Matrix recovery from nonconvex regularized least absolute deviations

In this paper, we consider the low-rank matrix recovery problem. We propose the nonconvex regularized least absolute deviations model via $\ell_1-\alpha\ell_2 \ (0<\alpha<1)$ minimization. We establish the theoretical analysis of the proposed model and obtain a stable error estimation. Our result is a nontrivial extension of some previous work. Different from most of the state-of-the-art methods, our method does not need any knowledge of standard deviation or any moment assumption of the noise. Numerical experiments show that our method is effective for many types of noise distributions.