refined {out}}$ . establish sufficient conditions under which guaranteed recover entire support, {out}}\supseteq \mathbf {s}^{\ast} $ These imply, for instance, in high dimension can correct sublinear number errors made by Orthogonal Matching Pursuit (OMP). The computational complexity notation="LaTeX">${\mathcal{O}}(m n d)$ Experimental results random Gaussian design matrices show substantially reduces needed via Compressive Sampling Pursuit, Basis (BP), OMP. Interestingly, adding OMP yields procedure more accurate significantly faster than BP. This observation carries over noisy measurement combination LASSO. Finally, standalone initialization, experiments LiRE’s performance lies between used generically, on top any suboptimal baseline algorithm, improve or operate smaller measurements, at cost relatively small overhead. Alternatively, competitive respect