Original ArticleRMP: Reduced-set matching pursuit approach for efficient compressed sensing signal reconstruction

Compressed sensing enables the acquisition of sparse signals at a rate that is much lower than the Nyquist rate. Compressed sensing initially adopted ℓ1 minimization for signal reconstruction which is computationally expensive. Several greedy recovery algorithms have been recently proposed for signal reconstruction at a lower computational complexity compared to the optimal ℓ1 minimization, while maintaining a good reconstruction accuracy. In this paper, the Reduced-set Matching Pursuit (RMP) greedy recovery algorithm is proposed for compressed sensing. Unlike existing approaches which either select too many or too few values per iteration, RMP aims at selecting the most sufficient number of correlation values per iteration, which improves both the reconstruction time and error. Furthermore, RMP prunes the estimated signal, and hence, excludes the incorrectly selected values. The RMP algorithm achieves a higher reconstruction accuracy at a significantly low computational complexity compared to existing greedy recovery algorithms. It is even superior to ℓ1 minimization in terms of the normalized time-error product, a new metric introduced to measure the trade-off between the reconstruction time and error. RMP superior performance is illustrated with both noiseless and noisy samples.