Stochastic Systems Group  

Dmitry Malioutov
SSG Master's Student
We address the problem of source localization using a novel nonparametric dataadaptive approach based on a regularized linear inverse problem solution with sparsity constraints. The notion of sparsity in this context refers to assuming a small number of sources with each source being localized spatially, which fits well into a standard source localization scenario. We express the problem in a variational framework and use a particular class of nonquadratic cost functionals which favor solutions with few nonzero entries (sparse). We present a computationally efficient technique for the numerical solution of the ensuing optimization problem.
In comparison to conventional source localization methods, the proposed approach provides increased resolution, reduced sidelobes, and offers better robustness to noise and limited number of time samples. In addition, the method works equally well for the case of coherent sources, and has a lower sensitivity to mismatches in source frequency for narrowband signals, and to the coarseness of the search grid (e.g. if the actual locations of the sources fall outside the grid of searched locations).
We will also touch upon the general problem of finding sparse representations of signals by overcomplete bases (the source localization problem formulated as a linear inverse problem can be looked at from this perspective), its motivation, some applications, and some theoretical results.
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