A comparison of truncated total least squares with Tikhonov regularization in imaging by ultrasound inverse scattering

For good image quality using ultrasound inverse scattering, one alternately solves the well-posed forward scattering equation for an estimated total field and the ill-posed inverse scattering equation for the desired object property function. In estimating the total field, error or noise contaminates the coefficients of both matrix and data of the inverse scattering equation. Previous work on ill-posed inverse ultrasonic scattering commonly used Tikhonov regularization, which considers error only in the data. The solution so obtained is not precise enough to reconstruct the quantitative internal structure of a large or high-contrast object. This paper adopts the truncated total least squares method, simultaneously considering error and noise on both sides of the inverse scattering equation, and compares it with the classical Tikhonov regularization. We show that it can substantially improve reconstruction fit and image quality when the inverse scattering equation system is strongly ill-posed.