Localizing multiple sound sources in reverberant environments is a challenging problem in acoustic signal processing. A room with strong reverberation will cause sounds to reflect off the walls, which makes localization difficult compared to localizing sources in a completely anechoic environment. Instead of using traditional methods involving a single sensor, this thesis focuses on leveraging the many microphones that can be found in our modern-day environment. When we approach source localization and separation with a distributed set of microphones, we can frame a joint-sparsity problem where we wish to solve for source signals and positions with the knowledge of having many more microphones and potential source locations than actual sources. Once we frame the problem as a joint-sparsity problem, we can employ traditional sparse recovery approaches used in compressive sensing to solve for the source locations. This thesis mainly looks at the greedy matching pursuit algorithm Compressive Sampling Matching Pursuit (CoSaMP) that solves a mixed l1-l2 norm minimization problem to solve for source locations. CoSaMP is tested through acoustic simulations and a physical lab experiment.
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