The previous exercises have dealt with acoustic signals. We will now look at the usefulness
of Wiener filtering when applied to an image. The image is in color and both the
“distortion” filter and the subsequent Wiener filter are applied separately to each of the
colors {r, g,
b}. The magnitude of the spectrum of the distortion
filter is displayed as will the SNR. You can rotate the display of the spectrum.
Choose among different filters and different levels of additive, independent, Gaussian noise.
For each of the filters, including the “identity” filter which is simply no filtering at
all, answer the following:
At the highest value of the SNR, 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)?
At what SNR is the filter no longer useful to restore the image? You might also
consider making a distinction between “recognizing an image” and “restoring an
image”.