June 2014
Intermediate to advanced
576 pages
16h 43m
English
book
Image Analysis, Classification and Change Detection in Remote Sensing, 3rd Edition
by Morton J. Canty
Content preview from Image Analysis, Classification and Change Detection in Remote Sensing, 3rd Edition
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420 Mathematical Tools
A.4 Least squares procedures
In this section, ordinary linear regression is extended to a recursive proce-
dure for sequential data. This forms the basis of one of the neural network
training algorithms derived in Appendix B. In addition, the orthogonal lin-
ear regression procedure used in Chapter 9 for radiometric normalization is
explained.
A.4.1 Recursive linear regression
Consider the statistical model given by Equation (2.92), now in a slight
ly
different notation:
Y (j) =
N
X
i=0
w
j
x
i
(j) + R(j), j = 1 . . . ν. (A.1)
This model r elates the independent variables x(j) = (1, x
1
(j) . . . x
N
(j))
⊤
to
a measured quantity Y (j) via the
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