频域振动声成像逆问题的近轴方法
A paraxial approach for the inverse problem of vibro-acoustic imaging in frequency domain
AI总结：
针对振动声成像的建模与参数反演问题，本文提出基于二阶波动方程、微扰和近轴变换的建模方法，并采用Landweber-Kaczmarz方法求解逆问题以重建感兴趣区域的空间图像。
摘要：
本文提出了一种用于vibro-acoustography（振动声成像）的近轴建模方法，vibro-acoustography是一种高频超声成像技术，它利用受激的低频场来获得更高的分辨率，同时避免散斑。我们从一般的二阶波动方程出发，引入二阶微扰，并利用近轴变量转换来过渡到定向波束。根据二阶微扰与波束指向性之间的关系，这会导出不同的偏微分方程（PDE）系统，这些系统包含一个空间可变参数，该参数控制入射波束的相互作用以产生传播的声场。随后我们研究了其中一个模型下确定该参数的逆问题，为此我们提出了Landweber-Kaczmarz重建方法，以获取感兴趣区域的空间图像。
英文摘要：
This paper presents a paraxial modeling approach for vibro-acoustography, a high-frequency ultrasound imaging technique that makes use of the excited low-frequency field to achieve a higher resolution while avoiding speckles. We start from a general second order wave equation, introduce a second order perturbation and make use of a paraxial change of variables to pass over to directed beams. Depending on the relation between the second order perturbation and the directivity of the beams this leads to different systems of PDEs that involve a spatially variable parameter governing the interaction of the incoming beams to generate the propagating acoustic field. We then consider the inverse problem of determining this parameter for one of these models where we present a Landweber-Kaczmarz reconstruction method to obtain a spatial image of the region of interest.
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