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

Ahmad W. Bitar; Jean-Philippe Ovarlez; Loong-Fah Cheong

doi:10.1109/CAMSAP.2017.8313124

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

Ahmad W. Bitar ¹ Jean-Philippe Ovarlez ^{2, 1} Loong-Fah Cheong ³

1 SONDRA - Laboratoire franco-singapourien de recherche en électromagnétisme et radars

2 Palaiseau - ONERA - The French Aerospace Lab

3 NUS - National University of Singapore

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.

Keywords : covariance matrix Cholesky factor sparsity Hyperspectral anomaly detection

Type de document :

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〉

Domaine :

Statistiques [stat] / Applications [stat.AP]

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https://hal-centralesupelec.archives-ouvertes.fr/hal-01656619
Contributeur : Ahmad W. Bitar <>
Soumis le : mardi 5 décembre 2017 - 18:43:12
Dernière modification le : jeudi 5 avril 2018 - 12:30:11

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