Title: Relationship exploration among PPI, ATGP and VCA via theoretical analysis

Authors: Chein-I Chang; Chia-Hsien Wen; Chao-Cheng Wu

Addresses: Remote Sensing Signal and Image Processing Laboratory, Department of Computer Science and Electrical Engineering, University of Maryland, Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250, USA; Department of Computer Science and Information Engineering, Providence University, Taichung, Taiwan ' Department of Computer Science and Information Management, Providence University, 200, Sec. 7, Taiwan Boulevard, Shalu Dist., Taichung City 43301, Taiwan ' Department of Electrical Engineering, National Taipei University of Technology, 1, Sec. 3, Zhongxiao E. Rd., Taipei 106, Taiwan

Abstract: The principle of orthogonality using orthogonal projection (OP) is the key concept to develop mean squared error estimation theory in signal processing and communications. It has also found its way in a wide variety of applications in hyperspectral imaging. This paper explores close relationships among three OP-based algorithms, pixel purity index (PPI), vertex component analysis (VCA) in endmember extraction, automatic target generation process (ATGP) in mixed pixel classification and target detection, etc. and further shows that they indeed can be interpreted one way or another. Specifically, VCA and ATGP are essentially the same algorithm in the sense that they both extract targets via maximal OP from a nested sequence of successive orthogonal subspace projection spaces.

Keywords: automatic target generation process; ATGP; endmember extraction; orthogonal projection; pixel purity index; PPI; vertex component analysis; VCA; signal processing; communications; hyperspectral imaging; pixel classification; target detection; nested sequences.

DOI: 10.1504/IJCSE.2013.057303

International Journal of Computational Science and Engineering, 2013 Vol.8 No.4, pp.361 - 367

Received: 19 Oct 2012
Accepted: 19 Oct 2012

Published online: 27 Dec 2013 *

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