A Compressive Sensing Approach for the Reconstruction of the Soundfield Produced by Directive Sources in Reverberant Rooms

State-of-the-art soundfield reconstruction methods are computationally expensive and their performance is generally undermined by the presence of strong reverberation and of near-field sources, which are usually modeled using omnidirectional radiation patterns. In this work, we propose a compressive sensing approach for the reconstruction of the soundfield produced by arbitrary directive sources in a reverberant room. Assuming sparsity in the distribution of sources, along with a loose prior knowledge on their position and on the geometry of the environment, we reconstruct both the direct and the reverberant components of the soundfield by modeling early reflections as near-field sources. Moreover, the directivity of sources is explicitly modeled by first expressing the soundfield produced by arbitrarily directive sources as an expansion of multipoles, and then introducing group sparsity constraints. Numerical simulations in two rooms with different reverberation characteristics are conducted to perform the validation of the proposed method.