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.