Home Court Speaker: Anne Gelb
Professor, Department of Mathematics and Statistics, Arizona State University


Title: Shaq and the Gibbs phenomenon


Abstract: "Mr. O'Neal, may I call you Shaq? I'm Dr. Smith, the bone and joint specialist for the Lakers. I understand you are having trouble with your right knee. I viewed the MRI scan, and it appears that you have suffered serious ligament tear. Then again, it may only be a minor tear, or not a tear at all. It's hard to tell, and we can't really be sure how much fluid is built up. These MRI machines sometimes don't give completely accurate results. And after all, Mr. Shaq, you are a very large man and, well, your knees take quite a beating in your line of work. So we just can't be too sure. My suggestion is that we do some exploratory surgery. We might be able to solve your problem, assuming we find it, and anyway, the worst thing that could happen is that your out six months or so. Sorry about it being during the playoffs. What do you say?"

Shaq scratches his head and says, "Dr. Smith, I wish MRI technology would finally reach the stage where there is no more confusion regarding those pesky Gibbs ringing artifacts. Would you like me to explain what the Gibbs ringing artifacts are? Well, as any mathematician can tell you, they are oscillations, or wiggles, in images, making it difficult to distinguish the real features in the image from the mistakes that the machine makes. Let me give you an example. Do you ever download images off the internet that appear to be a little blurry? That's because of this "Gibbs phenomenon". In the case of MRI, there are so many different tissues present in each scan, that the infamous Gibbs phenomenon makes it very difficult to tell whether or not I have an actual tear or it's just the machine's error. I don't want to undergo needless surgery. I want to fix the problem with the machine!"

In this talk, we explain why these ``wiggles'' occur in MRI, or in any kind of image, and further explain how using mathematics will get rid of them. Once these techniques are incorporated into MRI technology, we can drastically improve its diagnostic ability, making it more effective and less costly, and ensuring proper treatment of patients.