A least-squares approach to fully constrained linear spectral mixture analysis using linear inequality constraints

Zhibin Sun; Chein-I Chang; Hsuan Ren; Francis M. D’Amico; James O. Jensen

doi:10.1117/12.508088

7 January 2004 A least-squares approach to fully constrained linear spectral mixture analysis using linear inequality constraints

Zhibin Sun, Chein-I Chang, Hsuan Ren, Francis M. D’Amico, James O. Jensen

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Proceedings Volume 5159, Imaging Spectrometry IX; (2004) https://doi.org/10.1117/12.508088
Event: Optical Science and Technology, SPIE's 48th Annual Meeting, 2003, San Diego, California, United States

Abstract

Fully constrained linear spectral mixture analysis (FCLSMA) has been used for material quantification in remotely sensed imagery. In order to implement FCLSMA, two constraints are imposed on abundance fractions, referred to as Abundance Sum-to-one Constraint (ASC) and Abundance Nonnegativity Constraint (ANC). While the ASC is linear equality constraint, the ANC is a linear inequality constraint. A direct approach to imposing the ASC and ANC has been recently investigated and is called fully constrained least-squares (FCLS) method. Since there is no analytical solution resulting from the ANC, a modified fully constrained least-squares method (MFCLS) which replaces the ANC with an Absolute Abundance Sum-to-one Constraint (AASC) was proposed to convert a set of inequality constraints to a quality constraint. The results produced by these two approaches have been shown to be very close. In this paper, we take an oopposite approach to the MFCLS method, called least-squares with linear inequality constraints (LSLIC) method which also solves FCLSMA, but replaces the ASC with two linear inequalities. The proposed LSLIC transforms the FCLSMA to a linear distance programming problem which can be solved easily by a numerical algorithm. In order to demonstrate its utility in solving FCLSMA, the LSLIC method is compared to the FCLS and MFCLS methods. The experimental results show that these three methods perform very similarly with only subtle differences resulting from their problem formations.

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Zhibin Sun, Chein-I Chang, Hsuan Ren, Francis M. D’Amico, and James O. Jensen "A least-squares approach to fully constrained linear spectral mixture analysis using linear inequality constraints", Proc. SPIE 5159, Imaging Spectrometry IX, (7 January 2004); https://doi.org/10.1117/12.508088

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KEYWORDS

Computer programming

Chemical elements

Error analysis

Signal to noise ratio

Transform theory

Chemical analysis

Reflectivity

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