NDLI: Estimation of hyperspectral covariance matrices

Content Provider	IEEE Xplore Digital Library
Author	Ben-David, A. Davidson, C.E.
Copyright Year	2011
Description	Author affiliation: Edgewood Chemical Biological Center, Research, Development, and Engineering Command, Aberdeen Proving Ground, Maryland, USA (Ben-David, A.) \|\| Science and Technology Corporation, Edgewood, Maryland, USA (Davidson, C.E.)
Abstract	Estimation of covariance matrices is a fundamental step in hyperspectral remote sensing where most detection algorithms make use of the covariance matrix in whitening procedures. We present a simple method to improve the estimation of the eigenvalues of a sample covariance matrix. With the improved eigenvalues we construct an improved covariance matrix. Our method is based on the Marcenko-Pastur law, theory of eigenvalue bounds, and energy conservation. Our objective is to add a new method for estimating the eigenvalues of Wishart covariance matrices in scenarios where the sample size is small. Our method is simple, practical and easy to implement (it consists of a multiplication of 3 matrices). We did our study with extensive simulations and a few examples of hyperspectral remote sensing data that were measured in the long infrared wavelength region (8–12µm). We show examples of the improved eigenvalues over the sampled eigenvalues. We choose the following five figures-of-merit for evaluating our method as ratios of properties between sampled data and our solution: (i) residual (rms) that gives the improvement of the solution over the sampled data with respect to the population eigenvalues, (ii) area under the scree-plot, (iii) condition number that gives the improvement in the stability (regularization), (iv) a distance-measure that gives the average statistical improvement between the improved and the sampled eigenvalues, and (v) Kullback-Leibler distance. We show hyperspectral matched-filter detection performance (ROC curves) for TELOPS data where we use our improved covariance matrix. We compare the improved ROC to the one that are obtained with sampled (data) covariance matrix.
Starting Page	1
Ending Page	4
File Size	320173
Page Count	4
File Format	PDF
ISBN	9781467302159
ISSN	15505219
e-ISBN	9781467302166
DOI	10.1109/AIPR.2011.6176368
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2011-10-11
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Eigenvalues and eigenfunctions Covariance matrix Hyperspectral imaging Estimation Energy conservation regularization covariance matrices eigenvalues and eigenfunctions hyperspectral detection and signal processing algorithms
Content Type	Text
Resource Type	Article

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

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