The performance guarantees of generalized orthogonal matching pursuit（ gOMP） are considered in the framework of mutual coherence. The gOMP algorithmis an extension of the well-known OMP greed algorithmfor compressed...The performance guarantees of generalized orthogonal matching pursuit（ gOMP） are considered in the framework of mutual coherence. The gOMP algorithmis an extension of the well-known OMP greed algorithmfor compressed sensing. It identifies multiple N indices per iteration to reconstruct sparse signals.The gOMP with N≥2 can perfectly reconstruct any K-sparse signals frommeasurement y = Φx if K 〈1/N（1/μ-1） ＋1,where μ is coherence parameter of measurement matrix Φ. Furthermore,the performance of the gOMP in the case of y = Φx ＋ e with bounded noise ‖e‖2≤ε is analyzed and the sufficient condition ensuring identification of correct indices of sparse signals via the gOMP is derived,i. e.,K 〈1/N（1/μ-1）＋1-（2ε/Nμxmin） ,where x min denotes the minimummagnitude of the nonzero elements of x. Similarly,the sufficient condition in the case of G aussian noise is also given.展开更多
基金Supported by the National Natural Science Foundation of China(60119944,61331021)the National Key Basic Research Program Founded by MOST(2010C B731902)+1 种基金the Program for Changjiang Scholars and Innovative Research Team in University(IRT1005)Beijing Higher Education Young Elite Teacher Project(YET P1159)
文摘The performance guarantees of generalized orthogonal matching pursuit（ gOMP） are considered in the framework of mutual coherence. The gOMP algorithmis an extension of the well-known OMP greed algorithmfor compressed sensing. It identifies multiple N indices per iteration to reconstruct sparse signals.The gOMP with N≥2 can perfectly reconstruct any K-sparse signals frommeasurement y = Φx if K 〈1/N（1/μ-1） ＋1,where μ is coherence parameter of measurement matrix Φ. Furthermore,the performance of the gOMP in the case of y = Φx ＋ e with bounded noise ‖e‖2≤ε is analyzed and the sufficient condition ensuring identification of correct indices of sparse signals via the gOMP is derived,i. e.,K 〈1/N（1/μ-1）＋1-（2ε/Nμxmin） ,where x min denotes the minimummagnitude of the nonzero elements of x. Similarly,the sufficient condition in the case of G aussian noise is also given.
