A Variational Approach of Waveform Design

In Tomographic Imaging Systems

Hector Morales

Universidad Autónoma Metropolitana

In this talk, we analyze the problem of optimal waveform design for imaging systems through a dispersive medium. We use a scalar model for wave propagation, together with the single-scattering approximation, and we assume that measurements are polluted with thermal noise whose statistics are known. For image formation, we use a filtered back-projection algorithm in which the filter is determined by knowledge of the power spectral densities of the scene and noise. In this framework, we derive an optimal waveform by minimizing the mean-square error of the reconstructed image. We show the simulation results for imaging point scatterers embedded in a specific dispersive background. We show that for low signal-to-noise ratios, the optimal waveform resembles what is known as a precursor: a wave generated from propagating ultrawideband waveforms through the medium.

US-Mexico WOA

The 12th US-Mexico Workshop on Optimization and its Applications will be held from January 9–January 13, 2023 at Camino Real Zaashila, Huatulco, Oaxaca, Mexico. The workshop will also hold a special dinner celebrating Stephen Wright’s (belated) 60th birthday.

Organizers

Jeff Linderoth, University of Wisconsin, Madison

Harvey D. Spangler Professor, Industrial & Systems Engineering

Jorge Nocedal, Northwestern University

Director, Center for Optimization and Statistical Learning

Walter P. Murphy Professor of Industrial Engineering and Management Sciences

Katya Scheinberg, Cornell University

Professor, Operations Research and Information Engineering

All local organization and registration was done by Eunae Jo, Northwestern University.