Sparse Representation Using Multidimensional Mixed-Norm Penalty With Application to Sound Field Decomposition - 2018


A sparse representation methodology for multidimensional signals is proposed. In typically used group-sparse representation algorithms, the sparsity is imposed only on a single dimension and therefore the signals in the opposite dimensions are solved in the least-sq.-error sense. However, multidimensional signals can be sparse in multiple dimensions. For example, in acoustic array processing, additionally to the sparsity of the spatial distribution of acoustic sources, acoustic source signals can conjointly be sparse in the time-frequency domain. We outline a multidimensional mixed-norm penalty, which allows the sparsity to be controlled in each dimension. The majorization-minimization approach is applied to derive the optimization algorithm. The proposed algorithm has the benefits of a wide selection for the sparsity-controlling parameters, a little cost of adjusting the balancing parameters, and a coffee computational price compared with current methods. Numerical experiments indicate that the proposed methodology is also effective for application to sound field decomposition.

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