Research

I am interested in random matrix questions arising in Compressed Sensing (CS). Compressing Sensing is a new paradigm in signal processing were signals are measured at the information (compressed) rate as opposed to traditionally measuring signals at the Nyquist rate. CS is therefore very beneficial where taking fewer measurements greatly save cost and time like in medical imaging or the storage or transmission of signals in telecommunication.

Most of the analysis in CS use the Restricted Isometry Constant (RIC) of the sensing matrix. The computation of RIC for deterministic matrices is intractable but it is possible to compute RIC bounds for some random ensembles. Results of my work include the derivation of the sharpest RIC bounds for Gaussian random matrix published in the paper that won the 2010 Best SIAM Student Paper Award (see publications); and the derivation of asymptotic approximations of these RIC bounds with simpler functions.

My work involves ideas and tools from a range of areas in mathematics including linear algebra, combinatorics, graph theory, probability, optimization and numerical analysis. In my work I do both the mathematical analysis and the numerical computation using Matlab.

I have a repository of codes that I used for the numerical results in my publication and are being used for the calculation of RIC bounds in the Edinburgh Compressed Sensing Group research webpage. These codes can be made available upon request.

SMSTC

The Scottish Mathematical Sciences Training Centre (SMSTC) courses are first year PhD coursework for students in Scotland. I took Mathematical Models and Probability streams (courses).