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In this paper, we present new results on using orthogonal matching pursuit(OMP), to solve the sparse approximation problem over redundant dictionariesfor complex cases (i.e., complex measurement vector, complex dictionary andcomplex additive white Gaussian noise (CAWGN)). A sufficient condition that OMPcan recover the optimal representation of an exactly sparse signal in thecomplex cases is proposed both in noiseless and bound Gaussian noise settings.Similar to exact recovery condition (ERC) results in real cases, we extend themto complex case and derivate the corresponding ERC in the paper. It leveragesthis theory to show that OMP succeed for k-sparse signal from a class ofcomplex dictionary. Besides, an application with geometrical theory ofdiffraction (GTD) model is presented for complex cases. Finally, simulationexperiments illustrate the validity of the theoretical analysis.

Complex Orthogonal Matching Pursuit and Its Exact Recovery Conditions