Handbook of Biomedical Optics

156 Handbook of Biomedical Optics

the area being imaged and the spectra in the emitted radiation.

e linear mixing model (LMM) (Keshava 2003) is expressed as

p w Ax w= + = +

=

∑

x a

i i

i

n

1

(7.24)

where

A ∈

+



m n×

is the endmember matrix

a

i

is the spectral signature of the ith endmember

x ∈

+



n

is the vector of the abundances

p ∈

m

is the measured pixel spectrum

w is the noise vector

n is the number of endmembers

A is considered positive in order to have physical meaning;

in addition, the abundance vector needs to satisfy x ≥ 0 and

x x

i

n

i

n

≤ =

∑ ∑

1 1or

in order for the abundance estimation

to have a physical meaning as well.

A nonlinear mixing model is needed ...