Numerical comparison of iterative and functional-analytical algorithms for reconstruction of refraction-absorbing scatterers

Numerical simulation was carried out for comparative study of iterative and functional-analytical algorithms for solving inverse scattering problem of sound speed and absorption reconstruction. The mathematical properties of these algorithms were previously described in works of R.G. Novikov for the Schrödinger equation. In the present paper, for the case of two-dimensional scalar Helmholtz equation, the efficiency of iterative algorithm in reconstructing medium-strength scatterers and the advantages of functional-analytic approach in reconstructing strong scatterers are demonstrated, which corresponds to the known theoretical estimates of these algorithms’ convergence. To improve the convergence of iterations, a filtering procedure in the space of wave vectors is used, which gradually takes into account the high-frequency components of the spatial spectrum of the scatterer function.