Missing Low-Rank and Sparse Decomposition Based on Smoothed Nuclear Norm

摘要

Recovering low-rank and sparse components from missing observations is an essential problem in various fields. In this paper, we have proposed a method to address the missing low-rank and sparse decomposition problem. We have used the smoothed nuclear norm and the L-1 norm to impose the low-rankness and sparsity constraints on the components, respectively. Furthermore, we have suggested a linear modeling for the corrupted observations. The problem has been solved with the aid of alternating minimization. Moreover, some simplifications have been applied to the relations to reduce the computational complexity, which makes the algorithm suitable for large-scale problems. To evaluate the proposed method, different simulation scenarios have been devised. The superiority of the suggested scheme over its counterparts has been confirmed on both the recovery accuracy and the convergence speed in various applications.