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
2017 IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP 2014), Dec 2017, Curaçao, Netherlands. 〈10.1109/CAMSAP.2017.8313124〉
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Soumis le : mardi 5 décembre 2017 - 18:43:12
Dernière modification le : jeudi 5 avril 2018 - 12:30:11

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Ahmad W. Bitar, Jean-Philippe Ovarlez, Loong-Fah Cheong. Sparsity-based Cholesky Factorization and Its Application to Hyperspectral Anomaly Detection. 2017 IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP 2014), Dec 2017, Curaçao, Netherlands. 〈10.1109/CAMSAP.2017.8313124〉. 〈hal-01656619〉

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