HW 6, EECS 203A
Problem 5.27, Digital Image Processing, 2nd edition by Gonzalez, Woods.
Nasser Abbasi, UCI. Fall 2004
Question
A certain Xray imaging geometry produces a blurring degradation that can be
modeled as the convolution of the sensed image with the spatial, circularly
symmetric function
where
.
Show that the degradation in the frequency domain is given by
Solution
In general,
Since we are told what the model is (no noise involved), then the model is
Here
is the sensed image, and
is the degraded, produced image and
is the impulse response.
This means if the input image is an impulse, then the output image will be
or
since
is a function of
So a degraded output image can be considered to be
convolved with impulse. Since the Fourier transform of an impulse is 1, then
in the frequency domain, the fourier transform of a degraded output image is
the fourier transform of
times 1.
i.e. in frequency domain, degraded output image transform
But
=
But
but from tables, we know that
Hence we get
do not know what I am doing wrong, can't get the exact expression needed,
getting very close...