Abstract—Sparse representation of signals over overcomplete dictionaries shows state-of-art results in lots of applications. Though the problem is NP-hard, approximate solutions are proposed based on a wide variety of techniques. In this paper, we propose a method over a learned dictionary based on nonparametric methods for this problem. The structure follows the two steps of normal dictionary learning procedure. In one step we fix the dictionary and learn the sparse coefficient vector based on Bayesian nonparametric variable selection, while in the other step we minimize the objective based on the dictionary with the coefficient vector fixed by matrix-inversion free procedure.

Index Terms—Sparse representation, nonparametric methods, dictionary learning.

The authors are with College of Computer Science and Technology, Zhejiang University, Hangzhou, China, and with Zhejiang Zhejiang Financial College, Hangzhou, China (e-mail: heheyan@126.com,dhwang@zju.edu.cn, zhum@zju.edu.cn).

Cite: Yan He, Donghui Wang, and Miaoliang Zhu, "Sparse Representation Over Overcomplete Dictionary Based on Bayesian Nonparametric Approximation," International Journal of Computer and Electrical Engineering vol. 4, no. 4, pp. 546-549, 2012.