If we look through an optical sensing device then that device has a finite aperture h
and an object to be viewed o. At the “viewing distance” the result i will
be distorted,
the convolution of the object with the aperture to produce the image i, that is,
i = h ⊗ o. If the aperture is circular it will have only one
parameter, its radius.
In this exercise we examine how Wiener filtering is affected when the aperture’s radius is
changed, the aperture being a lowpass filter that distorts the object by smoothing. The
magnitude of the spectrum of the aperture filter will be displayed as well as the SNR.
You can rotate the display of the spectrum.
Choose both the radius of the aperture and different levels of additive, independent,
Gaussian noise. For various values of the aperture’s radius and the SNR, answer
the following.
At the highest value of the SNR and the smallest radius, which version
resembles the original version most: the noisy and distorted version (lower,
left panel) or the restored version (lower, right panel)?
As the SNR decreases, which version resembles the original version most:
the noisy and distorted version (lower, left panel) or the restored version (lower,
right panel)? Vary the aperture size and SNR in a systematic way to
evaluate performance.
For each aperture size, at what SNR is the filter not useful
for restoring the image? You might also consider making a distinction between
“recognizing an image” and “restoring an image”. Can you explain this on the
basis of Equation
10.29?