Recovering Low-Rank and Sparse Matrices via Robust Bilateral Factorization

Recovering low-rank and sparse matrices from partial, incomplete or corrupted observations is an important problem in many areas of science and engineering. In this paper, we propose a scalable robust bilateral factorization (RBF) method to recover both structured matrices from missing and grossly corrupted data such as robust matrix completion (RMC), or incomplete and grossly corrupted measurements such as compressive principal component pursuit (CPCP). With the unified framework, we first present two robust trace norm regularized bilateral factorization models for RMC and CPCP problems, which can achieve an orthogonal dictionary and a robust data representation, simultaneously. Then, we apply the alternating direction method of multipliers to efficiently solve the RMC problems. Finally, we provide the convergence analysis of our algorithm, and extend it to address general CPCP problems. Experimental results verified both the efficiency and effectiveness of our RBF method compared with the state-of-the-art methods.