Regularization of the boundary control method for numerical solutions of the inverse problem for an acoustic wave equation

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.