Image Reconstruction Toolbox for MATLAB (and Freemat)
Jeffrey A. Fessler
The University of Michigan
fessler@umich.edu
January 30, 2007
1 Introduction
This is an initial attempt at documentation of the image reconstruction toolbox (IRT) for MATLAB, and any other MATLAB
emulator that is sufficiently complete. This documentation is, and will always be, hopelessly incomplete. The number of
options and features in this toolbox is near infinite.
2 Overview
Although there are numerous options in the IRT, most image reconstruction examples in the toolbox have the following outline.
A concrete example is example/recon_limited_angle1.m.
• Pick an image size and generate a “true” digital phantom image such as the Shepp-Logan phantom.
• Generate a system matrix (usually called G), typically a Fatrix object (see below), that will be used for iterative recon-
struction.
• Generate simulated measurements y, possibly using the Fatrix object or possibly using an analytical model (e.g., the line-
integrals through the phantom). (Using the Fatrix object is cheating because in the real world there is model mismatch
that contaminates the measurements.)
• Perform a conventional non-iterative reconstruction method (e.g., fbp2) to get a baseline image for comparison.
• Generate a regularization object (usually R).
• Check the predicted resolution properties of that R using qpwls_psf, and adjust the regularization parameter β if necessary.
• Apply an iterative algorithm to the data y using the system model G and the regularizer R for some user-specified number of
iterations.
2.1 Getting started
The best way to learn is probably to run an example file like recon_limited_angle1.m, possibly inserting keyboard
commands within the m-file to examine the variables. Most of IRT routines have a built-in help message; e.g., typing im
without any arguments will return usage information. Many IRT routines have a built-in test routine, e.g., ellipse_sino
test runs a built-in test of the routine for generating the sinogram of ellipse objects.
2.2 Masking
One subtle point is that we usually display images as a rectangular grid of nx × ny pixels, but the iterative algorithms work
on column vectors. Often only a subset of the pixels are updated. A logical array called the mask specifies which pixels are to
be updated. The function call x_col = x_array(mask(:)) extracts the relevant pixel elements “within the mask” into a
column vector. Conversely, the call x_array = embed(x_col, mask) puts the elements of the column vector back into
the appropriate places in the array.
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