Two novel models with nuclear norm for robust matrix recovery

Abstract

In this paper, we investigate the low-rank matrix recovery problem from linear observations. Inspired by the matrix Lasso and Dantzig selector, we propose nuclear norm regularized models with two data fitting items: ℓ2-loss function and Dantzig selector. We establish the recovery errors for both constrained and unconstrained models under the matrix restricted isometry property frame. For the unconstrained model, we obtain a tighter error bound compared with the previous study by W. Wang et al. (2021) under certain conditions. Furthermore, we design an effective solving algorithm for the proposed unconstrained model. Our numerical experiments demonstrate that our method outperforms the Lasso and Dantzig selector models.