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In this paper, an efficient sparse recovery algorithm called random refined orthogonal matching pursuit (RROMP) is proposed for signal denoising. Given a noisy signal, the RROMP algorithm first generates several sparse representations of it by applying a multi-selection strategy and a false discovery rate (FDR) control, instead of seeking the sparsest one. The multi-selection strategy accelerates the whole process of generating the representations, while the FDR control enables each representation to be competitive. Then the generated representations are averaged to form a more accurate estimate in the sense of mean-square-error (MSE). Our experiments on both synthetically generated signals and natural images demonstrate the superiority of the RROMP algorithm.