Exploitation de la parcimonie par la factorisation de Cholesky et son application pour la détection d'anomalies en imagerie hyperspectrale

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 demonstrate the effectiveness of our estimators for hyperspectral anomaly detection using the Kelly anomaly detector.
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Submitted on : Wednesday, December 6, 2017 - 10:52:02 AM
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Ahmad W. Bitar, Jean-Philippe Ovarlez, Loong-Fah Cheong. Exploitation de la parcimonie par la factorisation de Cholesky et son application pour la détection d'anomalies en imagerie hyperspectrale. GRETSI 2017, Sep 2017, Juan-Les-Pins, France. ⟨hal-01656899⟩

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