Improved nonconvex optimization model for low-rank matrix recovery

LI Ling-zhi(李玲芝)^{1, 2}, ZOU Bei-ji(邹北骥)^{1, 2}, ZHU Cheng-zhang(朱承璋)^{1, 2}

(1. School of Information Science and Engineering, Central South University, Changsha 410083, China;
2. Mobile-Health Key Lab Attached to Education Ministry and China Mobile, Changsha 410083, China)

Abstract:Low-rank matrix recovery is an important problem extensively studied in machine learning, data mining and computer vision communities. A novel method is proposed for low-rank matrix recovery, targeting at higher recovery accuracy and stronger theoretical guarantee. Specifically, the proposed method is based on a nonconvex optimization model, by solving the low-rank matrix which can be recovered from the noisy observation. To solve the model, an effective algorithm is derived by minimizing over the variables alternately. It is proved theoretically that this algorithm has stronger theoretical guarantee than the existing work. In natural image denoising experiments, the proposed method achieves lower recovery error than the two compared methods. The proposed low-rank matrix recovery method is also applied to solve two real-world problems, i.e., removing noise from verification code and removing watermark from images, in which the images recovered by the proposed method are less noisy than those of the two compared methods.

Key words:machine learning; computer vision; matrix recovery; nonconvex optimization