A comparison of compressive equivalent source methods for distributed sources

Sparse sound-field reconstruction methods based on compressive sensing and the equivalent source method have gained a lot of interest in recent years, offering a wide frequency range. An irregular array must be employed, and the sound field must be representable by a sparse vector of source-model amplitudes. With few and concentrated physical sources, the sparsity assumption can be fulfilled, but distributed sources cause problems. Several methods have therefore been introduced to support sparse representation of distributed sources. One set of such methods represents the amplitude vector as a linear combination of modal amplitude distributions. In that case, the coefficient vector just has to be sparse. The present paper gives an overview of such methods, and the performance of the methods is compared based on a set of simulated measurements. Overall the modal representations work well if the true source distribution can be represented by relatively few modes. The results show that even for a vibrating plate this may not be the case if the source model size does not match the plate size and/or if a non-central plate excitation is applied. If, in addition, there are also compact sources, then the basic method without modes may be the best choice.