Mathematics & Statistics Colloquium – Dr. Leonid Kunyansky
- Colloquium 4:00-5:00 p.m., Neill Hall 5w |
- Open Discussion and Refreshments 3:30 - 4:00 p.m., Neill Hall 216 (Hacker Lounge) |
- Zoom Meeting ID: 917 5509 6307 |
- Zoom Meeting Passcode: 033186
About the event
Hybrid Imaging Modalities and the Range of the Spherical Means Transform
Abstract: The last two decades saw proliferation of novel coupled-physics imaging modalities. A variety of sensitive but safe and inexpensive medical imaging methods has been developed, that hold great promise for the breast imaging for cancer, detection of ischemia, hemorrhaging, blood clots, etc. These imaging techniques work by combining high-resolution ultrasound with electromagnetic fields that are highly sensitive to the features of interest. In the first part of my talk I will overview the most interesting of these modalities, with emphasis on the underlying mathematics.
Inevitably, the introduction of the new techniques has posed a variety of new and exciting inverse problems. In particular, a prominent role in this field is played by the spherical means operator, that maps a function into a collection of integrals over spheres with centers lying on a given surface. The problem I will discuss is the description of the range of this operator. As it happens, all of the classical results are suboptimal, in that they use twice the amount of needed data. I will present a novel range description, that overcomes this issue.
(This is a joint work with Peter Kuchment, Texas A&M University)
Speaker Bio: Dr. Leonid Kunyansky is a Professor of mathematics at the University of Arizona and and received his Ph.D. of Applied Mathematics from Wichita State University. He is a member of the BIO5 Institute and a member of the Graduate Interdisciplinary Program at the University of Arizona.