Statistical Analysis of Multilook Polarimetric Radar Images with the Mellin Transform

DSpace/Manakin Repository

Statistical Analysis of Multilook Polarimetric Radar Images with the Mellin Transform

 

Tweet Share on Facebook
Title: Statistical Analysis of Multilook Polarimetric Radar Images with the Mellin Transform
Author: Anfinsen, Stian Normann
Date: 19-May-2010
Type: Doctoral thesis; Doktorgradsavhandling
Abstract: This thesis presents methods for statistical analysis of the probability distributions used to model multilook polarimetric radar images. The methods are based on a matrix-variate version of Mellin's integral transform. The proposed theoretical framework is referred to as Mellin kind statistics. It is an extension of a theory recently developed for single polarisation amplitude and intensity data to the complex matrix-variate case describing multilook polarimetric images. This generalisation is made possible by the rediscovery of a generalised Mellin transform, which is defined for functions of positive definite Hermitian matrices. The domain makes it suited for application to the distributions used to model the polarimetric covariance and coherency matrix. The analysis tools include the matrix-variate Mellin kind characteristic function, which is defined with the Mellin transform in place of the conventional Fourier transform. Matrix log-moments and matrix log-cumulants are retrieved from this function. The matrix log-cumulants are used in a moment based approach to parameter estimation of the distribution parameters. The estimators make efficient use of all the statistical information in the polarimetric covariance matrix, and are superior to all known alternatives. The matrix log-cumulants are also used to construct the first known goodness-of-fit test for matrix distributions based on the multilook polarimetric product model. The algorithms are interpreted by means of a highly informative graphical visualisation tool displaying a space spanned by certain matrix log-cumulants. It is demonstrated that the matrix-variate Mellin transform is the natural tool for analysing multilook polarimetric radar images. This conclusion is based on the simple and elegant mathematical expressions obtained, the superb statistical properties of developed estimators, as well as the intuitive interpretations offered by the Mellin kind statistics.
Publisher: Universitetet i Tromsø; University of Tromsø
URI: http://hdl.handle.net/10037/2471


File(s) in this item

Files Size Format View Description
thesis_entire.pdf 8.649Mb PDF View/Open Entire thesis in one comprehensive file
paper_3.pdf 1.585Mb PDF View/Open Stian Normann Anfinsen, Anthony Paul Doulgeris and Torbjørn Eltoft: «Goodness-of-Fit Tests for Multilook Polarimetric Radar Data Based on the Mellin Transform», submitted to IEEE Transactions on geoscience and remote sensing. Reprinted with permission
paper_2.pdf 598.9Kb PDF View/Open Stian Normann Anfinsen and Torbjørn Eltoft: «Application of the Matrix-Variate Mellin Transform to Analysis of Polarimetric Radar Images», submitted to IEEE Transactions on geoscience and remote sensing. Reprinted with permission
paper_1.pdf 5.276Mb PDF View/Open Stian Normann Anfinsen, Anthony P. Doulgeris and Torbjørn Eltoft: «Estimation of the Equivalent Number of Looks in Polarimetric Synthetic Aperture Radar Imagery», IEEE transactions on geoscience and remote sensing, Vol. 47, No. 11, November 2009 (http://dx.doi.org/10.1109/TGRS.2009.2019269). Reprinted with permission
thesis.pdf 1.892Mb PDF View/Open Thesis introduction and appendices

The following license file are associated with this item:

This item appears in the following collection(s)

Show full item record

Search Munin




Advanced Search

Browse

Statistics

Help