Riemann-Hilbert problem approach for two-dimensional flow inverse scatteringa)

We consider inverse scattering for the time-harmonic wave equation with first-order perturbation in two dimensions. This problem arises in particular in the acoustic tomography of moving fluid. We consider linearized and nonlinearized reconstruction algorithms for this problem of inverse scattering. Our nonlinearized reconstruction algorithm is based on the non-local Riemann-Hilbert problem approach. Comparisons with preceding results are given.