NDLI: Beyond Moore-Penrose: Sparse pseudoinverse

Content Provider	IEEE Xplore Digital Library
Author	Dokmanic, I. Kolundzija, M. Vetterli, M.
Copyright Year	2013
Description	Author affiliation: Sch. of Comput. & Commun. Sci., Ecole Polytech. Fed. de Lausanne (EPFL), Lausanne, Switzerland (Dokmanic, I.; Kolundzija, M.; Vetterli, M.)
Abstract	Frequently, we use the Moore-Penrose pseudoinverse (MPP) even in cases when we do not require all of its defining properties. But if the running time and the storage size are critical, we can do better. By discarding some constraints needed for the MPP, we gain freedom to optimize other aspects of the new pseudoinverse. A sparser pseudoinverse reduces the amount of computation and storage. We propose a method to compute a sparse pseudoinverse and show that it offers sizable improvements in speed and storage, with a small loss in the least-squares performance. Differently from previous approaches, we do not attempt to approximate the MPP, but rather to produce an exact but sparse pseudoinverse. In the underdetermined (compressed sensing) scenario we prove that the rescaled sparse pseudoinverse yields an unbiased estimate of the unknown vector, and we demonstrate its potential in iterative sparse recovery algorithms, pointing out directions for future research.
Starting Page	6526
Ending Page	6530
File Size	674832
Page Count	5
File Format	PDF
ISBN	9781479903566
ISSN	15206149
DOI	10.1109/ICASSP.2013.6638923
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2013-05-26
Publisher Place	Canada
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Sparse matrices Signal to noise ratio Iterative methods Covariance matrices Vectors Compressed sensing Signal processing algorithms sparse pseudoinverse Efficient computation Moore-Penrose pseudoinverse
Content Type	Text
Resource Type	Article

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