# Speeding Medical Images

### From Mathsreach

**Download article: Speeding Medical Images**(IMAges Issue 10: March 2011)

MRI scans are one of the most important diagnostic techniques

that doctors can use, but it is very expensive technology, partly due

to the time it takes to produce and analyse such complex images.

Mathematics provides the central algorithms for analysing and

reconstructing the images in real time.

Sequential Forward Selection, force a compromise between analytical

speed and image quality.

Tappenden and supervisor, Associate Professor Ian Coope at the University of

Canterbury, chose this issue for her PhD as “the most interesting that uses the skill base

I have – linear algebra and optimisation,” she says.

approximation criteria, like the L1 norm, may be useful. The images are compressed before

processing using Fourier methods, but recent techniques such as compressed sensing are

also being explored as an alternative. MRI data comes in the form of a matrix

but it is not feasible to look at every combination of rows. “An existing criterion

uses the trace of the matrix,” says Tappenden, “whereas we’ve created an algorithm

which uses the determinant criterion to choose an optimal subset of rows to give an

accurate image.” Her paper was published in September in the IEEE journal Transactions

on Image Processing. The algorithms will be implemented by the engineers who

programme the machines.

Tappenden has also written some algorithms to reconstruct MRI scans from sparse

data sets. “If you have some conditions on the image – lots of zeros and few nonzeroes

– then you can do a really good reconstruction with only a tiny bit of data.

These are optimisation problems with some really nice properties.”