Low-rank Representation Models Based On Matrix Factorization Algorithms And Its Applications

Low-rank representation models based rank minimization method is one of the most important problems in sparse representation and compressed sensing. In this paper, by introducing matrix factorization algorithm and multiple penalty terms, we propose a series of low-rank representation models. We solve the resulting models by an alternating direction method of multipliers and derive their fast algorithm. To investigate the effectiveness of the proposed models, we apply our low-rank representation models to digital image processing applications, including dictionary learning and low-rank representation. Numerical results show that the low-rank representation models are able to preserve salient structures in images. The study in this paper presents a framework of the issues on the relationship between low-rank representation model and matrix factorization algorithm,and it provides guiding references for future research.