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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 dictionaries for complex cases (i.e., complex measurement vector, complex dictionary and complex additive white Gaussian noise (CAWGN)). A sufficient condition that OMP can recover the optimal representation of an exactly sparse signal in the complex cases is proposed both in noiseless and bound Gaussian noise settings. Similar to exact recovery condition (ERC) results in real cases, we extend them to complex case and derivate the corresponding ERC in the paper. It leverages this theory to show that OMP succeed for k-sparse signal from a class of complex dictionary. Besides, an application with geometrical theory of diffraction (GTD) model is presented for complex cases. Finally, simulation experiments illustrate the validity of the theoretical analysis.
The orthogonal matching pursuit (OMP) algorithm is a commonly used algorithm for recovering $K$-sparse signals $xin mathbb{R}^{n}$ from linear model $y=Ax$, where $Ain mathbb{R}^{mtimes n}$ is a sensing matrix. A fundamental question in the performan
Exact recovery of $K$-sparse signals $x in mathbb{R}^{n}$ from linear measurements $y=Ax$, where $Ain mathbb{R}^{mtimes n}$ is a sensing matrix, arises from many applications. The orthogonal matching pursuit (OMP) algorithm is widely used for reconst
Greed is good. However, the tighter you squeeze, the less you have. In this paper, a less greedy algorithm for sparse signal reconstruction in compressive sensing, named orthogonal matching pursuit with thresholding is studied. Using the global 2-coh
Recovery algorithms play a key role in compressive sampling (CS). Most of current CS recovery algorithms are originally designed for one-dimensional (1D) signal, while many practical signals are two-dimensional (2D). By utilizing 2D separable samplin
In this paper, we put forth a new joint sparse recovery algorithm called signal space matching pursuit (SSMP). The key idea of the proposed SSMP algorithm is to sequentially investigate the support of jointly sparse vectors to minimize the subspace d