A sparse equivalent source method for near-field acoustic holography

This study examines a near-field acoustic holography method consisting of a sparse formulation of the equivalent source method, based on the compressive sensing (CS) framework. The method, denoted Compressive-Equivalent Source Method (C-ESM), encourages spatially sparse solutions (based on the superposition of few waves) that are accurate when the acoustic sources are spatially localized. The importance of obtaining a non-redundant representation, i.e., a sensing matrix with low column coherence, and the inherent ill-conditioning of near-field reconstruction problems is addressed. Numerical and experimental results on a classical guitar and on a highly reactive dipole-like source are presented. C-ESM is valid beyond the conventional sampling limits, making wide-band reconstruction possible. Spatially extended sources can also be addressed with C-ESM, although in this case the obtained solution does not recover the spatial extent of the source.