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...