Efficiency of orthogonal super greedy algorithm under the restricted isometry property

Abstract

We investigate the efficiency of orthogonal super greedy algorithm (OSGA) for sparse recovery and approximation under the restricted isometry property (RIP). We first show that under the RIP conditions of the measurement matrix Φ and the minimum magnitude of the nonzero coordinates of the signal, for l 2 bounded or l ∞ bounded noise vector e, with explicit stopping rules, OSGA can recover the support of an arbitrary K-sparse signal x from y = Φx + e in at most K steps. Then, we investigate the error performance of OSGA in m term approximation with regards to dictionaries satisfying the RIP in a separable Hilbert space. We establish a Lebesgue-type inequality for OSGA. Based on this inequality, we obtain the optimal rate of convergence for the sparse class induced by such dictionaries.

A Sparse Recovery Algorithm Based on Arithmetic Optimization

“…In this section, we experimentally investigate the performance of the proposed algorithm and compare it with the basis pursuit algorithm (BP) [27,28], a typical algorithm in convex optimization, and the orthogonal matching tracking algorithm (OMP) [29,30], a typical algorithm in greedy algorithms. The experimental data in this paper comes from the bearing database of Case Western Reserve University, the object of this experiment is deep groove ball bearing, the sensors are installed in the drive end and fan end respectively for fault data collection, SKF620 is the drive end bearing, SKF6203 is the fan end bearing.…”