Abstract

We propose a new method for solving nonlinear inverse scattering problems. Our goal is to determine numerically an unknown interaction potential V from external scattering data Φ by solving the equation F[V] = Φ, where F[·] is a known nonlinear functional. We bring this equation to the form AT[V]B = Φ, where T[V] is the T-matrix and A and B are known matrices. The above equation does not allow one to determine T uniquely because, in all practical cases, T is much larger than Φ (there is not enough degrees of freedom in the data). However, we can use the one-to-one correspondence between T and V to search iteratively for T that corresponds to a diagonal V. We refer to this iteration process as to data-compatible T-matrix completion (DCTMC). We have applied this algorithm to the problem of inverse scattering of scalar waves (e.g., ultrasound tomography) and have achieved excellent convergence and reliability. DCTMC is well suited for overdetermined problems with large data sets whose solution by conventional means such as the Newton-type methods is problematic.

© 2016 Optical Society of America