Abstract

My research lies at the intersection of machine learning for high dimensional problems, signal and information processing and applications in video, big-data analytics and bio-imaging. More specifically, I have worked on designing and analyzing online algorithms for various high-dimensional structured data recovery problems and on demonstrating their usefulness in dynamic magnetic resonance imaging (MRI) and in video analytics. In the last two decades, the sparse recovery problem, or what is now more commonly referred to as compressive sensing (CS), has been extensively studied, see for example [1, 2, 3, 4, 5, 6] and later works. More recently various other structured data recovery problems, such as low-rank or low-rank plus sparse matrix recovery, have also been studied in detail. Sparse recovery or CS refers to the problem of recovering a sparse signal from a highly reduced set of its projected measurements. Many medical imaging techniques image cross-sections of human organs non-invasively by acquiring their linear projections one at a time and then reconstructing the image from these projections. For example, in magnetic resonance imaging (MRI), one acquires Fourier projections one at a time, while in Computed Tomography (CT), one acquires the Radon transform coefficients one a time. For all these applications, the ability to accurately reconstruct using fewer measurements directly translates into reduced scan times and hence sparse recovery methods have had a huge impact in these areas. Low-rank