Conventional direction-of-arrival (DOA) estimators are vulnerable to impulsive noise. In this work, to tackle this issue, a class of weakly convex-inducing penalties is introduced for robust DOA estimation via low-rank matrix approximation, where $\ell_{2,1}$ -norm is adopted as the metric for suppressing the outliers. Two iterative algorithms are developed to construct the noise-free data matrix. To avoid determining the number of sources, the DOAs are estimated by exploiting the special joint diagonalization structure of the constructed signal covariance matrix. Compared with several existing algorithms, the proposed methods enjoy faster computation, similar DOA estimation performance against impulsive noise and requiring no a priori information of the source number. Numerical experiments are included to demonstrate the outlier-resistance of our solutions.

In this letter, a gridless one-bit direction-of-arrival (DOA) estimation approach with one-snapshot is proposed to be robust against the off-grid errors and sign inconsistency because of the one-bit measurements corrupted by additive noise. Different with the existing off-grid DOA estimators, an atomic norm minimization is considered to mitigate the grid mismatch with atoms instead of pre-divided discretized dictionary. Then, the sign inconsistency of one-bit measurements is solved by introducing a linear loss function. The resulting optimization problem is convex and can be equivalent to a semidefinite programming (SDP) problem, which, however, is computational demanding. Therefore, alternating direction multiplier method (ADMM) is employed to speed up the implementation. To avoid the spectrum searching, an effective dual polynomial method is developed with closed-form solution for DOA estimation. Meanwhile, the proposed method does not require a prior information of the number of targets. Simulation results demonstrate the superiority and effectiveness of the proposed method.

A foremost task in frequency diverse array multiple-input multiple-output (FDA-MIMO) radar is to efficiently obtain the target signal in the presence of interferences. In this paper, we employ a novel "low-rank + low-rank + sparse" decomposition model to extract the low-rank desired signal and suppress the jamming signals from both barrage and burst jammers. In the literature, the barrage jamming signals, which are intentionally interfered by enemy jammer radar, are usually assumed Gaussian distributed. However, such assumption is oversimplified to hold in practice as the interferences often exhibit non-Gaussian properties. Those non-Gaussian jamming signals, known as impulsive noise or burst jamming, are involuntarily deviated from friendly radar or other working radio equipment including amplifier saturation and sensor failures, thunderstorms and man-made noise. The estimation performance of the existing estimators, relied crucially on the Gaussian noise assumption, may degrade substantially since the probability density function (PDF) of burst jamming has heavier tails that exceed a few standard deviations than the Gaussian distribution. To capture a more general signal model with burst jamming in practice, both barrage jamming and burst jamming are included and a two-step "Go Decomposition" (GoDec) method via alternating minimization is devised for such mixed jamming signal model, where the a priori rank information is exploited to suppress two kinds of jammers and estimate the desired target. Simulation results verify the robust performance of the devised scheme.

In the problem of image inpainting, one popular approach is based on low-rank matrix completion. Compared with other methods which need to reshape the image into vectors or dividing the image into patches, matrix completion operates on the whole image directly. Therefore, it can preserve latent information of the two-dimensional image. An efficient method for low-rank matrix completion is to employ the matrix factorization technique. However, low-rank matrix factorization-based methods often require a prespecified rank, which is challenging to determine in practice. The proposed method models an image matrix as a summation of a set of rank-one matrices so that it does not require rank information in advance as it can be determined by the algorithm itself via minimizing root mean square error. On that basis, greedy matching pursuit is applied to search for the best rank-one matrix at each iteration. To be robust against impulsive noise, the residual error between the observed and estimated matrices is minimized by ${\mathcal{l_p}}$ -norm with 0<p<2. Then the resultant ${\mathcal{l_p}}$ -norm minimization is solved by the iteratively reweighted least squares method. The proposed model is beneficial for the robustness against outliers, and does not require the rank information. Experimental results verify the effectiveness and higher accuracy of the proposed method with comparison to several state-of-the-art matrix completion-based image inpainting approaches.