Math 2270-1 Project 2, Fall 2002

Seeing things...

The Project:

The goal is to recover (as well as you can) information about an image from a noisy, blurred data set. This is sort of like doing Project 1 backwards: this time you are given the blurring matrix A and the blurred image; your goal is to find the unblurred image.

  • Load the file data2.mat. This file contains a blurred, noisy version of the image you are to try to reconstruct.
  • Load the file Amult.m. This linear transformation performs the blurring responsible for ruining the original image.
  • Try to solve the equation Ax = b, where b is the image in data2.mat, and A is the linear transformation performed by Amult.m. You will need to use Matlab's preconditioned conjugate gradient algorithm 'pcg'. For the preconditioner, use the linear transformation Mmult.m. First try to solve the equation directly, then try to solve the least-squares problem using the normal equations. We will discuss the specifics of doing this in class.
  • Turn in:
    (1) A plot of the blurred data image b.
    (2) A plot of your "best" reconstruction x.
    (3) A list of the commands you used to obtain part (2).
  • After all projects are turned in, you can grab the original image here image2.mat.