Two and three-dimensional sparse models for compressed sensing in multiple sound zones

To create multiple sound zones, it is often necessary to get a measure of room impulse responses of a region of interest to devise an accurate corrective measure. Often in practice it is not feasible to measure the required physical values of the soundfield. Compressed sensing can provide a practical and cost-effective solution to obtain input value at any location in a domain. The whole soundfield in a domain can be modeled by a sparse set of two or three-dimensional basis functions. The sparse model parameters are then estimated via L1–norm minimization, providing a spatially sparse representation of the soundfield. The estimated room responses are then used to derive the required loudspeaker filter functions to create the optimized multiple sound zones. The experimental results report that in general reverberant conditions the two and three-dimensional models allow for the accurate estimation of the room impulse responses, especially up to 500 Hz. It is shown that the three-dimensional models can decrease the estimation error under certain conditions. As a result, the performance of the sound zone system could be improved through a full continuous broadband spectrum of frequency from 300 to 3000 Hz using a significantly reduced amount of inputs.