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.

翻译：本文提出了一种面向振动声成像的傍轴建模方法。振动声成像是一种高频超声成像技术，通过利用激发产生的低频场在避免散斑噪声的同时实现更高分辨率。我们从一般二阶波动方程出发，引入二阶扰动项，并利用傍轴变量变换过渡到定向波束。根据二阶扰动项与波束方向性之间的关系，可推导出不同的偏微分方程组，其中包含一个空间变参数，该参数控制入射波束相互作用以生成传播声场。随后，我们针对其中一个模型研究了该参数的反演问题，并提出一种Landweber-Kaczmarz重建方法，以获取感兴趣区域的空间图像。