Fast wideband acoustical holography

Patch near-field acoustical holography methods like statistically optimized near-field acoustical holography and equivalent source method are limited to relatively low frequencies, where the average array-element spacing is less than half of the acoustic wavelength, while beamforming provides useful resolution only at medium-to-high frequencies. With adequate array design, both methods can be used with the same array. But for holography to provide good low-frequency resolution, a small measurement distance is needed, whereas beamforming requires a larger distance to limit sidelobe issues. The wideband holography method of the present paper was developed to overcome that practical conflict. Only a single measurement is needed at a relatively short distance and a single result is obtained covering the full frequency range. The method uses the principles of compressed sensing: A sparse sound field representation is assumed with a chosen set of basis functions, a measurement is taken with an irregular array, and the inverse problem is solved with a method that enforces sparsity in the coefficient vector. Instead of using regularization based on the 1-norm of the coefficient vector, an iterative solution procedure is used that promotes sparsity. The iterative method is shown to provide very similar results in most cases and to be computationally much more efficient.