This paper investigates the source reconstruction problem in underwater mediums using a compressive Near-Field Electromagnetic Holography (NEH) approach. More specifically we investigate the use of ℓ1 regularization for the purpose of decomposing near-field magnetic and/or electric surface measurements into electric and magnetic dipole sources. Our study indicates that not only do ℓ1 decompositions enable much higher resolution of sources than traditional ℓ2 approaches, but important features of the dipoles are preserved in the reconstruction. Our hypothesis are supported by numerical experiments as well as underwater physical measurements obtained in an earth field simulator facility.
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