Near-field acoustic imaging based on Laplacian sparsity

We present a sound source identification method for near-field acoustic imaging of extended sources. The methodology is based on a wave superposition method (or equivalent source method) that promotes solutions with sparse higher order spatial derivatives. Instead of promoting direct sparsity, as in standard compressive sensing or basis pursuit approaches, solutions with a piecewise constant gradient or curvature are promoted, suitable for modeling extended sources that are subject to smooth spatial variations. The obtained results are compared to Least Squares and Compressive Sensing solutions, and the validity of the wave extrapolation used for the reconstruction is examined. It is shown that this methodology can overcome conventional limits of spatial sampling, and is therefore valid for wide-band acoustic imaging of extended sources.