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Novel estimators of equivalent number of looks in polarimetric SAR imagery based on sub-matrices

Science China(Information Sciences) 2016年第6期59卷 212-224页

作者： Tao LIU Haogui CUI Zemin XI Jun GAO School of Electronic Engineering Naval University of Engineering

The equivalent number of looks(ENL) is an important parameter in the multilook statistical model of polarimetric synthetic aperture radar(Pol-SAR). Recently, the maximum likelihood(ML) method was proposed and gave a good performance in the Gaussian model case by using the full covariance matrix instead of the intensity of Pol-SAR data, but it generated underestimates in the product model case. In this paper several novel ENL estimators are presented via certain cumulants of the log-determinant of the sub-matrices of the multilook polarimetric covariance matrix. The texture effect to the ENL estimates is eliminated, and the analytic estimators are derived. The estimators use the full covariance matrix and sub-matrices information, rather than the intensities of polarization channels. All the novel estimators are suitable for any texture model and thus provide more accurate results than many existing ones. Experiments using simulated data and real data are presented to evaluate the performance of different estimators. The results show that the second log-determinant moment(SLDM3)-based method is the best one among the novel estimators. At the same time this estimator has much less computational complexity. In addition, a novel distribution classification method is proposed by coloring the image via second- and third-order log-cumulants of the covariance matrix(MLC), which is helpful to assess the estimation result.

关键词： radar polarimetry synthetic aperture radar parameter estimation moment methods sub-matrix log-cumulants

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Minimal Time of Null Controllability for the 1D Heat Equation by a Strategic Zone Profile

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Journal of Applied Mathematics and Physics 2021年第7期9卷 1707-1717页

作者： Cheikh Seck Mame Libasse Laye Ane Département de Mathématiques de la FASTEF ex ENS de l’Université Cheikh Anta Diop de Dakar Dakar Sénégal Laboratoire d’Analyse Numérique et d’Informatique (LANI) de l’UFR SAT de l’Université Gaston Berger de Saint-Louis Saint-Louis Sénégal Département de mathématiques et d’Informatique de la Faculté des Sciences et Techniques de l’Université Cheikh Anta Diop de Dakar Dakar Sénégal

The aim of this work is to improve the minimum time of null controllability of the 1D heat equation by using the notion of strategic zone actuators. In fact, motivated by the work of Khodja on the null controllability of the heat equation and of El Jai on the controllability by the use of strategic zone actuators, we managed, in this work, to improve the minimal time of null controllability to the 1D heat equation. However, the restrictions and difficulties to establish the inequality of coercivity of the parabolic operator, require to seek other methods of internal control. Thus in this paper, a mixed method combining the method of moments and the notion of strategic profile was used to find a better minimal time of null controllability of the 1D heat equation.

关键词： Control Null Controllability moment methods Estimations Strategic Actuator

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