Soundfield Reconstruction in Reverberant Rooms Based on Compressive Sensing and Image-Source Models of Early Reflections

The estimation of the soundfield in locations different from the measurement points in a room is a complex problem widely discussed in the literature. One of the key challenges in virtual acoustics is soundfield reconstruction in environments characterized by nearfield sources and strong reverberation. Most of the existing solutions are computationally expensive and they often just achieve the reconstruction of the direct soundfield. Considering a sparse distribution of acoustic sources in a room and a compressive sensing framework, in this work, we propose a method that targets the reconstruction of both the direct and the reverberant soundfield by explicitly modeling early reflections as near-field sources. We show how, by exploiting some loose prior knowledge on the position of the source and the geometry of the environment, the computational complexity can be reduced, while ensuring robustness to errors in the prior knowledge. The proposed method is validated through simulations.