Endmember extraction in hyperspectral images using l-1 minimization and linear complementary programming

Dzung Nguyen; Trac Tran; Chiman Kwan; Bulent Ayhan

doi:10.1117/12.850139

12 May 2010 Endmember extraction in hyperspectral images using l-1 minimization and linear complementary programming

Dzung Nguyen, Trac Tran, Chiman Kwan, Bulent Ayhan

Proceedings Volume 7695, Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery XVI; 76951M (2010) https://doi.org/10.1117/12.850139
Event: SPIE Defense, Security, and Sensing, 2010, Orlando, Florida, United States

Abstract

Endmember extraction in Hyperspectral Images (HSI) is a critical step for target detection and abundance estimation. In this paper, we propose a new approach to endmember extraction, which takes advantage of the sparsity property of the linear representation of HSI's spectral vector. Sparsity is measured by the l0 norm of the abundance vector. It is also well known that l1 norm well resembles l0 in boosting sparsity while keeping the minimization problem convex and tractable. By adding the l1 norm term to the objective function, we result in a constrained quadratic programming which can be solved effectively using the Linear Complementary Programming (LCP). Unlike existing methods which require expensive computations in each iteration, LCP only requires pivoting steps, which are extremely simple and efficient for the un-mixing problem, since the number of signatures in the reconstructing basis is reasonably small. Preliminary experiments of the proposed methods for both supervised and unsupervised abundance decomposition showed competitive results as compared to LS-based method like Fully Constrained Least Square (FCLS). Furthermore, combination of our unsupervised decomposition with anomaly detection makes a decent target detection algorithm as compared to methods which require prior information of target and background signatures.

Citation Download Citation

Dzung Nguyen, Trac Tran, Chiman Kwan, and Bulent Ayhan "Endmember extraction in hyperspectral images using l-1 minimization and linear complementary programming", Proc. SPIE 7695, Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery XVI, 76951M (12 May 2010); https://doi.org/10.1117/12.850139

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