Beyond Moore-Penrose: Sparse pseudoinverse

Ivan Dokmanic, Mihailo Kolundzija, Martin Vetterli

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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.

Original languageEnglish (US)
Title of host publication2013 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2013 - Proceedings
Pages6526-6530
Number of pages5
DOIs
StatePublished - Oct 18 2013
Externally publishedYes
Event2013 38th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2013 - Vancouver, BC, Canada
Duration: May 26 2013May 31 2013

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
ISSN (Print)1520-6149

Other

Other2013 38th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2013
CountryCanada
CityVancouver, BC
Period5/26/135/31/13

Keywords

  • Efficient computation
  • Moore-Penrose pseudoinverse
  • sparse pseudoinverse

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Electrical and Electronic Engineering

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