Goodness-of-Fit Tests for Multilook Polarimetric Radar Data Based on the Mellin Transform

Anfinsen, Stian Normann; Doulgeris, Anthony P.; Eltoft, T.

doi:10.1109/tgrs.2010.2104158

Cited by 49 publications

(85 citation statements)

References 26 publications

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“…Further, in GMoLC, the covariance matrix of sample LCs, instead of sample moments, is used as a weighting matrix. For the matrix-variate case, these methods are intuitively called method of matrix log cumulants (MoMLC) [29] and generalized MoMLC (GMoMLC) [31].…”

Section: Methods Of Log Cumulant Estimationmentioning

confidence: 99%

“…A specialized GoF statistic, based on multiple LCs, has been recently developed for PolSAR distributions [31]. Traditionally, GoF testing has been performed by assessing the fitting of intensity or amplitude pdfs to data histogram for each channel separately.…”

Section: Goodness Of Fit Using Log Cumulantsmentioning

confidence: 99%

“…Further, it captures more statistical information by performing GoF using multiple LCs. In the following, we briefly list the most relevant results for the simple hypothesis case, where the model parameters are considered known (for details see [31]). …”

Section: Goodness Of Fit Using Log Cumulantsmentioning

confidence: 99%

“…, v p }. The equation to construct K matrix using MLCs up to order 2v max is given in the appendix of [31]. We can define a test statistic, Q p , which uses p sample MLCs:…”

Section: Goodness Of Fit Using Log Cumulantsmentioning

confidence: 99%

“…Also, we apply the polarimetric MoLC estimators for G 0 , K, and Kummer-U distributions to real PolSAR data [29], [30]. Finally, we compute a formal χ 2 distributed Goodness-of-Fit (GoF) test statistic, based on multiple log cumulants and specially designed for polarimetric data [31]. This facilitates the GoF comparison between different estimators and distributions on real data.…”

Section: Introductionmentioning

confidence: 99%

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Application of Mellin-Kind Statistics to Polarimetric <inline-formula> <tex-math notation="TeX">${\cal G}$</tex-math></inline-formula> Distribution for SAR Data

Khan

Guida

2014

IEEE Trans. Geosci. Remote Sensing

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Abstract-The K distribution can be arguably regarded as one of most successful and widely used models for radar data. However, in the last two decades we have seen tremendous growth in even more accurate modeling of radar statistics. In this regard, the relatively recent G 0 distribution filled some deficiencies left unaccounted by the K model. The G 0 model actually resulted as a special case of a more general model; the G distribution, which also has the K model as its special form. Singlelook complex (SC) and multilook complex (MC) polarimetric extensions of these models (and many others) have also been proposed in this prolific era. Unfortunately, statistical analysis using the polarimetric G distribution remained limited, primarily because of more complicated parameter estimation. In this paper, the authors have analyzed the G model for its parameter estimation using state-of-the-art univariate and matrix-variate Mellin Kind Statistics (MKS). The outcome is a class of estimators based on Method of Log Cumulants (MoLC), and Method of Matrix Log Cumulants (MoMLC). These estimators show superior performance characteristics for product model distributions like the G model. Diverse regions in TerraSAR-X polarimetric SAR (PolSAR) data have also been statistically analyzed using the G model with its new and old estimators. Formal Goodness-of-fit (GoF) testing, based on MKS theory, has been used to assess the fitting accuracy between different estimators and also between G, K, G 0 , and Kummer-U models.

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Section: Methods Of Log Cumulant Estimationmentioning

confidence: 99%

Section: Goodness Of Fit Using Log Cumulantsmentioning

confidence: 99%

Section: Goodness Of Fit Using Log Cumulantsmentioning

confidence: 99%

“…, v p }. The equation to construct K matrix using MLCs up to order 2v max is given in the appendix of [31]. We can define a test statistic, Q p , which uses p sample MLCs:…”

Section: Goodness Of Fit Using Log Cumulantsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Application of Mellin-Kind Statistics to Polarimetric <inline-formula> <tex-math notation="TeX">${\cal G}$</tex-math></inline-formula> Distribution for SAR Data

Khan

Guida

2014

IEEE Trans. Geosci. Remote Sensing

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Goodness‐of‐fit measures based on the Mellin transform for beta generalized lifetime data

Vasconcelos

Cintra

Nascimento

2021

Math Methods in App Sciences

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In recent years various probability models have been proposed for describing lifetime data. Increasing model flexibility is often sought as a means to better describe asymmetric and heavy tail distributions. Such extensions were pioneered by the beta-G family. However, efficient (GoF) measures for the beta-G distributions are sought. In this paper, we combine probability weighted moments (PWMs) and the Mellin transform (MT) in order to furnish new qualitative and quantitative GoF tools for model selection within the beta-G class. We derive PWMs for the Fréchet and Kumaraswamy distributions, and we provide expressions for the MT, and for the log-cumulants (LC) of the beta-Weibull, beta-Fréchet, beta-Kumaraswamy, and beta-log-logistic distributions. Subsequently, we construct LC diagrams and, based on the Hotelling's T 2 statistic, we derive confidence ellipses for the LCs. Finally, the proposed GoF measures are applied on five real data sets in order to demonstrate their applicability.

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Polarimetric SAR Modelling: Mellin Kind Statistics and Time-Frequency Analysis

Eltoft¹,

Ferro-Famil²,

Anfinsen³

et al. 2017

Mathematical Models for Remote Sensing Image Processing

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Goodness-of-Fit Tests for Multilook Polarimetric Radar Data Based on the Mellin Transform

Cited by 49 publications

References 26 publications

Application of Mellin-Kind Statistics to Polarimetric <inline-formula> <tex-math notation="TeX">${\cal G}$</tex-math></inline-formula> Distribution for SAR Data

Application of Mellin-Kind Statistics to Polarimetric <inline-formula> <tex-math notation="TeX">${\cal G}$</tex-math></inline-formula> Distribution for SAR Data

Goodness‐of‐fit measures based on the Mellin transform for beta generalized lifetime data

Polarimetric SAR Modelling: Mellin Kind Statistics and Time-Frequency Analysis

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