Image Processing Reference
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Fig. 4.1 Correlation coeffi-
cient (CC) over the adjacent
bands in the hyperspectral
data. The black line represents
the CC for the urban data
from the Hyperion, and the
blue line represents the CC
for the moffett 2 data from the
of hyperspectral bands that contain a higher amount of independent information, and
fusing this subset of bands instead of processing the entire set of hyperspectral bands.
Fusion of such a subset would generate an output image without much loss in the
quality when compared with the output image obtained from fusion of the entire data
using the same fusion technique. We explore this possibility of selection of subset
of bands where each band possesses a certain amount of additional information with
respect to other bands, and thus, together they capture of the information content in
the hyperspectral image cube. We describe a conditional entropy-based scheme for
the selection of a fewer number of image bands which are mutually less correlated
in order to facilitate a faster visualization. This scheme turns out to be quite faster
and memory efficient as one can achieve the required quality of fusion using only a
much smaller subset of the hyperspectral data.
4.2.1 Redundancy Elimination
An image band undergoing fusion should possess a significant amount of addi-
tional information for the fusion process to be efficient. We shall now explain
an algorithm to select a subset of image bands based on conditional entropy. Let
I k ;
be the hyperspectral image consisting of K bands. We
seek to identify only a subset of bands that will actually undergo fusion. We denote
this subset of cardinality
K as I , such that I
K . The first band is
trivially selected for fusion, which forms the first element of the subset of bands
to be fused, i.e., I
I , and
. The conditional entropies of the successive bands with
respect to this band are evaluated. The next band is selected when the corresponding
conditional entropy exceeds a pre-determined threshold, i.e., when the additional
information content in the given band is sufficiently high. This threshold has been
selected as an appropriate fraction of the entropy of the band under consideration.
The newly selected band becomes a member of I subset. Subsequently, for every
image band, the conditional entropy with respect to each of the previously selected
I 1 }
I k is calculated. The motivation lies in the fact that a newly available image
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