Theme Editor's Introduction: Computational Inverse Problems in Medicine

• Authors: Christopher R. Johnson
• Venue: IEEE Computational Science & Engineering
• Year: 1995

Inverse methods are the opposite of prediction. They're a little like imitating the great detective Sherlock Holmes except that the math is more complicated. Basically, you carefully study the evidence of the scene and from it try to infer who was there and what happened. To do this you might simply observe, but more likely, you will poke or tap at the scene--send various signals through it, for instance, and take sensitive detector readings of what happens to them.Then, fitting the evidence to your knowledge of how the world works and your common sense, you figure out what must have occurred, even though you were not an eyewitness. You essentially throw out all scenarios that are impossible (mathematicians call this constraining the problem), and whatever is left, however improbable, must be the truth. The difficulty comes when the evidence is so inconclusive or sparse or smooth that almost anything could have happened--or at least a very wide range of things--and still produced the same result. Mathematicians call this "ill-posed."Introducing this first of various theme sections that IEEE CS&E will carry from time to time, Chris Johnson explains some of the mathematical and computational techniques that have been devised to solve inverse problems, which are closely related to remote sensing, imaging, and the whole business of parameter estimation in science and engineering. He touches on the vast generality of the subject, and some of the specific uses it is put to, especially in medicine. Though the theme articles focus on a particular branch of inverse problem-solving, a look at the diversity of the references Johnson cites gives a small taste of the interdisciplinary usefulness of the technique as a whole, and underscores an underlying purpose of this publication: that CSE practitioners can learn much from each other across discipline boundaries.