3-C (DUE 11/17 23:59)
Assume that pixel values in following images represent densities (to simplify the problem, say
linear attenuation coefficients) of an object. Based on CT principles introduced in class,
[Reconstruction algorithm 1]

Use MatLab program: Generate two linear systems from all projection profiles of the two
images:
• Use PINV (Pseudo-inverse)
• Use SVD (Singular Value Decomposition, see MatLab sample code 9) to solve these two
linear systems. Compare your result with original data.


HW6-1 (DUE 11/30)
Objective: Simulation of noiseless, 1st generation CT using MatLab.
Requirement: The projection is in *.mat format. Unzip BME620-211-projections.zip and use
“Projection04.mat” to conduct Step 7 of the below table, submit an electronic copy of code
that generates all resultant images, and associated input images in a zip file
(211ProjFirstName.zip). You can use load command, e.g., load 'projection-*.mat' then you can
see a new variable, usually p, that holds the projection data.
PROCESS DESCRIPTION OUTPUT
1 Use “Paintbrush” or any graphical app to
generate three images (single object, two
separated objects and two objects
overlapped) and F14 image, convert all
images to gray scale. Image intensity will be
used to simulate object density.
You can copy some
steps from previous
homework.
4 pairs of images, each
has original and gray
scale image. Following
processes will be
applied to the 4 gray
scale images (f1~f4).
2 Perform Radon transform, generate
projection images (p) for the 4 images in step
1.
Procedures of how to
generate p.
4 projection images
(p1~p4)
4 Generate reconstructed images (g) using
direct back projection algorithm.
Procedures of how to
generate g. Compare
the difference between
recovered images and
original images
4 reconstructed images
(g1~g4) by direct back
projection, 4 difference
images (fg1~fg4)
5 Use frequency domain filter (ff) to reduce
“overlapping” effects on g image, generate
filtered back projection images h.
Procedures of how to
generate h. Compare
the differences
between g and h,
explain the reason.
Frequency filter (ff), 4
filtered projection
images (ff.*p) and 4
reconstructed images
h1~h4 and difference
(fh1~fh4)
6 Use spatial domain filter (sf) to generate
filtered back projected images k.
Procedures of how to
generate k. Compare
the difference between
g and k, explain the
reason.
Frequency filter (sf), 4
filtered projection
images (sfp) and 4
reconstructed images
k1~k4 and difference
(fk1~fk4)
7 You are given 1 projection matrix (called q),
use the programs you write in 4, 5 and 6 to
generate reconstructed images dbq (direct
BP), ffbq (frequency filtered BP) and sfbq
(spatial filtered BP). q is posted on
blackboard.
Does your program
work?
q
dbq
ffbq
sfbq



HW6-2 (DUE 11/30)
Objective:
Medical image requires relatively “flat” background when no object is imaged. However,
due to many factors, particularly from hardware, such as heel effect, un-uniformity,
obliquity, or film/detector flaw, complete-flat background (errorless) is almost
impossible. Software can correct (or at least mitigate) these errors.
Requirement:
Write a short program that can calibrate an imaging system so that a flat background
can be established. A simple interface should be provided because users do not know
how to modify MatLab code. For example, when start program, prompts: “Please enter
calibration image file name”, “Please enter image name”, etc. should be provided.
Inputs:
1) one blank image with background of OD close to 0 (but with randomly distributed
low-OD noise), 2) one image with objects imaged with noise background, 3) New blank
image with background of OD close to 0 (but with randomly distributed low-OD noise),
4) New image with objects imaged with noise background. To evaluate the program, 3)
and 4) are NOT given to student but used for grading only.
Outputs:
1) the blank image with removed noises, 2) the image with objects with removed noises.
New images used for grading evaluation.
Grading:
New images are used for grading evaluation.

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