Abstract-As an extension of orthogonal matching pursuit (OMP) improving the recovery performance of sparse signals, generalized OMP (gOMP) has recently been studied in the literature. In this paper, we present a new analysis of the gOMP algorithm using restricted isometry property (RIP). We show that if the measurement matrix Φ ∈ R m×n satisfies the RIP withthen gOMP performs stable reconstruction of all K-sparse signals x ∈ R n from the noisy measurements y = Φx + v within max K, ), especially for large K.

Abstract-In this paper, we propose an algorithm referred to as multipath matching pursuit (MMP) that investigates multiple promising candidates to recover sparse signals from compressed measurements. Our method is inspired by the fact that the problem to find the candidate that minimizes the residual is readily modeled as a combinatoric tree search problem and the greedy search strategy is a good fit for solving this problem. In the empirical results as well as the restricted isometry property (RIP) based performance guarantee, we show that the proposed MMP algorithm is effective in reconstructing original sparse signals for both noiseless and noisy scenarios.Index Terms-Compressive sensing (CS), sparse signal recovery, orthogonal matching pursuit, greedy algorithm, restricted isometry property (RIP), Oracle estimator.

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