In this paper we consider the inverse problem of vibro-acoustography, a technique for enhancing ultrasound imaging by making use of nonlinear effects. It amounts to determining two spatially variable coefficients in a system of PDEs describing propagation of two directed sound beams and the wave resulting from their nonlinear interaction. To justify the use of Newton's method for solving this inverse problem, on one hand we verify well-definedeness and differentiability of the forward operator corresponding to two versions of the PDE model; on the other hand we consider an all-at-once formulation of the inverse problem and prove convergence of Newton's method for its solution.

翻译：---- 在频域中同时重建声速和非线性参数的波动声学中轴模型 翻译后的摘要: 本文考虑了波动声学的反问题，这是一种通过利用非线性效应来增强超声成像的技术。其目的是确定描述两个定向声波传播和它们的非线性相互作用所产生的波的两个空间可变系数的偏微分方程系统中的系数。为了验证该反问题的牛顿法解的使用，在一方面我们验证了与两个版本的PDE模型相对应的正演算子的良定义性和可微性;在另一方面，我们考虑了反问题的同时全部公式，并证明了牛顿方法可以用于解决它的收敛性。