This research examines theoretical, algorithmic, and computational issues that arise in signal processing problems where there is a need to compute sparse solutions. There are numerous signal-processing applications where sparsity constraint on the solution vector naturally arises. Brain imaging techniques such as MEG and EEG, sparse communication channels with large delay spread, high-resolution spectral analysis, direction of arrival estimation and compressed sensing are a few examples. The generalization and extension of the sparse Bayesian learning (SBL) techniques considered in this research will broaden the application domain and provide a very powerful complement to the existing maximum a posteriori (MAP) methods commonly used and in some cases even surpass them. The investigators study extensions and generalizations of the sparse source recovery problem to greatly broaden the application domain. A key consideration in the work is developing a rigorous framework to deal with dependency in the sparsity framework. Motivated by applications with sparse but local structure, the research considers intra-vector dependency in the single measurement case, as well as intra-vector dependency as required in the multiple measurement contexts, among others. The research also includes the development of connections between multi-user communication theory and the sparse signal recovery problem to shed light on the stability with which sparse signal recovery is possible and to develop an understanding of the limits of suboptimal source recovery methods. To deal with non-stationary environments, the research develops on-line adaptive algorithms that exploit the inherent sparse structure of the application. The research also includes evaluation of the resulting algorithms in several important application domains.
Level of Effort Statement At the recommended level of support, the PI and co-PI will make every attempt to meet the original scope and level of effort of the project.
