Research on Stability Problem of Ultrasonic Inverse Scattering Equation

Abstract

The ill-posed problem of the ultrasonic inverse scattering equation is presented as existence, uniqueness, and stability. Among these three points, stability plays a significant role. Generally speaking, solving the stability problems requires the use of regularization method. The Tikhonov regularization method is at the core of the regularization method. This method has some disadvantages, such as not considering the coefficient matrix error, the regularization parameter is difficult to adjust, etc. Based on the all above reasons, truncated full least squares regularization method that considers the existence of errors in both the data term and the coefficient matrix is introduced into solving the ultrasonic inverse scattering equation. It is verified by simulation experiments that the truncated complete least squares regularization method can not only improve the data fitting degree, but also has higher imaging quality.