Log-elastographic and non-marching full inversion schemes

The goal of elastography is to image the shear stiffness of tissue for cancer diagnosis and the focus of this paper is on single frequency elastographic data. Assuming that the measured displacement of the propagating shear wave satisfies the acoustic wave equation, the shear modulus μ can be recovered by solving a first-order partial differential equation in the inverse problem. To capture possible exponential growth and decay of the targeted parameter μ numerically in a stable manner, we propose a log-elastographic nonlinear scheme and a linear finite difference based elliptic scheme. Both methods are shown to be convergent at first order and their performances are compared with the performances of a semi-implicit upwind scheme and the direct inversion model previously investigated (see [23]). We present shear modulus reconstructions from synthetic data with and without noise. (Some figures in this article are in colour only in the electronic version)