April 2013
Intermediate to advanced
1164 pages
39h 37m
English
Content preview from Hyperspectral Data Processing: Algorithm Design and AnalysisBecome an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
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6.8 Constrained Band Selection
By re-inventing a wheel Chang and Wang (2006) recently developed a new approach to BS, called constrained band selection (CBS). Its idea was derived from the Linearly Constrained Minimum Variance (LCMV) adaptive beamforming (Frost, 1972) and can be described as follows.
Let 
denote the selected band subset where for each 
the kth spectral band in ΩBS is represented by a column vector denoted by bBS,k. Furthermore, let bl represent the lth spectral band as a column vector. Then the entire image correlation matrix is defined by 
. Following the LCMV approach outlined in Chang (2002b; 2003a) we can consider a CBS problem by finding a Finite Impulse Response (FIR) filter specified by a weighting matrix WBS that linearly constrains the selected bands in ΩBS with a constraint matrix, C, while minimizing the band correlation matrix Q through the following optimization equation:
where 
, , and C is a constraint matrix. In light of the J(ΩBS) in (6.72) the constrained ...
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