Inverse Problems and Imaging (IPI)

Template matching via $l_1$ minimization and its application to hyperspectral data

Pages: 19 - 35, Volume 5, Issue 1, February 2011      doi:10.3934/ipi.2011.5.19

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Zhaohui Guo - Department of Mathematics, University of California, Los Angeles, Los Angeles, CA 90095, United States (email)
Stanley Osher - Department of Mathematics, University of California, Los Angeles, CA 90095, United States (email)

Abstract: Detecting and identifying targets or objects that are present in hyperspectral ground images are of great interest. Applications include land and environmental monitoring, mining, military, civil search-and-rescue operations, and so on. We propose and analyze an extremely simple and efficient idea for template matching based on $l_1$ minimization. The designed algorithm can be applied in hyperspectral classification and target detection. Synthetic image data and real hyperspectral image (HSI) data are used to assess the performance, with comparisons to other approaches, e.g. spectral angle map (SAM), adaptive coherence estimator (ACE), generalized-likelihood ratio test (GLRT) and matched filter. We demonstrate that this algorithm achieves excellent results with both high speed and accuracy by using Bregman iteration.

Keywords:  Hyperspectral, template matching, Bregman, $l_1$ minimization.
Mathematics Subject Classification:  65N21, 86A21.

Received: May 2010;      Revised: August 2010;      Available Online: February 2011.