Tutorial 11: Microlocal Analysis in Imaging

Presented by

B. Yazici, V. Krishnan, M. Cheney

Abstract

Multiple advances in diverse fields are expected to transition scattered-field-based sensing and imaging technology from a dedicated single sensor requiring an operator to a large number of small sensors operating autonomously. Such a swarm of sensors is expected to provide orders-of-magnitude performance gains relative to a single, dedicated sensor. They are also expected to operate in complex environments involving dynamically changing scenes and multiple scattering. Such imaging systems pose a number of challenges to image formation in addition to those involving wave propagation in complex environments. These challenges require reconstruction algorithms to be fast, decentralized, and be able to handle non-ideal imaging conditions including incomplete data, arbitrary sensor positions, multiple scattering, clutter and noise.

This tutorial will show that many challenging image formation problems including those in RF, acoustic, seismic and medical imaging can be posed as an inversion of a Fourier Integral Operator (FIO).

Microlocal analysis is the mathematical study of FIOs, singularities and associated high-frequency structures. This theory is important for imaging, because it provides approximate inverses to FIOs that can be made computationally efficient and adaptive to accommodate non-ideal imaging conditions. Additionally, it provides a geometric insight into challenging imaging problems that cannot be obtained by statistical signal processing or algebraic approaches alone.

Speaker Biography

Birsen Yazıcı received BS degrees in Electrical Engineering and Mathematics in 1988 from Bogazici University, Istanbul Turkey and MS and Ph.D. degrees from Mathematics and Electrical Engineering in 1990 and 1994, respectively both from Purdue University, W. Lafayette IN. From September 1994 until 2000, she was a research engineer at the General Electric Company Global Research Center, Schenectady NY. During her tenure in industry, she worked on radar, transportation, industrial and medical imaging systems. Her work on industrial systems received the 2nd best paper award in 1997 given by IEEE Transactions in Industrial Applications. In 2003, she joined Rensselaer Polytechnic Institute where she is currently an associate professor in the Department of Electrical, Computer and Systems Engineering and in the Department of Biomedical Engineering. Her research interests span the areas of statistical signal processing, inverse problems in imaging, biomedical optics, and radar. She is the recipient of the Rensselaer Polytechnic Institute 2007 School of Engineering Research Excellence Award. She holds 11 US patents.

Margaret Cheney is a Professor of Mathematics at Rensselaer Polytechnic Institute. After receiving her Ph.D. in 1982 from Indiana University, she held positions at Stanford University and Duke University before moving to RPI. She has held visiting appointments at NYU's Courant Institute (1987-1988) at the Minnesota Institue for Mathematics and Its Applications (1994-1995, 1997, and 2005), the Berkeley Mathematical Sciences Research Institute (2001), the Naval Air Warfare Center Weapons Division (2002), the UCLA Institute for Pure and Applied Mathematics (2003), and the Air Force Research Laboratory (2007-2008). Most of her work has been on the inverse problems that arise in quantum mechanics, acoustics, and electromagnetic theory; since 2001, she has been working on radar imaging.

Cheney has received several awards, including the Office of Naval Research Young Investigator Award in 1986, a National Science Foundation Faculty Award for Women in Science and Engineering in 1990, the Lise Meitner Visiting Professorship at Lund Institute of Technology in 2000, and a National Research Council fellowship in 2007.She is a Fellow of the Institute of Physics, has served on the SIAM Board of Trustees, and currently serves on the editorial boards of four journals.

Venky Krishnan is a post-doctoral research associate in the Department of Electrical, Computer and Systems Engineering working with Birsen Yazici. He received his Master of Science degree in Mathematics from Pondicherry University, India and Ph D in Mathematics from the University of Washington, Seattle in 2007 under the guidance of Gunther Uhlmann. His research interests are in the fields of image reconstruction, integral geometry on Riemannian manifolds, inverse problems and microlocal analysis.