Sparsity-Based cholesky factorization and its application to hyperspectral anomaly detection
- Resource Type
- Conference
- Authors
- Bitar, Ahmad W.; Ovarlez, Jean-Philippe; Cheong, Loong-Fah
- Source
- 2017 IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP) Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), 2017 IEEE 7th International Workshop on. :1-5 Dec, 2017
- Subject
- Communication, Networking and Broadcast Technologies
Computing and Processing
Signal Processing and Analysis
Covariance matrices
Hyperspectral imaging
Object detection
Sparse matrices
Detectors
Conferences
Hyperspectral anomaly detection
covariance matrix
sparsity
Cholesky factor
- Language
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 L 1 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.