My group's applied research generally deals with structured, often high-dimensional, inference problems.  Often the quantities of interest in a particular application are known to exhibit some kind of structure (sparsity, non-negativity, smoothness, etc.).  The overall performance in these estimation tasks can be improved - often dramatically - using algorithms that leverage appropriate structural assumptions.  We have developed methods along these lines for imaging systems (including MRI), structural health monitoring, and communication systems, to name just a few.  My group's current analytical work focuses on development and theoretical analysis of algorithmic methods and optimization procedures (convex and non-convex) for problems in data science and machine learning.

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