随机波导中源成像的定量研究
A quantitative study of source imaging in random waveguides
AI总结：
本文研究了随机扰动波导中远程源相干阵列成像的限制，提出通过优化图像质量度量来缓解边界散射，指出介质扰动更难抑制，需采用更复杂的非相干方法。
摘要：
我们对随机扰动波导中远程源相干阵列成像进行了定量研究。研究了边界和介质扰动对成像过程的远距离累积散射影响。证明通过增强数据相干部分的滤波器可缓解边界散射效应。滤波器通过优化图像质量度量获得。指出在这样的波导中，图像鲁棒性与分辨率之间存在最优折衷，可通过自适应处理数据来找到。介质扰动的远距离散射比随机扰动边界更难抑制。相干成像方法不适用，需采用基于能量传输模型的更复杂非相干方法。此类方法在有扰动边界的波导中并不需要。通过严格渐近随机分析波场，解释了所有这些事实。还分析了自适应相干成像方法，并与数值模拟结果取得定量一致。
英文摘要：
We present a quantitative study of coherent array imaging of remote sources in randomly perturbed waveguides with bounded cross-section. We study how long range cumulative scattering by perturbations of the boundary and the medium impedes the imaging process. We show that boundary scattering effects can be mitigated with filters that enhance the coherent part of the data. The filters are obtained by optimizing a measure of quality of the image. The point is that there is an optimal trade-off between the robustness and resolution of images in such waveguides, which can be found adaptively, as the data are processed to form the image. Long range scattering by perturbations of the medium is harder to mitigate than scattering by randomly perturbed boundaries. Coherent imaging methods do not work and more complex incoherent methods, based on transport models of energy, should be used instead. Such methods are nor useful, nor needed in waveguides with perturbed boundaries. We explain all these facts using rigorous asymptotic stochastic analysis of the wave field in randomly perturbed waveguides. We also analyze the adaptive coherent imaging method and obtain a quantitative agreement with the results of numerical simulations.
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