Localization of point sources in wave fields from boundary measurements using new sensing principle

We address the problem of localizing point sources in 3D from boundary measurements of a wave field. Recently, we proposed the sensing principle which allows extracting volumetric samples of the unknown source distribution from the boundary measurements. The extracted samples allow a non-iterative reconstruction algorithm that can recover the parameters of the source distribution projected on a 2-D plane in the continuous domain without any discretization. Here we extend the method for the 3-D localization of multiple point sources by combining multiple 2-D planar projections. In particular, we propose a three-step algorithm to retrieve the locations by means of multiplanar application of the sensing principle. First, we find the projections of the locations onto several 2-D planes. Second, we propose a greedy algorithm to pair the solutions in each plane. Third, we retrieve the 3D locations by least squares regression.