Statistical Analysis of Multilook Polarimetric Radar Images with the Mellin Transform
Thesis introduction and appendices (PDF)
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 (PDF)
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 (PDF)
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 (PDF)
Entire thesis in one comprehensive file (PDF)
AuthorAnfinsen, Stian Normann
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.
PublisherUniversitetet i Tromsø
University of Tromsø
The following license file are associated with this item:
Showing items related by title, author, creator and subject.
Doulgeris, Anthony Paul (Doctoral thesis; Doktorgradsavhandling, 2011-02-18)This thesis describes general methods to analyse polarimetric synthetic aperture radar images, with the primary application of unsupervised image segmentation. The fundamental physics of electromagnetic scattering from ...
Interferometric and high time-resolution observations of naturally enhanced ion-acoustic echoes at the EISCAT Svalbard radar: Software radar and incoherent scattering Grydeland, Tom (Doctoral thesis; Doktorgradsavhandling, 2003-06-24)We know that the visible Aurora Borealis is structured on many different scales, down to a few tens of metres. By using the EISCAT radars on Svalbard as an interferometer, we have found structures in the radio echoes from ...
On the Generalized Curvature Ocean Surface Scattering Model for the NRCS and Doppler Frequency and its application to ocean surface wind retrieval from Synthetic Aperture Radar data Said, Faozi (Doctoral thesis; Doktorgradsavhandling, 2015-01-23)Ocean wind monitoring is an integral part of weather forecasting, maritime shipping lane planning, offshore wind research, as well as the study of climate patterns. Satellite radar instruments, such as Synthetic Aperture ...