April 2013
Intermediate to advanced
1164 pages
39h 37m
English
Content preview from Hyperspectral Data Processing: Algorithm Design and Analysis
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14.2 Abundance-Constrained LSMA (AC-LSMA)
When the abundance-unconstrained LSMA specified by (12.1) is considered, its unconstrained LSE solution to (14.2) is given by
(14.3) 
A commonly used least squares method is to minimize the LSE problem specified by (12.1) over the abundance vector 
subject to the constraints imposed by ASC and/or ANC on α. If we impose either ASC or ANC or both on (14.1), three LSE problems derived from AC-LSMA can be formulated as follows (Heinz and Chang 2001; Chang, 2003b).
i. Abundance sum-to-one constrained LSMA (ASCLS-LSMA) problem:
ii. Abundance nonnegativity-constrained LSMA (ANCLS-LSMA) problem:
(14.5) 
iii. Abundance fully constrained LSMA (AFCLS-LSMA) problem:
The solutions to (14.4)–(14.6) were well documented by Heinz and Chang (2001) and Chang (2003a) and will be referred to as SCLS, NCLS, and FCLS solutions, respectively.
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