CS/ECE 545 Homework 6

Complete by Class 16

Wiener Filtering

In this problem, we investigate the Wiener Filter discussed in class and described in Section 5.8. Use the moon images (moon1.img, moon1.tif, moon1.gif, or moon2.img, moon2.tif, moon2.gif)

Implement the following operations:

Compute the DFT of the uncorrupted image.
Estimate the power spectrum of the image.
Add Gaussian white noise to the image. Try s = 10 or other value. Call this the "corrupted" image.
Compute the optimal Wiener filter modulation transfer function (MTF) given by

You may assume that and that . Use from part 2.
Multiply the DFT of the corrupted image by the Wiener filter MTF to produce the best estimate of .
Inverse DFT to produce the best estimate of the uncorrupted image.

Display the output of each step as an image. Also display the point spread function h(x,y) corresponding to the Wiener filter MTF from part 4.

What to hand in
Hand in to class

Your filtering program, including enough comments so we can understand what you have done, with examples.
The Gaussian noise program, with examples, and the answer to the question.
Answer to the convolution problem.