(1) From 1st – 6th October I will be attending Sequences and Their Application (SETA) held at the HKUST Institute for Advanced Study in Hong Kong. During the conference, I will be presenting my paper “On Regular Schemes and Tight Frames”. The abstract is below, the paper can be found here.
Title: On Regular Schemes and Tight Frames
Abstract: Finite frames are sequences of vectors in finite dimensional Hilbert spaces that play a key role in signal processing and coding theory. In this paper, we study the class of tight unit-norm frames for C d that also form regular schemes, called tight regular schemes (TRS). Many common frames that arise in applications such as equiangular tight frames and mutually unbiased bases fall in this class. We investigate characteristic properties of TRSs and prove that for many constructions, they are intimately connected to weighted 1-designs—arising from quadrature rules for integrals over spheres in Cd —with weights dependent on the Voronoi regions of each frame element. Aided by additional numerical evidence, we conjecture that all TRSs in fact satisfy this property.
(2) Next month from the 18-22 November 2018 along with speakers including Petar Popovski, I will be lecturing in the 1st Winter School on Information Theory and Signal Processing for Internet of Things. If you are a PhD student interested in these subjects, please see here for registration information.