The last decade has seen numerous advances in sparsity-based signal processing methods. Sparsity is usually invoked through the formulation of an inverse problem with suitably designed regularization terms. Many signal processing applications (eg. source separation, deconvolution, super-resolution, tomography, and nonlinear component analysis) can be expressed as inverse problems within an optimization framework. In this talk, I will be discussing the theory of the formulation of inverse problems within an optimization framework and their application to the problems of signal separation and estimation in the field of audio processing, radar and sleep EEG analysis. I will also briefly discuss the open problems and current trends relating to the topics above. This work was supported by the National Science Foundation (NSF), USA, under grant no. CCF-1010820 and has been published in peer reviewed conferences and journals.
Ankit Parekh received his B.S. in Computer Engineering, M.S. in Applied Mathematics from School of Engineering, New York University (then called Polytechnic Institute of New York University). He is currently in his final year of PhD in Applied Mathematics with the School of Engineering, New York University and is also a Lecturer with the Department of Mathematics at School of Engineering. His current research interests are in sparse signal and image processing, bio-medical signal processing, and optimization. He currently collaborates with the Division of Pulmonary, Critical Care and Sleep Medicine at NYU School of Medicine for applications of signal processing to sleep EEG and with the Electrical and Computer Engineering Department at NYU with funding from the National Science Foundation.