
7.4
Least Squares
Filtering: The
Discrete Case
287
where we have used Eq. (111a) from Chapter 2. If the noise process is ergodic
(Section 2.4.6), R
vv
(x, v) can be determined by applying Eq. (28) of Chapter 2
to a picture containing noise only, i.e., to an output picture g(x, y) obtained
when the input picturef(x, y) is zero.
If no statistical properties of the random processes involved are known, it
is not uncommon to approximate (41) by
H(u,v)\H(u,v)\
2
+ T
where Γ, the noise-to-signal power density ratio, is approximated by a suitable
constant. The value of this constant evidently reflects some a priori knowledge
about the relative magnitude ...