SCIENTIFIC PROGRAMS AND ACTIVITIES

Upcoming Seminars

John Sylvester, University of Washington
The Inverse Source Problem

The inverse source problem for the Helmholtz equation seeks to recover information about a source from remote observations of its radiated field. This is a linear inverse problem, but the existence of non-radiating sources means that we must accommodate the non-uniqueness inherent in the problem. I will explain why it is theoretically possible to distinguish between "well-separated" sources (distance between supports strictly greater than diameters) and describe recent work exploring the well-posedness of "distinguishing" fields radiated by well-separated sources. Just as in inverse scattering, the restricted Fourier transform, and how it transforms with respect to translations and rotations plays a major role.

Professor Mats Gustafsson
Lund University, Sweden

Near-field Diagnostics of Antennas and Radomes

Visualization of electromagnetic fields and currents facilitates our understanding of the interaction between the fields and devices. This is easily done in numerical simulations where the electromagnetic fields can be calculated. It is very difficult in most measurement situations where the fields cannot be measured directly but must instead be reconstructed from measurements of the fields outside the region of interest. This reconstruction requires the solution of an inverse source problem. Reconstructions of field and current distributions are useful in applications such as non-destructive diagnostics of antennas and radomes and assessment of specific absorption ration (SAR) in the body due to base station radiation.
In this presentation, we show how the field and current distribution can be reconstructed and visualized from near- and far-field measurement data. We illustrate how they can be used in antenna and radome diagnostics to, for example, identify faulty components. We discuss recent developments in inverse source problems to accurately reconstruct electromagnetic fields on a surface or volume from near- and far-field measurements. We review the theory for inverse source problems, non-uniqueness, and regularization. We present formulations based on equivalent currents using integral equations and integral representations for planar, spherical, body of revolution, and general geometries.

Thursday Jan. 23
1:30 p.m.

Room 230

Martin Bauer, University of Vienna
Riemannian Geometry of Shape Spaces

I will provide an overview of various notions of shape spaces, including the space of parametrized and unparametrized surfaces. I will discuss the Riemannian metrics that can be defined thereon, and what is known about the properties of these metrics. I will put particular emphasis on the induced geodesic distance, the geodesic equation and its well-posedness, geodesic and metric completeness and properties of the curvature. In addition I will present selected numerical examples illustrating the behavior of these metrics.

Klas Modin, University of Toronto and Chalmers University of Technology, Göteborg, Sweden
Diffeomorphic Image Registration

In this informal talk, I will present the framework of "large deformation diffeomorphic metric matching". This framework is used for non-rigid registration of grey-scale images. I will focus on the underlying Riemannian geometry and the connection to fluid mechanics through Euler-Arnold equations.

Thursday July 18
2:00 p.m.

Stewart Library

Sung Ha Kang, Georgia Institute of Technoogy
Variational and RKHS Approach for Image Colorization and Segmentation

This talk will start with an introduction to image restoration, starting from Total Variation minimizing denoising, and consider inpainting and colorization problems. The term ``colorization'' was introduced by Wilson Markle who first processed the gray scale moon image from the Apollo missions. A couple of variational colorization models will be presented which demonstrate different effects. Another appeoach that uses a Reproducing Kernel Hilbert Space method will be presented for an effective colorization application. A link to image segmentation will be made through a medical image application. Image segmentation separates the image into different regions to simplify the image and identify the objects easily. The Mumford-Shah and Chan-Vese models are some of the most well-known variational models in the field. If time permits, this talk will include a model segmenting piecewise constant images with irregular object boundaries, and consider some features of multiphase segmentation.