Compressed Sensing or sparse signal processing is the process of estimating sparse vectors using significantly fewer measurements. Mathematically, this corresponds to solving an underdetermined system of linear equations under the constraint that the solution is sparse. Many techniques have been developed to solve this problem. We focus on sparse Bayesian learning (SBL) which is based on the Bayesian framework and its variations. We apply SBL for parameter estimation tasks such as direction-of-arrival estimation.

We are interested in the localization and tracking of multiple sources based on microphone array recordings. We use compressive sensing methods such as SBL for localization which provide high resolution. The challenges include presence of ambient noise, tracking using speech signals which are intermittent and highly non-stationary, and varying number of sources.

Many commonly used arrays such as uniform linear arrays and uniform rectangular arrays have a lot of redundancy for tasks such as direction-of-arrival (DOA) estimation. Specifically designed arrays called sparse arrays can significantly reduce the number of sensors required for the same task. Additionally they can also resolve more sources than the number of sensors. Examples of sparse arrays are co-prime and nested arrays. We work on combining sparse arrays with compressive sensing techniques for DOA estimation application.

Unlike traditional signals which are defined as functions of time or space, graph signals are defined over the irregular domain of graph. The recently emerging field of graph signal processing (GSP) aims to develop tools and algorithms to process graph signals which take into account its unique structure. We are interested in exploring GSP techniques for extracting useful information from sensor network data.