NDLI: A multidimensional shrinkage-thresholding operator

Content Provider	IEEE Xplore Digital Library
Author	Puig, A.T. Wiesel, A. Hero, A.O.
Copyright Year	2009
Description	Author affiliation: University of Michigan - Department of Electrical Engineering, 1301 Beal Avenue Ann Arbor, 48109-2122, USA (Puig, A.T.; Wiesel, A.; Hero, A.O.)
Abstract	The scalar shrinkage-thresholding operator (SSTO) is a key ingredient of many modern statistical signal processing algorithms including: sparse inverse problem solutions, wavelet denoising, and JPEG2000 image compression. In these applications, it is customary to select the threshold of the operator by solving a scalar sparsity penalized quadratic optimization. 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 penalty, however, here the optimization is performed over a domain of dimension N ≥ 1. The solution to this convex optimization problem is called the multidimensional shrinkage threshold operator (MSTO). The MSTO reduces to the standard SSTO in the special case of N = 1. In the general case of N ≫ 1 the optimal MSTO threshold can be found by a simple convex line search. We present three illustrative applications of the MSTO in the context of non-linear regression: l-penalized linear regression, Group LASSO linear regression and Group LASSO logistic regression.
Starting Page	113
Ending Page	116
File Size	164991
Page Count	4
File Format	PDF
ISBN	9781424427093
e-ISBN	9781424427116
DOI	10.1109/SSP.2009.5278625
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2009-08-31
Publisher Place	United Kingdom
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Multidimensional systems Linear regression Signal processing algorithms Logistics Multidimensional signal processing Ambient intelligence Inverse problems Noise reduction Transform coding Image coding Group LASSO regression Multidimensional Shrinkage-Thresholding Operator Iterative Group Shrinkage-Thresholding
Content Type	Text
Resource Type	Article

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