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Publications about Mellin transform
Result of the query in the list of publications :
Article |
1 - SAR amplitude probability density function estimation based on a generalized Gaussian model.
G. Moser and J. Zerubia and S.B. Serpico. IEEE Trans. on Image Processing, 15(6): pages 1429-1442, June 2006.
Keywords : SAR Images, Generalised Gaussians, Mellin transform.
Copyright : IEEE
@ARTICLE{moser_ieeeip05,
|
| author |
= |
{Moser, G. and Zerubia, J. and Serpico, S.B.}, |
| title |
= |
{SAR amplitude probability density function estimation based on a generalized Gaussian model}, |
| year |
= |
{2006}, |
| month |
= |
{June}, |
| journal |
= |
{IEEE Trans. on Image Processing}, |
| volume |
= |
{15}, |
| number |
= |
{6}, |
| pages |
= |
{1429-1442}, |
| url |
= |
{http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=1632197}, |
| pdf |
= |
{http://hal.archives-ouvertes.fr/inria-00561372/en/}, |
| keyword |
= |
{SAR Images, Generalised Gaussians, Mellin transform} |
| } |
Abstract :
In the context of remotely sensed data analysis, an important problem is the development of accurate models for the statistics of the pixel intensities. Focusing on synthetic aperture radar (SAR) data, this modeling process turns out to be a crucial task, for instance, for classification or for denoising purposes. In this paper, an innovative parametric estimation methodology for SAR amplitude data is proposed that adopts a generalized Gaussian (GG) model for the complex SAR backscattered signal. A closed-form expression for the corresponding amplitude probability density function (PDF) is derived and a specific parameter estimation algorithm is developed in order to deal with the proposed model. Specifically, the recently proposed “method-of-log-cumulants” (MoLC) is applied, which stems from the adoption of the Mellin transform (instead of the usual Fourier transform) in the computation of characteristic functions and from the corresponding generalization of the concepts of moment and cumulant. For the developed GG-based amplitude model, the resulting MoLC estimates turn out to be numerically feasible and are also analytically proved to be consistent. The proposed parametric approach was validated by using several real ERS-1, XSAR, E-SAR, and NASA/JPL airborne SAR images, and the experimental results prove that the method models the amplitude PDF better than several previously proposed parametric models for backscattering phenomena. |
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Technical and Research Report |
1 - SAR Image Filtering Based on the Heavy-Tailed Rayleigh Model.
A. Achim and E.E. Kuruoglu and J. Zerubia. Research Report 5493, INRIA, France, February 2005.
Keywords : Synthetic Aperture Radar (SAR), MAP estimation, Alpha-stable distribution, Mellin transform.
@TECHREPORT{5493,
|
| author |
= |
{Achim, A. and Kuruoglu, E.E. and Zerubia, J.}, |
| title |
= |
{SAR Image Filtering Based on the Heavy-Tailed Rayleigh Model}, |
| year |
= |
{2005}, |
| month |
= |
{February}, |
| institution |
= |
{INRIA}, |
| type |
= |
{Research Report}, |
| number |
= |
{5493}, |
| address |
= |
{France}, |
| url |
= |
{https://hal.inria.fr/inria-00070514}, |
| pdf |
= |
{https://hal.inria.fr/file/index/docid/70514/filename/RR-5493.pdf}, |
| ps |
= |
{https://hal.inria.fr/docs/00/07/05/14/PS/RR-5493.ps}, |
| keyword |
= |
{Synthetic Aperture Radar (SAR), MAP estimation, Alpha-stable distribution, Mellin transform} |
| } |
Résumé :
Les images issues d'un radar à synthèse d'ouverture (RSO) sont affectées de manière inhérente par un bruit dépendant du signal, généralement connu sous le nom de bruit de chatoiement et qui est dû à la cohérence de l'onde radar. Dans ce rapport, nous proposons un nouveau filtre adaptatif pour débruiter les images RSO et nous déduisons un estimateur du maximum a posteriori (MAP) pour la section efficace du diagramme de gain en radar. On utilise d'abord une transformée logarithmique afin de changer le bruit multiplicatif en bruit additif. Nous modélisons la section efficace à l'aide d'une densité de probabilité récemment introduite - la densité de Rayleigh à queue lourde, qui a été obtenue en supposant que les parties réelles et imaginaires du signal complexe reçu peuvent être mieux caractérisées à l'aide de la famille des distributions alpha-stables. Nous estimons les paramètres du modèle à partir d'observations bruitées en faisant appel à la théorie statistique de deuxième espèce qui est fondée sur la transformée de Mellin. Enfin, nous faisons la comparaison entre la méthode que nous proposons et d'autres filtres classiques pour le débruitage d'images RSO. Nos résultats expérimentaux démontrent que le filtre MAP homomorphique fondé sur le modèle de Rayleigh à queue lourde est parmi les meilleurs pour enlever le bruit de chatoiement. |
Abstract :
Synthetic aperture radar (SAR) images are inherently affected by a signal dependent noise known as speckle, which is due to the radar wave coherence. In this report, we propose a novel adaptive despeckling filter and derive a maximum a posteriori (MAP) estimator for the radar cross section (RCS). We first employ a logarithmic transformation to change the multiplicative speckle into additive noise. We model the RCS using the recently introduced heavy-tailed Rayleigh density function, which was derived based on the assumption that the real and imaginary parts of the received complex signal are best described using the alpha-stable family of distribution. We estimate model parameters from noisy observations by means of second-kind statistics theory, which relies on the Mellin transform. Finally, we compare our proposed algorithm with several classical speckle filters applied on actual SAR images. Experimental results show that the homomorphic MAP filter based on the heavy-tailed Rayleigh prior for the RCS is among the best for speckle removal. |
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