
2.5 Vector Space Representation of Images
47
By substituting (124) in this equation, differentiating e with respect to the a^s
and setting each derivative equal to zero, we can show that
£{(s - 8)x
i
} - 0, i = 1,
2,...,
Ν (126)
These results are known as the orthogonality principle in linear mean-square
estimation. The principle says that the error s — s must be statistically or-
thogonal to all the random variables used in estimation.
In deriving the above principle, no assumptions were made about the
mean values of the random variables. If they are all zero, the estimate in
(124) would indeed result in the least estimation error. For the cas ...