PIMS-UBC Distinguished Colloquium: Yaniv Plan

Random models lead to a precise and comprehensive theory of compressed sensing and matrix completion. The number of random linear measurements needed to recover a sparse signal, or a low-rank matrix, or, more generally, a structured signal, are now well understood. This is appealing in practice since it helps to determine the pros and cons of different models and gives a benchmark for success. Nevertheless, a practitioner with a fixed data set will wonder: Can they apply theory based on randomness? Is there any hope to get the same guarantees? We discuss these questions in compressed sensing and matrix completion, which, surprisingly, seem to have divergent answers.

Yaniv Plan is the 2016 winner of the PIMS UBC Math Sciences Prize