BME 210 Spring 2009
Note: The following material has been taken from: Kak and Slaney.
Principles of Computerized Tomographic
IEEE Press, 1987; Jain.
Fundamentals of Digital Image Processing
Prentice Hall, 1989; and from
Harris and Kamel, "Iterative Reconstruction in Computerized Tomography”, UMAP Modules, 1990.
Tomography refers to the cross-sectional imaging of an object from either transmission or
reflection data collected by illuminating the object from many different directions.
The impact of
this technique in diagnostic medicine has been revolutionary, since it has enabled physicians to
view internal organs with unprecedented precision and safety to the patient.
The first medical
application utilized x-rays for forming images of tissues based on their x-ray attenuation coefficient.
More recently, however, medical imaging has also been successfully accomplished with
radioisotopes, ultrasound, and magnetic resonance, the imaged properties being different in each
There are numerous nonmedical imaging applications which lend themselves to the methods
of computerized tomography.
Researchers have applied this methodology to the mapping of
underground resources via crossborehole imaging, some specialized cases of cross-sectional
imaging for nondestructive testing, the determination of the brightness distribution over a celestial
sphere, and three-dimensional imaging with electron microscopy.
Fundamentally, tomographic imaging deals with reconstructing an image from its
In the strict sense of the word, a projection at a given angle is the integral of the image
in the direction specified by that angle, as illustrated in Fig. 1.
However, in a loose sense,
projection means the information derived from the transmitted energies, when an object is
illuminated from a particular angle; the phrase "diffracted projection" may be used when energy
sources are diffracting, as is the case with ultrasound and microwaves.
Although, from a purely mathematical standpoint, the solution to the problem of how to
reconstruct a function from its projections dates back to the paper by Radon in 1917, the current
excitement in tomographic imaging originated with Hounsfield's invention of the x-ray computed
tomographic scanner for which he received a Nobel prize.
He shared the prize with Allan Cormack
who independently discovered some of the algorithms.
His invention showed that it is possible to