Laboratoire d'Acoustique de l'Université du Maine (LAUM Unité Mixte de Recherche-CNRS 6613), avenue O. Messiaen, 72085 Le Mans Cedex 09, France.
J Acoust Soc Am. 2011 Jun;129(6):3777-87. doi: 10.1121/1.3586790.
Near-field acoustic holography is a measuring process for locating and characterizing stationary sound sources from measurements made by a microphone array in the near-field of the acoustic source plane. A technique called real-time near-field acoustic holography (RT-NAH) has been introduced to extend this method in the case of nonstationary sources. This technique is based on a formulation which describes the propagation of time-dependent sound pressure signals on a forward plane using a convolution product with an impulse response in the time-wavenumber domain. Thus the backward propagation of the pressure field is obtained by deconvolution. Taking the evanescent waves into account in RT-NAH improves the spatial resolution of the solution but makes the deconvolution problem "ill-posed" and often yields inappropriate solutions. The purpose of this paper is to focus on solving this deconvolution problem. Two deconvolution methods are compared: one uses a singular value decomposition and a standard Tikhonov regularization and the other one is based on optimum Wiener filtering. A simulation involving monopoles driven by nonstationary signals demonstrates, by means of objective indicators, the accuracy of the time-dependent reconstructed sound field. The results highlight the advantage of using regularization and particularly in the presence of measurement noise.
近场声全息技术是一种通过在声源平面的近场中使用麦克风阵列进行测量，来定位和描述稳定声源的测量方法。为了将该方法扩展到非稳定声源的情况，引入了一种称为实时近场声全息（RT-NAH）的技术。该技术基于一种在时间波数域中使用卷积积与脉冲响应来描述时变声压信号在正向平面上传播的公式。因此，通过反卷积来获得压力场的反向传播。在 RT-NAH 中考虑消逝波可以提高解的空间分辨率，但会使反卷积问题“不适定”，并且常常产生不合适的解。本文的目的是专注于解决这个反卷积问题。比较了两种反卷积方法：一种使用奇异值分解和标准的 Tikhonov 正则化，另一种基于最优维纳滤波。涉及由非稳定信号驱动的单极子的模拟通过客观指标演示了时变重建声场的准确性。结果突出了使用正则化的优势，特别是在存在测量噪声的情况下。
