NDLI: Dictionary learning with ℓ1/2 regularizer for sparsity based on proximal operator

Content Provider	IEEE Xplore Digital Library
Author	Zhenni Li Shuxue Ding Yujie Li Wuhui Chen
Copyright Year	2015
Description	Author affiliation: Sch. of Comput. Sci. & Eng., Univ. of Aizu, Aizu-Wakamatsu, Japan (Zhenni Li; Shuxue Ding; Yujie Li; Wuhui Chen)
Abstract	In this study, we propose a fast and efficient algorithm for learning overcomplete dictionary for sparse representation of signals using the nonconvex $ℓ_{1/2}$ regularizer for sparsity. The special importance of $ℓ_{1/2}$ regularizer has been recognized in recent studies on sparse modeling. The $ℓ_{1/2}-norm,$ however, leads to a nonconvex and nonsmooth optimization problem that is difficult to solve efficiently. In this paper, we propose a method based on a decomposition scheme and alternating optimization that can turn the whole problem into a set of subminimizations of univariate functions, each of which is dependent on only one dictionary atom or the coefficient vector. Although the subproblem with respect to the coefficient vector is still nonsmooth and nonconvex due to the $ℓ_{1/2}$ regularizer, remarkably, it becomes much simpler and it has a closed-form solution by introducing a technique that is proximal operator. The main advantages of the proposed algorithm is that, as suggested by the simulation study, it is faster and more efficient than state-of-the-art algorithms with different sparsity constraints.
Starting Page	105
Ending Page	110
File Size	1111956
Page Count	6
File Format	PDF
e-ISBN	9781467376587
DOI	10.1109/ICAwST.2015.7314029
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2015-09-22
Publisher Place	China
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Algorithm design and analysis Dictionaries Closed-form solutions Noise Regularizer ℓ1/2 Cost function Sparse representation Proximal operator Yttrium Alternating optimization Dictionary learning
Content Type	Text
Resource Type	Article

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