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The method of superposition is proposed in combination with a sparse $\ell_1$optimisation algorithm with the aim of finding a sparse basis to accuratelyreconstruct the structural vibrations of a radiating object from a set ofacoustic pressure values on a conformal surface in the near-field. The natureof the reconstructions generated by the method differs fundamentally from thosegenerated via standard Tikhonov regularisation in terms of the level ofsparsity in the distribution of charge strengths specifying the basis. In manycases, the $\ell_1$ optimisation leads to a solution basis whose size is only asmall fraction of the total number of measured data points. The effects ofchanging the wavenumber, the internal source surface and the (noisy) acousticpressure data in general will all be studied with reference to a numericalstudy on a cuboid of similar dimensions to a typical loudspeaker cabinet. Thedevelopment of sparse and accurate reconstructions has a number of advantageousconsequences including improved reconstructions from reduced data sets, theenhancement of numerical solution methods and wider applications in sourceidentification problems.

On sparse reconstructions in near-field acoustic holography using the method of superposition