Fast matrix based computation of eigenvalues and the Loewner order in PolSAR data

Allan Aasbjerg Nielsen

doi:10.1109/LGRS.2019.2952202

Fast matrix based computation of eigenvalues and the Loewner order in PolSAR data

Allan Aasbjerg Nielsen

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Abstract

We describe calculation of eigenvalues of 2×2 or3 ×3 Hermitian matrices as used in the analysis of multilook polarimetric SAR data. The eigenvalues are calculated as the roots of quadratic or cubic equations. We also describe pivot based calculation of the Loewner order for partial ordering of differences between such matrices. The methods are well suited for fast matrix oriented computer implementation and the speedup over simpler calculations based on built-in eigenproblem solvers is enormous.

Original language	English
Journal	I E E E Geoscience and Remote Sensing Letters
Volume	17
Issue number	10
Pages (from-to)	1727-1731
ISSN	1545-598X
DOIs	https://doi.org/10.1109/LGRS.2019.2952202
Publication status	Published - 2020

Keywords

Complex covariance matrices
Hermitian matrices
Polarimetric SAR

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10.1109/LGRS.2019.2952202

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abstract = "We describe calculation of eigenvalues of 2×2 or3 ×3 Hermitian matrices as used in the analysis of multilook polarimetric SAR data. The eigenvalues are calculated as the roots of quadratic or cubic equations. We also describe pivot based calculation of the Loewner order for partial ordering of differences between such matrices. The methods are well suited for fast matrix oriented computer implementation and the speedup over simpler calculations based on built-in eigenproblem solvers is enormous. ",

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AB - We describe calculation of eigenvalues of 2×2 or3 ×3 Hermitian matrices as used in the analysis of multilook polarimetric SAR data. The eigenvalues are calculated as the roots of quadratic or cubic equations. We also describe pivot based calculation of the Loewner order for partial ordering of differences between such matrices. The methods are well suited for fast matrix oriented computer implementation and the speedup over simpler calculations based on built-in eigenproblem solvers is enormous.

KW - Complex covariance matrices

KW - Hermitian matrices

KW - Polarimetric SAR

U2 - 10.1109/LGRS.2019.2952202

DO - 10.1109/LGRS.2019.2952202

M3 - Journal article

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JO - I E E E Geoscience and Remote Sensing Letters

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Fast matrix based computation of eigenvalues and the Loewner order in PolSAR data

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