Nonsingular approximations for a singular covariance matrix

Nir Gorelik, Dan Blumberg, Stanley Rotman, D. Borghys

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

3 Scopus citations

Abstract

Accurate covariance matrix estimation for high dimensional data can be a difficult problem. A good approximation of the covariance matrix needs in most cases a prohibitively large number of pixels, i.e. pixels from a stationary section of the image whose number is greater than several times the number of bands. Estimating the covariance matrix with a number of pixels that is on the order of the number of bands or less will cause, not only a bad estimation of the covariance matrix, but also a singular covariance matrix which cannot be inverted. In this article we will investigate two methods to give a sufficient approximation for the covariance matrix while only using a small number of neighboring pixels. The first is the Quasilocal Covariance Matrix (QLRX) that uses the variance of the global covariance instead of the variances that are too small and cause a singular covariance. The second method is Sparse Matrix Transform (SMT) that performs a set of K Givens rotations to estimate the covariance matrix. We will compare results from target acquisition that are based on both of these methods.

Original languageEnglish
Title of host publicationAlgorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery XVIII
PublisherSPIE
ISBN (Print)9780819490681
DOIs
StatePublished - 1 Jan 2012
Event18th Annual Conference on Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery - Baltimore, MD, United States
Duration: 23 Apr 201227 Apr 2012

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
Volume8390
ISSN (Print)0277-786X
ISSN (Electronic)1996-756X

Conference

Conference18th Annual Conference on Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery
Country/TerritoryUnited States
CityBaltimore, MD
Period23/04/1227/04/12

Keywords

  • Covariance
  • Hyperspectral
  • QLRX
  • SMT
  • Target detection

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