Rayan’s work is on the mathematics of information, data, and signals. His research is broadly motivated by problems in the acquisition, digitization, and processing of data. For example, he is interested in sampling and quantization, compressed sensing, sparse and low-dimensional representations of data, as well as inverse problems like phase retrieval and blind source separation.

Before joining UCSD as an assistant professor in 2013, he was a visiting assistant professor and a Banting postdoctoral fellow at Duke University (2011-2013). Before that, he completed his PhD at the University of British Columbia in 2010, where he was a member of the Institute of Applied Mathematics.