Hearing behind walls: Localizing sources in the room next door with cosparsity

Acoustic source localization is traditionally performed using cues such as interchannel time of arrival and intensity differences to infer the geometric localization of emitting sources with respect to the receiving microphone array. However the presence of obstacles between the sources and the array makes it impossible to rely on the direct path, and more advanced techniques are needed. The huge body of work on sparse recovery suggests an approach where source localization is expressed as a linear inverse problem and the spatial sparsity of the sources is exploited. An inverse problem can be naturally expressed in the recently introduced cosparse framework, exploiting the fact that the acoustic pressure satisfies the homogeneous wave equation except in the few locations of the sources. The resulting optimization problem involves a discretized second derivative analysis operator, which is extremely sparse. In this paper, we demonstrate the performance of the cosparse approach on an extreme source localization problem, where the microphone array is installed in the room next door to the room where the emitting sources are located, somehow hearing behind a wall.