Proximal Operator Splitting for Multi-Constraint Dictionary Learning

Although the dictionary learning (DL) problem has been extensively studied for about 15 years since the work of Olshausen, the DL problem with multi-constraints on the dictionary atoms has not yet been paid attentions. This paper first explore the DL problem using the newly emergence methods-the proximal splitting methods, such as the iterative shrinkage-thresholding algorithm (ISTA), the fast ISTA (FISTA) and the augmented Lagrange multiplier method (ALMM). Then propose a calculation method, called proximal operator splitting, to split the proximal operator with multi-constraints into several sub-proximal operator. Using this method, the existing proximal splitting methods can be easily extended to deal with the DL problem with multi-constraints. Experiments show that ALMM is a more efficient method than ISTA and FISTA. At last, compare the learned dictionaries of ALMM with the state-of-the-art methods, K-SVD and Majorization. The experimental results show that ALMM outperforms K-SVD and Majorization for correctly chosen constraints.