NDLI: Properness and Widely Linear Processing of Quaternion Random Vectors

Content Provider	IEEE Xplore Digital Library
Author	Vía, J. Ramírez, D. Santamaría, I.
Copyright Year	1963
Abstract	In this paper, the second-order circularity of quaternion random vectors is analyzed. Unlike the case of complex vectors, there exist three different kinds of quaternion properness, which are based on the vanishing of three different complementary covariance matrices. The different kinds of properness have direct implications on the Cayley-Dickson representation of the quaternion vector, and also on several well-known multivariate statistical analysis methods. In particular, the quaternion extensions of the partial least squares (PLS), multiple linear regression (MLR) and canonical correlation analysis (CCA) techniques are analyzed, showing that, in general, the optimal linear processing is full-widely linear. However, in the case of jointly Q-proper or C^η-proper vectors, the optimal processing reduces, respectively, to the conventional or semi-widely linear processing. Finally, a measure for the degree of improperness of a quaternion random vector is proposed, which is based on the Kullback-Leibler divergence between two zero-mean Gaussian distributions, one of them with the actual augmented covariance matrix, and the other with its closest proper version. This measure quantifies the entropy loss due to the improperness of the quaternion vector, and it admits an intuitive geometrical interpretation based on Kullback-Leibler projections onto sets of proper augmented covariance matrices.
Sponsorship	IEEE Information Theory Society
Starting Page	3502
Ending Page	3515
Page Count	14
File Size	441586
File Format	PDF
ISSN	00189448
Volume Number	56
Issue Number	7
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2010-07-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Quaternions Vectors Covariance matrix Statistical analysis Array signal processing Signal processing Least squares methods Linear regression Gaussian distribution Loss measurement widely linear (WL) processing Canonical correlation analysis (CCA) properness propriety quaternions second-order circularity
Content Type	Text
Resource Type	Article
Subject	Library and Information Sciences Information Systems Computer Science Applications

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

Quaternion ICA From Second-Order Statistics

Generalized Likelihood Ratios for Testing the Properness of Quaternion Gaussian Vectors

A Quaternion Widely Linear Adaptive Filter

A Unifying Discussion of Correlation Analysis for Complex Random Vectors

Testing for Quaternion Propriety

Locally Most Powerful Invariant Tests for the Properness of Quaternion Gaussian Vectors

A Quaternion Widely Linear Series Expansion and Its Applications

A Quaternion Widely Linear Model for Nonlinear Gaussian Estimation

Quaternion VAR Modelling and Estimation

Properness and Widely Linear Processing of Quaternion Random Vectors

Similar Documents

Quaternion ICA From Second-Order Statistics

Generalized Likelihood Ratios for Testing the Properness of Quaternion Gaussian Vectors

A Quaternion Widely Linear Adaptive Filter

A Unifying Discussion of Correlation Analysis for Complex Random Vectors

Testing for Quaternion Propriety

Locally Most Powerful Invariant Tests for the Properness of Quaternion Gaussian Vectors

A Quaternion Widely Linear Series Expansion and Its Applications

A Quaternion Widely Linear Model for Nonlinear Gaussian Estimation

Quaternion VAR Modelling and Estimation

Properness and Widely Linear Processing of Quaternion Random Vectors