Regularization methods for near-field acoustical holography.
Regularization methods for near-field acoustical holography.
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DOI：
10.1121/1.1404381
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发表时间：
2001-10
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影响因子：
--
通讯作者：
E. Williams
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文献类型：
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作者：
E. Williams
由近场声全息（NAH）从振动结构附近的压力测量中重建压力和法向表面速度是一个线性的、不适定的反问题，这是由于存在强衰减的、类倏逝波。正则化提供了一种克服不适定性的技术，并以自动化的方式生成线性问题的解决方案。我们提出了四个强大的正则化方法，标准的Tikhonov过程沿着一个新的改进版本，Landweber迭代，共轭梯度法。这些方法中的每一种都可以应用于所有形式的内部或外部NAH问题;平面，圆柱，球形和共形。我们还研究了两个参数选择程序，Morozov差异原则和广义交叉验证，这是至关重要的任何正则化理论。特别是，我们集中在这里的平面和柱面全息。这些形式的NAH依赖于离散傅立叶变换是重要的，因为它们的流行性和巨大的计算速度。为了使用正则化理论的可分离的几何问题，我们重新制定的平面，圆柱形和球形NAH的方程到一个特征值问题。由此产生的特征值和特征向量很容易耦合到正则化理论，这可以被纳入NAH软件，在计算速度上几乎没有牺牲。由此产生的完全自动化的NAH算法的可分离和不可分离的几何克服了NAH的最后一个重大障碍。
The reconstruction of the pressure and normal surface velocity provided by near-field acoustical holography (NAH) from pressure measurements made near a vibrating structure is a linear, ill-posed inverse problem due to the existence of strongly decaying, evanescentlike waves. Regularization provides a technique of overcoming the ill-posedness and generates a solution to the linear problem in an automated way. We present four robust methods for regularization; the standard Tikhonov procedure along with a novel improved version, Landweber iteration, and the conjugate gradient approach. Each of these approaches can be applied to all forms of interior or exterior NAH problems; planar, cylindrical, spherical, and conformal. We also study two parameter selection procedures, the Morozov discrepancy principle and the generalized cross validation, which are crucial to any regularization theory. In particular, we concentrate here on planar and cylindrical holography. These forms of NAH which rely on the discrete Fourier transform are important due to their popularity and to their tremendous computational speed. In order to use regularization theory for the separable geometry problems we reformulate the equations of planar, cylindrical, and spherical NAH into an eigenvalue problem. The resulting eigenvalues and eigenvectors couple easily to regularization theory, which can be incorporated into the NAH software with little sacrifice in computational speed. The resulting complete automation of the NAH algorithm for both separable and nonseparable geometries overcomes the last significant hurdle for NAH.