The total variation minimization is proposed for use in recovering the mass density of a fluid medium from back-scattered acoustic waves by the dynamical version of the boundary control method. This may be of particular interest to underwater acoustic imaging or ultrasound tomography. In particular, an analogue of the regularized mean curvature flow equation is proposed and developed to obtain numerical solution of the system of linear equations with the ill-conditioned Gram matrix. To demonstrate the computational effectiveness of the proposed numerical technique, we conduct a series of numerical experiments with the inverse problem for a 1 + 1 dimensional acoustic wave equation.

提出将总变化最小化用于通过边界控制方法的动态形式从反向散射声波中恢复流体介质的质量密度。这对于水下声成像或超声层析成像可能特别感兴趣。特别是，提出并发展了正则化平均曲率流方程的类似物，以获得带有病态革兰氏矩阵的线性方程组的数值解。为了证明所提出的数值技术的计算效率，我们针对1 +1维声波方程的反问题进行了一系列数值实验。