Image recovery and recognition: a combining method of matrix norm regularisation

摘要

The technology of image recovery, as a part of image processing, becomes more and more important. The robust principle component analysis (RPCA) serves as a key problem for low-rank matrix recovery. However, the existing methods for solving the RPCA are mostly based on nuclear norm minimisation. These methods have the disadvantage that matrix's rank cannot be well approximated because they minimise all singular values. Moreover, these methods will lead to instability when images are highly correlated. In this study, the authors set up a novel model which combines the truncated nuclear norm with Frobenius norm to enhance solution accuracy and stability. Based on the idea of elastic-net, which is composed of $l_1$l1 norm and $l_2$l2 norm, this model is based on elastic-net of the singular values can be composed of the truncated nuclear norm and the square of Frobenius norm. In order to solve this problem, the TNNF algorithm was proposed based on the alternating direction method of multipliers. Compared with traditional methods, the numerical simulation results show that the proposed TNNF can achieve higher accuracy and better stability.