Homework 3 due Wednesday Oct 21.  Submit Matlab parts via email to ee528homeworks AT gmail.com

Image Enhancement and Restoration

1. Take the famous lena image used for all of image processing
2. Image enhancement:
   
• Apply spatially varying illumination to it,
  
• generate an illumination-image using an  i.i.d. log-normal distribution with zero mean, very small variance) so that all image values are close to 1
• element-wise multiply this image with the lena image (using .* in Matlab)  - by the way this is called Hadamard product of matrices
• Apply histogram equalization to the resulting image and show results. Discuss what you get
3. Image restoration:
   
1. Pick any low pass filter, h(m,n), apply it to the original lena image, and then add i.i.d. Gaussian noise to the resulting image. This creates a "bad" image
   
2. Use FIR spatially-varying Wiener filter to restore this image
1. Assume that the image has spatially varying mean and variance, but spatially invariant autocorrelations, estimate these from the image itself
   
2. Use these and the knowledge of h(m,n) to estimate the noise variance 
   
3. Use all the above to compute the Wiener filters for each block and then apply them to the "bad" image
   
4. Visually compare the restored and original image and compute percentage error also
   
5. Extra: increase the blur and  noise variance and see the effect (do you need a longer Wiener filter to get small error restoration?), also try to add spatially varying Gaussian noise
   
3. Extra: restore the image assuming that h(m,n) is also not known 
4. Extra: compare results with inverse and pseudo-inverse filter