Fast wideband acoustical holography

Abstract

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.

A Compressed Equivalent Source Method Based on Equivalent Redundant Dictionary for Sound Field Reconstruction

“…where ε represents the tolerance. According to Hald [20], the constraints in Equation (14) can be adjusted, and the problem is described by Equation (15):…”

“…E. Fernandez-Grande has presented a detailed study of the compressive ESM (CESM) [18]. When the source is distributed sparsely, the CS theory can be directly applied to NAH to reduce the number of measurement points or to extend the frequency range, which has been intensively studied in many literatures [19][20][21]. When the source is not distributed sparsely (e.g., the spatially extended source), it is necessary to construct an appropriate basis or dictionary to sparsely decompose the sound field so that the sparsity condition required by the CS theory can be fulfilled.…”

Sparsely Sampled Wideband Radar Holographic Imaging for Detection of Concealed Objects

“…These results were also evaluated under sparse sampling conditions in order to demonstrate that the traditional sampling theorem is not an absolute requirement in image reconstruction of sparse target scenes. The concept has been investigated and implemented for applications in optical holography [3][4][5] and acoustic holography [6]. In the microwave regime, active millimeter-wave imaging using a continuous wave (CW) system has been developed for operating at 35 GHz [7] and at 94 GHz [8].…”

Extending the bandwidth of an acoustic beamforming array using phase unwrapping and array interpolation

“…10 These techniques do not attempt to give meaningful results above the spatial Nyquist frequency, f N , as accurate interpolation requires the array element spacing to be less than half a wavelength. 10 The most promising technique to date for increasing the bandwidth of a beamforming array involves carefully designed non-uniform microphone spacing patterns; even this technique only allows beamforming up to about 6 f N of the average spacing, 13 and does so at the cost of a significant decrease in SNR. 14 An essential element of our proposed method to extend the bandwidth above f N is phase unwrapping, which is the process of computing the absolute phase difference between signals from the ½Àp; p limited argument of the cross spectrum.…”