Signal processing on spherical manifolds

Dr. Jason McEwen (University College London)

APPLIED SIGNAL PROCESSING SERIES

DATE: 2013-03-13
TIME: 11:00:00 - 12:00:00
LOCATION: RSISE Seminar Room, ground floor, building 115, cnr. North and Daley Roads, ANU
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ABSTRACT:
Observations that live on a spherical manifold arise in many applications. In cosmology, for example, observations of the relic radiation of the Big Bang, the so-called cosmic microwave background (CMB), are inherently made on the celestial sphere. To analyse such data signal processing techniques defined on spherical manifolds are required. I will discuss recent advances in the area of signal processing on spherical manifolds. Firstly, I will highlight a new sampling theorem on the sphere, which reduces the spherical Nyquist sampling rate by a factor of two. I will then discuss wavelet constructions on the sphere, charting the historical development from continuous wavelet methodologies through to the scale-discretised wavelet framework that supports the exact reconstruction of signals from a discrete sampling of wavelet coefficients. I will discuss the non-trivial extension of scale-discretised wavelets to the ball, i.e. the sphere augmented with depth. Finally, I will conclude with a cosmological application of these techniques to search for cosmic strings in the CMB, a theoretically well-motivated but as yet unobserved phenomenon.
BIO:
Jason McEwen received a B.E. (Hons) degree in Electrical and Electronic Engineering from the University of Canterbury, New Zealand, in 2002 and a Ph.D. in Astrophysics from the University of Cambridge in 2006. He held a Research Fellowship at Clare College, Cambridge, from 2007 to 2008 and worked as a Quantitative Analyst from 2008 to 2010, before returning to academia in 2010. He recently held a postdoctoral position at Ecole Polytechnique Federale de Lausanne (EPFL), Switzerland, followed by a Leverhulme Trust Early Career Fellowship at University College London, where he remains as a Newton International Fellow, supported by the Royal Society and the British Academy. His research interests are focused on spherical signal processing, including sampling theorems, wavelets, compressed sensing and Bayesian statistics, and applications of these theories to cosmology and radio interferometry.