IBM Research Award 2015 - Reza Parhizkar
Euclidean Distance Matrices: Properties, Algorithms and Applications, EPFL thesis n° 5971 (2013)
Thesis director: Prof. M. Vetterli
“For his contributions in providing a unified theoretical framework for the use of Euclidean distance matrices and developing efficient algorithms to address important practical problems in medical imaging, acoustics and room geometry estimation.”
Euclidean distance matrices (EDMs) are central players in many diverse fields including psychometrics, NMR spectroscopy, machine learning and sensor networks. However, they are not often exploited in signal processing. In this thesis, we analyze attributes of EDMs and derive new key properties of them. These analyses allow us to propose algorithms to approximate EDMs and provide analytic bounds on the performance of our methods. We use these techniques to suggest new solutions for several practical problems in signal processing. Together with these properties, algorithms and applications, EDMs can thus be considered as a fundamental toolbox to be used in signal processing and other fields of engineering.