NDLI: A New Riemannian Averaged Fixed-Point Algorithm for MGGD Parameter Estimation

Content Provider	IEEE Xplore Digital Library
Author	Boukouvalas, Z. Said, S. Bombrun, L. Berthoumieu, Y. Adali, T.
Copyright Year	1994
Abstract	Multivariate generalized Gaussian distribution (MGGD) has been an attractive solution to many signal processing problems due to its simple yet flexible parametric form, which requires the estimation of only a few parameters, i.e., the scatter matrix and the shape parameter. Existing fixed-point (FP) algorithms provide an easy to implement method for estimating the scatter matrix, but are known to fail, giving highly inaccurate results, when the value of the shape parameter increases. Since many applications require flexible estimation of the shape parameter, we propose a new FP algorithm, Riemannian averaged FP (RA-FP), which can effectively estimate the scatter matrix for any value of the shape parameter. We provide the mathematical justification of the convergence of the RA-FP algorithm based on the Riemannian geometry of the space of symmetric positive definite matrices. We also show using numerical simulations that the RA-FP algorithm is invariant to the initialization of the scatter matrix and provides significantly improved performance over existing FP and method-of-moments (MoM) algorithms for the estimation of the scatter matrix.
Sponsorship	IEEE Signal Processing Society
Starting Page	2314
Ending Page	2318
Page Count	5
File Size	805889
File Format	PDF
ISSN	10709908
Volume Number	22
Issue Number	12
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2015-01-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Signal processing algorithms Symmetric matrices Method of moments Maximum likelihood estimation Shape Terrorism symmetric positive definite matrix Fixed-point algorithm maximum likelihood estimation multivariate generalized Gaussian distribution Riemannian geometry
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Signal Processing Electrical and Electronic Engineering

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

Parameter Estimation For Multivariate Generalized Gaussian Distributions

Fixed Point Algorithms for Estimating Power Means of Positive Definite Matrices

A Fixed-Point Algorithm for Estimating Power Means of Positive Definite Matrices

A Fixed-Point Algorithm for Estimating Power Means of Positive Definite Matrices

An exact forward-backward maximum likelihood autoregressive parameter estimation method

Cramér-Rao Lower Bounds on Covariance Matrix Estimation for Complex Elliptically Symmetric Distributions

On Kronecker and Linearly Structured Covariance Matrix Estimation

Exact Maximum Likelihood Estimates for SIRV Covariance Matrix: Existence and Algorithm Analysis

On local maxima of the likelihood function for Toeplitz matrix estimation

A New Riemannian Averaged Fixed-Point Algorithm for MGGD Parameter Estimation

Similar Documents

Parameter Estimation For Multivariate Generalized Gaussian Distributions

Fixed Point Algorithms for Estimating Power Means of Positive Definite Matrices

A Fixed-Point Algorithm for Estimating Power Means of Positive Definite Matrices

A Fixed-Point Algorithm for Estimating Power Means of Positive Definite Matrices

An exact forward-backward maximum likelihood autoregressive parameter estimation method

Cramér-Rao Lower Bounds on Covariance Matrix Estimation for Complex Elliptically Symmetric Distributions

On Kronecker and Linearly Structured Covariance Matrix Estimation

Exact Maximum Likelihood Estimates for SIRV Covariance Matrix: Existence and Algorithm Analysis

On local maxima of the likelihood function for Toeplitz matrix estimation

A New Riemannian Averaged Fixed-Point Algorithm for MGGD Parameter Estimation