Qun Wan

Qingshan You, Qun Wan, Yipeng Liu

In this paper, we address strongly convex programming for princi- pal component pursuit with reduced linear measurements, which decomposes a superposition of a low-rank matrix and a sparse matrix from a small set of linear measurements. We first provide sufficient conditions under which the strongly convex models lead to the exact low-rank and sparse matrix recov- ery; Second, we also give suggestions on how to choose suitable parameters in practical algorithms.

Ruiming Yang, Qun Wan, Yipeng Liu et al.

The feasibility of sparse signal reconstruction depends heavily on the inter-atom interference of redundant dictionary. In this paper, a semi-blindly weighted minimum variance distortionless response (SBWMVDR) is proposed to mitigate the inter-atom interference. Examples of direction of arrival estimation are presented to show that the orthogonal match pursuit (OMP) based on SBWMVDR performs better than the ordinary OMP algorithm.

Yipeng Liu, Qun Wan, Fei Wen et al.

Compressive sensing (CS) is a technique for estimating a sparse signal from the random measurements and the measurement matrix. Traditional sparse signal recovery methods have seriously degeneration with the measurement matrix uncertainty (MMU). Here the MMU is modeled as a bounded additive error. An anti-uncertainty constraint in the form of a mixed L2 and L1 norm is deduced from the sparse signal model with MMU. Then we combine the sparse constraint with the anti-uncertainty constraint to get an anti-uncertainty sparse signal recovery operator. Numerical simulations demonstrate that the proposed operator has a better reconstructing performance with the MMU than traditional methods.

Yipeng Liu, Qun Wan, Fei Wen et al.

Sparse support recovery (SSR) is an important part of the compressive sensing (CS). Most of the current SSR methods are with the full information measurements. But in practice the amplitude part of the measurements may be seriously destroyed. The corrupted measurements mismatch the current SSR algorithms, which leads to serious performance degeneration. This paper considers the problem of SSR with only phase information. In the proposed method, the minimization of the l1 norm of the estimated sparse signal enforces sparse distribution, while a nonzero constraint of the uncorrupted random measurements' amplitudes with respect to the reconstructed sparse signal is introduced. Because it only requires the phase components of the measurements in the constraint, it can avoid the performance deterioration by corrupted amplitude components. Simulations demonstrate that the proposed phase-only SSR is superior in the support reconstruction accuracy when the amplitude components of the measurements are contaminated.

Rong Fan, Qun Wan, Yipeng Liu et al.

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.