Representation, sampling and reconstruction of sparse signals has been an exciting and active area of research in signal processing for over a decade. Sparse support recovery techniques have gained popularity in the signal processing community for their capability to recover the sparsest solution to a linear underdetermined system Ax = y; where the measurement matrix A 2 CN, M < N, is fat. An immediate extension of such a model is that of Multiple Measurement Vectors (MMV) where a number (say, L) of unknown vectors share the same sparse support. Such signal models arise in a number of practical situations, such as data obtained from an array of sensors, MRI imaging, channel estimation etc. A wide variety of algorithms exist in literature for recovering the common support in the MMV model. However, for a given N, these methods so far can typically recover supports of size O(M). In this talk, we will show how prior knowledge on the correlation structure of the measurement vectors can drastically improve this bound. Direct exploitation of the correlation present in data has been largely ignored by most existing approaches for support recovery. To bridge this gap, we will develop the theory for Correlation Aware Support Recovery and demonstrate that under certain conditions on the statistics of the unknown vectors and the measurement matrix, it is fundamentally possible to increase the recoverable sparsity level to as large as O(M^2), in the limit as L-> infinity.
Piya Pal is a graduate student in the Department of Electrical Engineering at California Institute of Technology (Caltech), Pasadena, CA, working in the Digital Signal Processing Lab, supervised by Prof. P. P. Vaidyanathan. She received the B. Tech degree in Electronics and Electrical Communication Engineering from Indian Institute of Technology, Kharagpur in 2007 and the M.S. degree in Electrical Engineering from Caltech in 2008. Her research interests include statistical signal processing, sparse sampling and reconstruction techniques, optimization, and sensor array processing. She received the Best Student Paper Award at the 14th IEEE DSP Workshop, 2011 held at Sedona, Arizona, USA. She was also one of the recipients of the Student Paper Award at the 45th Asilomar Conference on Signals, Systems and Computers, 2011 held at Pacific Grove, California, USA.