A closed-form method of spatial de-aliasing for multiple speech source localization

The sparsity-based methods are widely used to localize multiple speech sources because of its high computational efficiency. But spatial aliasing is a challenging issue for sparsity-based speech source localization. For a pair of widely spaced microphones, there may be several candidates of time delays corresponding to a given phase difference in some high frequencies. Especially for planar arrays, there may exist a large number of possible combinations of these time-delay candidates across all microphone pairs. The purpose of spatial de-aliasing is to determine the number of aliasing periods, and select the most optimal combination from those aliasing combinations. This paper proposes a closed-form method of spatial de-aliasing for planar arrays. The convex cost function is defined as the weighted error function of the numbers of aliasing periods. The solutions to the numbers of aliasing periods is given by minimizing the cost function. The proposed method was evaluated in a simulated environment. The experimental results confirmed that the proposed method can well treat spatial aliasing.