Large Structures Seminar: Padraig Ó Catháin

Compressed sensing is a technique used in signal processing to reconstruct under-sampled data, subject to the assumption that the set of signals is ‘sparse’ in some basis. It has been intensively studied in the past fifteen years or so, and lies at the interface of mathematics, statistics and electrical engineering. One of the main challenges is the construction of good matrices for use in compressed sensing.

In this talk, we will give an introduction to compressed sensing, emphasizing the relation with well-known concepts in linear algebra. We then describe a new construction for compressed sensing matrices using combinatorial designs. This construction generalises and unifies a number of results in the literature. Using results on the asymptotic existence of certain designs, we obtain new asymptotic existence results on compressed sensing matrices.