Speaker: Ben Adcock
Location: ESB 4133 (PIMS Lounge)
Intended Audience: Public
Compressed sensing concerns the recovery of signals and images from seemingly incomplete data sets. Introduced nearly a decade ago, it has since become an intensive area of research in applied mathematics, engineering and computer science. However, many practical problems in which compressed sensing is applied, e.g. medical imaging, are not adequately explained by existing theory. In this talk I will present a new framework for compressed sensing that bridges this gap. This framework is based on replacing some of the standard principles of compressed sensing with new local notions; specifically, sparsity in levels, local coherence in levels and multilevel random subsampling. When combined, they lead to near-optimal recovery guarantees that explain the effectiveness of compressed sensing in such applications. Moreover, this framework is not just useful in understanding existing compressed sensing approaches. In the final part of this talk I will demonstrate how leveraging local sparsity through appropriately-designed locally incoherent sensing matrices also leads to substantially improved compressed sensing algorithms in a range of other applications.