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

Abstract

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, co...