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Author Puig, A.T. ♦ Wiesel, A. ♦ Fleury, G. ♦ Hero, A.O.
Sponsorship IEEE Signal Processing Society
Source IEEE Xplore Digital Library
Content type Text
Publisher Institute of Electrical and Electronics Engineers, Inc. (IEEE)
File Format PDF
Copyright Year ©1994
Language English
Subject Domain (in DDC) Natural sciences & mathematics ♦ Physics ♦ Electricity & electronics
Subject Keyword Optimization ♦ Signal processing algorithms ♦ Convex functions ♦ Signal processing ♦ Minimization ♦ Estimation ♦ Symmetric matrices ♦ proximity operator ♦ Shrinkage-thresholding operator ♦ group LASSO regression ♦ $\ell_2$ penalized least squares
Abstract The scalar shrinkage-thresholding operator is a key ingredient in variable selection algorithms arising in wavelet denoising, JPEG2000 image compression and predictive analysis of gene microarray data. In these applications, the decision to select a scalar variable is given as the solution to a scalar sparsity penalized quadratic optimization. In some other applications, one seeks to select multidimensional variables. In this work, we present a natural multidimensional extension of the scalar shrinkage thresholding operator. Similarly to the scalar case, the threshold is determined by the minimization of a convex quadratic form plus an Euclidean norm penalty, however, here the optimization is performed over a domain of dimension <i>N</i> ≥ 1. The solution to this convex optimization problem is called the multidimensional shrinkage threshold operator (MSTO). The MSTO reduces to the scalar case in the special case of <i>N</i>=1. In the general case of <i>N</i> >; 1 the optimal MSTO shrinkage can be found through a simple convex line search. We give an efficient algorithm for solving this line search and show that our method to evaluate the MSTO outperforms other state-of-the art optimization approaches. We present several illustrative applications of the MSTO in the context of Group LASSO penalized estimation.
Description Author affiliation :: Signal Process. & Electron. Syst. Dept., E3S - Supelec Syst. Sci., Supélec, France
Author affiliation :: Sch. of Comput. Sci. & Eng., Hebrew Univ. of Jerusalem, Jerusalem, Israel
Author affiliation :: Dept. of Electr. Eng. & Comput. Sci., Univ. of Michigan, Ann Arbor, MI, USA
ISSN 10709908
Education Level UG and PG
Learning Resource Type Article
Publisher Date 2011-06-01
Publisher Place U.S.A.
Rights Holder Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Volume Number 18
Issue Number 6
Size (in Bytes) 912.84 kB
Page Count 4
Starting Page 363
Ending Page 366


Source: IEEE Xplore Digital Library