We will now express the convolving kernel h in this equation in a form closer
to that given by (42). Since h(t) is the inverse Fourier transform of
|
w | in the
frequency domain:
we have
'2
Using the transformation
UD
W = w
T
= (121)
JD
2
+ s
2
we can rewrite (120) as follows:
/ UD \ D
2
+ 5
2
f
00
=
~Ü
Y
D
2
~
H(S S) (122)
Substituting this in (119) we get
/(»·.
9)
=
Γ
772
Γ
-
*)
J
dS
W
<
123
>
Jo U J-oo yJD + s
where
g(s) = ±h(s) (124)
For the purpose of computer implementation (123) may be interpreted as a
weighted filtered-backprojection algorithm. To snow this we rewrite (123)
as follows:
f(r,9)=
j^Q
ß
(s')dß
(125)
where
Q
ß
(s) = R' ...
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