Journal
IEEE TRANSACTIONS ON SIGNAL PROCESSING
Volume 62, Issue 9, Pages 2317-2329Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSP.2014.2309076
Keywords
Convergence; iterative half thresholding algorithm; L-q/L-1/2 regularization; nonconvex regularization
Categories
Funding
- National 973 Programs [2013CB329404, 2010CB731905]
- Key Program of National Natural Science Foundation of China [11131006]
- National Natural Science Foundations of China [61075054, 11001227, 11171272]
- Southwest China Institute of Electronic Techonology
Ask authors/readers for more resources
In recent studies on sparse modeling, the nonconvex regularization approaches (particularly, L-q regularization with q is an element of (0 ,1)) have been demonstrated to possess capability of gaining much benefit in sparsity-inducing and efficiency. As compared with the convex regularization approaches (say, L-1 regularization), however, the convergence issue of the corresponding algorithms are more difficult to tackle. In this paper, we deal with this difficult issue for a specific but typical nonconvex regularization scheme, the L-1/2 regularization, which has been successfully used to many applications. More specifically, we study the convergence of the iterative half thresholding algorithm (the half algorithm for short), one of the most efficient and important algorithms for solution to the L-1/2 regularization. As the main result, we show that under certain conditions, the half algorithm converges to a local minimizer of the L-1/2 regularization, with an eventually linear convergence rate. The established result provides a theoretical guarantee for a wide range of applications of the half algorithm. We provide also a set of simulations to support the correctness of theoretical assertions and compare the time efficiency of the half algorithm with other known typical algorithms for L-1/2 regularization like the iteratively reweighted least squares (IRLS) algorithm and the iteratively reweighted l(1) minimization (IRL1) algorithm.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available