Wouldn’t X-Ray vision be useful? (Superman agrees). If we could see the inner working of a body be it a human body or a mass of earth or rock, we would save a lot of anguish. Believe it or not this idea is already being realised in Electrical Impedance Tomography (EIT), where electrical fields are passed through a body. By collecting data around the edge we can try to piece together the electrical properties inside the body. Similar techniques are used in ultrasound and cat scans of the brain . However, reconstructing the inside picture from data on the edge is not always straight-forward.

Mathematically it resembles calculating the entries in a matrix given only the sum of the rows and columns. For a two by two matrix if we know a+b, c+d, a+c and b+d we can work out a, b, c and d (4 equations and 4 unknowns). But will it work for a 3 by 3 matrix? Often only a partial reconstruction is possible, and some other insights into the problem are required.

Catherine Belward at the University of Queensland is developing a numerical method for imaging the inside of a pipe. This will help engineers understand what is happening inside pipes as various materials are passed through them. Electrical field theory gives a first guess to the electrical properties inside the pipe. But it is not accurate enough, so Catherine has written a computer program that compares the results from the theory with the actual data and uses this to adjust her initial guess. If it is not sufficiently accurate the program repeats the process until it is. This reconstruction process is computationally intensive and requires high powered computers as well as some clever mathematical programming. The end product is a picture of the cross section of the pipe just as if it had been cut in two and gives us an insight into how the materials inside a pipe behave.