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

TL;DR

This paper introduces a sparse superposition method combined with l1 optimisation for near-field acoustic holography, achieving more accurate and sparse reconstructions of structural vibrations from limited acoustic data.

Contribution

It presents a novel approach that produces sparser, more accurate reconstructions compared to traditional methods, with potential benefits in data efficiency and source identification.

Findings

Sparse solutions often use only a small fraction of data points

Improved reconstructions with reduced data sets

Enhanced numerical methods and broader applications

Abstract

The method of superposition is proposed in combination with a sparse $\ell_1$ optimisation algorithm with the aim of finding a sparse basis to accurately reconstruct the structural vibrations of a radiating object from a set of acoustic pressure values on a conformal surface in the near-field. The nature of the reconstructions generated by the method differs fundamentally from those generated via standard Tikhonov regularisation in terms of the level of sparsity in the distribution of charge strengths specifying the basis. In many cases, the $\ell_1$ optimisation leads to a solution basis whose size is only a small fraction of the total number of measured data points. The effects of changing the wavenumber, the internal source surface and the (noisy) acoustic pressure data in general will all be studied with reference to a numerical study on a cuboid of similar dimensions to a typical loudspeaker cabinet. The development of sparse and accurate reconstructions has a number of advantageous consequences including improved reconstructions from reduced data sets, the enhancement of numerical solution methods and wider applications in source identification problems.