Augmented Lagrangian-Based Sparse Representation Method with Dictionary Updating for Image Deblurring

作者：Liu, Qiegen^*; Liang, Dong; Song, Ying; Luo, Jianhua; Zhu, Yuemin; Li, Wenshu

来源：SIAM Journal on Imaging Sciences, 2013, 6(3): 1689-1718.

DOI：10.1137/110857349

• image restoration
• sparse representation
• dictionary updating
• augmented Lagrangian
• alternating direction method
• modified ISTA

This paper presents an efficient alternating direction method with patch-based dictionary updating, ADMDU-DEB, for sparse representation regularization framework of image deblurring. The main idea of the proposed method is to reformulate the variational problem as a linear equality constrained problem and then minimize its augmented Lagrangian function. The alternating direction method decouples the minimization by alternately iterating the pixel-based regularization and the patch-based sparse representation. Typically, accelerated sparse coding and simple dictionary updating applied in the sparse representation stage enable the whole algorithm to converge at a relatively small number of iterations. Additionally, the approach is readily extended to solve the same kind of variational problem with a nonnegativity constraint. Experimental results on benchmark test images consistently validate the superiority of the proposed approach and demonstrate that it achieves very competitive deblurring performance, compared with state-of-the-art deconvolution algorithms.

• 出版日期2013
• 单位中国科学院深圳先进技术研究院; 浙江理工大学; 上海交通大学; 南昌大学