UBC Math Department Colloquium: Rayan Saab

We discuss two related problems that arise in the acquisition and processing of high-dimensional data. First, we consider distance-preserving fast binary embeddings. Here we propose fast methods to replace points from a set \mathcal{X} \subset \R^N with points in a lower-dimensional cube \{\pm 1\}^m, which we endow with an appropriate function to approximate Euclidean distances in the original space.

Second, we consider a problem in the quantization (i.e., digitization) of compressed sensing measurements. Here, we deal with measurements arising from the so-called bounded orthonormal systems and partial circulant ensembles, which arise naturally in compressed sensing applications. In both these problems we show state-of-the art error bounds, and to our knowledge, some of our results are the first of their kind.