Sparsity-based Cholesky Factorization and Its Application to Hyperspectral Anomaly Detection

Abstract : Estimating large covariance matrices has been a longstanding important problem in many applications and has attracted increased attention over several decades. This paper deals with two methods based on pre-existing works to impose sparsity on the covariance matrix via its unit lower triangular matrix (aka Cholesky factor) T. The first method serves to estimate the entries of T using the Ordinary Least Squares (OLS), then imposes sparsity by exploiting some generalized thresholding techniques such as Soft and Smoothly Clipped Absolute Deviation (SCAD). The second method directly estimates a sparse version of T by penalizing the negative normal log-likelihood with L1 and SCAD penalty functions. The resulting covariance estimators are always guaranteed to be positive definite. Some Monte-Carlo simulations as well as experimental data demonstrate the effectiveness of our estimators for hyperspectral anomaly detection using the Kelly anomaly detector.
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Communication dans un congrès
IEEE CAMSAP 2017 (IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing), Dec 2017, Curacao, Dutch Antilles, Netherlands
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Contributeur : Ahmad W. Bitar <>
Soumis le : mardi 5 décembre 2017 - 18:43:12
Dernière modification le : mardi 6 février 2018 - 01:21:44

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  • HAL Id : hal-01656619, version 1

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Ahmad W. Bitar, Jean-Philippe Ovarlez, Loong-Fah Cheong. Sparsity-based Cholesky Factorization and Its Application to Hyperspectral Anomaly Detection. IEEE CAMSAP 2017 (IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing), Dec 2017, Curacao, Dutch Antilles, Netherlands. 〈hal-01656619〉

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