Godfrey Hounsfield invented the CT scan in the 1970s. He realized images of the inside of an object could be created by taking x-rays from multiple angles and using a computer to reconstruct the images into slices. Early CT scans (1st generation) were slow, while later models improved speed by using fan beams and multiple detectors without requiring translation (2nd and 3rd generation). The current method, iterative reconstruction, uses an algorithm to calculate pixel values from each beam angle to reconstruct the final image.

1. Andrew O’Neill
Dt260/3
Supervised by Justin Donnelly

2. A technique for displaying a
representation of a cross section through a
human body or other solid object using X-
rays or ultrasound which then is
reconstructed by a computer.

3.  Godfrey Hounsfield (1919-2004) Invented
the CT. He came up with the Idea that
one could determine what is inside a
object by taking x-rays at all angles
around the object. He constructed a
computer that could take the input of
the x-rays at various angles and create
an image of the object in slices.

4.  1St Generation (Basic beam and
detector which ran slowly and required
multiple translations)

5.  2nd Generation had multiple detectors
and a fan beam which was quicker but
still required translation.
2nd Generation
CT

6.  Fan beam with multiple rotating
detectors which meant translation
wasn’t needed. Much faster 0.5s per
rotation.
3rd Generation CT

7.  Fan beam exactly like 3rd generation
however detector was static 360 on
gantry.
4th Generation CT

8.  Iterative Reconstruction:
Algorithm states that the ray sum is divided
by the number of pixels in a matrix then
at the next angle the pixel is added to the
pixel minus the ray sum then divided by
number of pixels in that row the answer to
this gives the pixel value at that angle. This
is then repeated for every pixel.

10.  The radon function computes projections of an image matrix
along specified directions. A projection of a two-dimensional
function f(x, y) is a set of line integrals. The radon function
computes the line integrals from beams in a certain direction.
The beams are spaced 1 pixel unit apart. To represent an image
the radon takes multiple, parallel-beam projections of the image
at different angles by rotating the source and translating it in the
x, y direction.

13.  The project met the brief that was stated
 Future work would include adding more
pixels and adding a z axis to create a 3D
model.

14.  The system worked however not as
efficiently as wanted
 There was many obstacles trying to
make a functional program
 If given more time more pixels and
beams could have been added

15.  [1] Timothy G Feeman ‘’ Mathematics of medical Imaging
a beginners guide ’’ Sumat 2009
 [2] Paul Suetens ‘’ Fundmentals of Medical Imaging ‘’
Second edition 2009
 [3] Barry Haycock ‘’ CT scan’’ 2007
 [4] Mathworks documentation centre.
 http://www.mathworks.co.uk/help/images/ref/iradon.html
 [5]Wolfram MathWorld
 http://mathworld.wolfram.com/RadonTransform.html
 [6]Mathworks Documentation centre
 http://mathworld.wolfram.com/RadonTransform.html
 [7] Science direct
 http://www.sciencedirect.com/science/article/pii/S01689
0021100461X