SAR probability density function estimation using a generalized form of K-distribution

In this paper, generalized forms of amplitude and intensity K-distributions are proposed to model multilook synthetic aperture radar (SAR) data. The approach is based upon a product model in which the amplitude and intensity distributions of the SAR backscatter component are assumed to be Laguerre orthogonal expansions of the traditional clutter distribution. The SAR intensity and amplitude probability density functions (pdfs) are derived and turn out to be the weighted combination of a series of K-distributions. Several theoretical and implementation issues regarding the proposed generalization are discussed. Comparative experimental results using real SAR data indicates that these generalized forms of K may allow better estimation of the SAR pdf than that of the traditional K distribution.

[1]  I. S. Gradshteyn,et al.  Table of Integrals, Series, and Products , 1976 .

[2]  Henri Maître,et al.  A new statistical model for Markovian classification of urban areas in high-resolution SAR images , 2004, IEEE Transactions on Geoscience and Remote Sensing.

[3]  Heng-Chao Li,et al.  On the Empirical-Statistical Modeling of SAR Images With Generalized Gamma Distribution , 2011, IEEE Journal of Selected Topics in Signal Processing.

[4]  D. Blacknell,et al.  Comparison of parameter estimators for K-distribution , 1994 .

[5]  Zhan Yu,et al.  Envelope Probability Density Functions for Fading Model in Wireless Communications , 2007, IEEE Transactions on Vehicular Technology.

[6]  John G. Proakis,et al.  Probability, random variables and stochastic processes , 1985, IEEE Trans. Acoust. Speech Signal Process..

[7]  Huaiyu Zhu.  On Information and Sufficiency , 1997 .

[8]  M. Omair Ahmad,et al.  Bayesian Wavelet-Based Image Denoising Using the Gauss–Hermite Expansion , 2008, IEEE Transactions on Image Processing.

[9]  Jean-Marie Nicolas,et al.  Application de la transformée de Mellin : étude des lois statistiques de l'imagerie cohérente , 2006 .

[10]  Gabriele Moser,et al.  SAR amplitude probability density function estimation based on a generalized Gaussian model , 2006, IEEE Transactions on Image Processing.

[11]  Corina da Costa Freitas,et al.  A model for extremely heterogeneous clutter , 1997, IEEE Trans. Geosci. Remote. Sens..

[12]  Torbjørn Eltoft,et al.  The Rician inverse Gaussian distribution: a new model for non-Rayleigh signal amplitude statistics , 2005, IEEE Transactions on Image Processing.

[13]  Joseph Lipka,et al.  A Table of Integrals , 2010 .

[14]  K. Bâ,et al.  Gamma-Laguerre Formalism: Rigorous Approach and Application to Hydrologic Time Series , 2004 .

[15]  H. Lew,et al.  Homodyned-K fluctuation model , 2002 .

[16]  Josiane Zerubia,et al.  Modeling SAR images with a generalization of the Rayleigh distribution , 2004, IEEE Transactions on Image Processing.

[17]  仲上 稔,et al.  The m-Distribution As the General Formula of Intensity Distribution of Rapid Fading , 1957 .

[18]  Bryan Mercer,et al.  Multilook polarimetric SAR data probability density function estimation using a generalized form of multivariate K-distribution , 2014 .

[19]  E. Jakeman,et al.  Generalized K distribution: a statistical model for weak scattering , 1987 .

[20]  M. Abramowitz,et al.  Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables (National Bureau of Standards Applied Mathematics Series No. 55) , 1965 .

[21]  Wen Hong,et al.  An Efficient and Flexible Statistical Model Based on Generalized Gamma Distribution for Amplitude SAR Images , 2010, IEEE Transactions on Geoscience and Remote Sensing.

[22]  Tjeng Thiang Tjhung,et al.  Unified Laguerre Polynomial-Series-Based Distribution of Small-Scale Fading Envelopes , 2009, IEEE Transactions on Vehicular Technology.

[23]  Jordi Inglada,et al.  A New Statistical Similarity Measure for Change Detection in Multitemporal SAR Images and Its Extension to Multiscale Change Analysis , 2007, IEEE Transactions on Geoscience and Remote Sensing.

[24]  S. Quegan,et al.  Understanding Synthetic Aperture Radar Images , 1998 .

[25]  D. Middleton.  New physical-statistical methods and models for clutter and reverberation: the KA-distribution and related probability structures , 1999 .

[26]  R. Fisher.  The Advanced Theory of Statistics , 1943, Nature.

[27]  Gabriele Moser,et al.  Dictionary-based stochastic expectation-maximization for SAR amplitude probability density function estimation , 2006, IEEE Transactions on Geoscience and Remote Sensing.

[28]  Peter Smith,et al.  Engineering Applications of Stochastic Processes: Theory, Problems and Solutions , 1989 .

[29]  S.A. Reza Zekavat,et al.  Statistical land clutter modeling for airborne radar , 1997, Proceedings of ICICS, 1997 International Conference on Information, Communications and Signal Processing. Theme: Trends in Information Systems Engineering and Wireless Multimedia Communications (Cat..

[30]  Jean-Marie Nicolas.  1 - Introduction aux Statistiques de deuxième espèce : applications des Logs-moments et des Logs-cumulants à l'analyse des lois d'images radar , 2002 .

[31]  V. Anastassopoulos,et al.  Radar clutter modelling using finite PDF tail , 1996 .

[32]  Tjeng Thiang Tjhung,et al.  A Unified Probability Density Function for Small Scale Fading Envelopes , 2007, 2007 IEEE 18th International Symposium on Personal, Indoor and Mobile Radio Communications.

[33]  F. Massey.  The Kolmogorov-Smirnov Test for Goodness of Fit , 1951 .

[34]  Pascal Bondon,et al.  Efficiency of high-order moment estimates , 1998, IEEE Trans. Signal Process..

[35]  Adolfo Martínez Usó,et al.  Clustering-Based Hyperspectral Band Selection Using Information Measures , 2007, IEEE Transactions on Geoscience and Remote Sensing.

[36]  R. S. Raghavan,et al.  A method for estimating parameters of K-distributed clutter , 1991 .

[37]  Milton Abramowitz,et al.  Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables , 1964 .

[38]  Anthony P Lyons,et al.  Reliable Methods for Estimating the $K$-Distribution Shape Parameter , 2010, IEEE Journal of Oceanic Engineering.

[39]  Mark R. Bell,et al.  Statistics of the scattering cross-section of a small number of random scatterers , 1995 .