Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: An augmented Lagrangian multi-scale dictionary learning algorithm | Liu et al. EURASIP Journal on Advances in Signal Processing 2011 2011 58 http content 2011 1 58 o EURASIP Journal on Advances in Signal Processing a SpringerOpen Journal RESEARCH Open Access An augmented Lagrangian multi-scale dictionary learning algorithm Qiegen Liu 1 Jianhua Luo1 Shanshan Wang1 Moyan Xiao1 and Meng Ye2 Abstract Learning overcomplete dictionaries for sparse signal representation has become a hot topic fascinated by many researchers in the recent years while most of the existing approaches have a serious problem that they always lead to local minima. In this article we present a novel augmented Lagrangian multi-scale dictionary learning algorithm ALM-DL which is achieved by first recasting the constrained dictionary learning problem into an AL scheme and then updating the dictionary after each inner iteration of the scheme during which majorizationminimization technique is employed for solving the inner subproblem. Refining the dictionary from low scale to high makes the proposed method less dependent on the initial dictionary hence avoiding local optima. Numerical tests for synthetic data and denoising applications on real images demonstrate the superior performance of the proposed approach. Keywords dictionary learning augmented Lagrangian multi-scale refinement image denoising. 1. Introduction In the last two decades more and more studies have focused on dictionary learning the goal of which is to model signals as a sparse linear combination of atoms that form a dictionary below a certain error toleration. Sparse representation of signals under the learned dictionary possesses significant advantages over the prespecified dictionary such as wavelet and discrete cosine transform DCT as demonstrated in many literatures 1-3 and it has been widely used in denoising inpainting and classification areas with state-of-the-art results obtained 1-5 . Considering there is a signal bl eRM it can be represented by a linear combination
