Texture analysis and physical interpretation of polarimetric SAR data

Abstract

This thesis is dedicated to the study of texture analysis and physical interpretation of PolSAR data. As the starting point, a complete survey of the statistical models for PolSAR data is conducted. All the models are classified into three categories: Gaussian distributions, texture models, and finite mixture models. The texture models, which assume that the randomness of the SAR data is due to two unrelated factors, texture and speckle, are the main subject of this study. The PDFs of the scattering vector and the sample covariance matrix in different models are reviewed.
 Since many models have been proposed, how to choose the most accurate one for a test data is a big challenge. Methods which analyze different polarimetric channels separately or require a filtering of the data are limited in many cases, especially when it comes to high resolution data. In this thesis, the L2-norms of the scattering vectors are studied, and they are found to be advantageous to extract statistical information from PolSAR data. Statistics based on the L2-norms can be utilized to determine what distribution the data actually follow.
 A number of models are suggested to model the texture of PolSAR data, and some are very complex. But most of them lack a physical explanation. The random walk model, which can be interpreted as a discrete analog of the SAR data focusing process, is studied with the objective to understand the data statistics from the point of view of scattering process. A simulator based on the random walk model is developed, where different variations in the scatterer types and scatterer numbers are considered. It builds a bridge between the mathematical models and underlying physical mechanisms.
 It is found that both the mixture and the texture could give the same statistics such as log-cumulants of the second order and the third order. The two concepts, texture and mixture, represent two quite different scenarios. A further study was carried on to see if it is possible to distinguish them. And higher order statistics are demonstrated to be favorable in this task. They can be physically interpreted to distinguish the scattering from a single type of target from a mixture of targets. Esta tesis está dedicada al estudio del análisis de texturas y de la interpretación física de datos PolSAR. Como punto de partida, se ha llevado a cabo un estudio completo de los modelos estadísticos para datos PolSAR. Todos los modelos se han clasificado en tres categorías: distribuciónes gaussianas, modelos de textura y modelos de mezcla finita. Los modelos de textura, que asumen que la aleatoriedad de los datos SAR se debe a dos factores no relacionados, la textura y el speckle, son el tema principal de este estudio. Las distribuciones del vector de dispersión y de la matriz de covarianza en diferentes modelos son revisados. Debido a que se han propuesto muchos modelos, cómo elegir el más preciso para unos datos en particular es un gran reto. Los métodos que analizan diferentes canales polarimétricos por separado o requieren de un filtrado de los datos presentan limitacions en muchos casos, especialmente cuando se trata de datos de alta resolución. En esta tesis, la norma L2 de los vectores de dispersión se estudian, demostrando su utilidad para extraer información estadística de los datos PolSAR. Las estadísticas basadas en la norma L2 se pueden utilizar para determinar la distribución de los datos. En la literatura, se sugieren una serie de modelos para modelar la textura de los datos PolSAR, siendo alguno de ellos muy complejos. Sin embargo, la mayoría de ellos carecen de una explicación física. El modelo de random walk, que se puede interpretar como un análogo discreto del proceso de enfocado de los datos SAR, se estudia con el objetivo de comprender las estadísticas de los datos desde el punto de vista de proceso de dispersión. Se desarrolla un simulador basado en el modelo de random walk, donde se consideran diversas variaciones en los tipos de dispersores y número de dispersores. Se construye un puente entre los modelos matemáticos y mecanismos físicos subyacentes. Se encontró que tanto la mezcla como la textura podrían dar las mismas estadísticas, tales como log-cumulantes de segundo orden y tercer orden. Los dos conceptos, la textura y la mezcla, representan dos escenarios muy diferentes. Se realizó un estudio adicional para ver si es posible distinguirlos, demostrando que las estadísticas de orden superior son favorables en esta tarea. Pueden interpretarse físicamente para distinguir la dispersión a partir de un solo tipo de blanco de una mezcla de blancos.

An Extended Zeta Function with Applications in Model Building and Bayesian Analysis

“…One can study various properties of the models introduced here. Such studies are likely to bring in more parameters from the set a j s and b j s. One can explore the applications of the models here, especially the ones in the complex domain, in quantum physics, communication theory and related areas in light of the evidence in [1,5].…”

“…In the PhD thesis written by [5], details of the applications of various types of statistical models, especially in the complex domain, are given. Most of the models are Gaussian-and Wishartbased.…”

“…Ref. [5] is mainly concerned with the analysis of PolSAR (Polarimetric Synthetic Aperture Radar) data on single-look and multi-look radar return signals. It is found that non-Gaussian models give better representations in certain regions such as forests, sea surface, urban areas, etc.…”

Extensions of Some Statistical Concepts to the Complex Domain

“…where sjk = ∑ n r=1 ( xjr − xj )( xrk − xk ) * . The motivation in using the sample sum of products matrix S is that 1 n−1 S is an unbiased estimator of Σ. Since we will be normalizing the eigenvectors, operate with S itself.…”

“…Most of the papers in these applied areas, concentrate on developing algorithms for computing eigenvalues and eigenvectors, which are useful and relevant in principal component analysis, independent component analysis, factor analysis, and so on. Statistical analysis in the complex domain is widely used in the analysis of multi-look return signals in radar [1], in multi-task learning in artificial intelligence and machine learning [2], in problems such as signal processing [3], in principal component analysis and independent component analysis in analyzing meteorological data in the complex domain [4], in optimal allocation of resources, especially energy resources [5], in holography, microscopy and optical metrology [6], in delayed mixing in speech processing, in biomedical signal analysis, and in financial data modeling, etc. [7].…”