|Stochastic Systems Group|
We start by describing the problem of signalrepresentation in overcomplete bases, motivating the use of sparsity, and describing how to find a numerical solution to the problem. A direct approach involves the hard task of combinatorial optimization. However, it has been shown that under certain sparsity conditions, the problem can be replaced by tractable convex optimization (linear, quadratic or second order cone programming, depending on the circumstances) which yields the same solutions.
Next, we describe how to represent the narrowband source localization problem for sensor arrays in the above form, and present simulation results, and bias and variance analysis. Our approach is observed to have some advantages over other source localization techniques including increased resolution, no need for an accurate initialization, and improved robustness to noise, to limitations in data quantity, and to correlation of the sources.
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