Convexification numerical algorithm for a 2D inverse scattering problem with backscatter data

This paper is concerned with the inverse scattering problem which aims to determine spatially distributed dielectric constant coefficient of 2D Helmholtz equation from multifrequency backscatter data associated a single direction incident plane wave. We propose globally convergent convexification numerical algorithm solve this nonlinear and ill-posed problem. The key advantage our method over conventional optimization approaches that it does not require good first guess about solution. First, we eliminate using change variables. Next, truncated expansion respect special Fourier basis, approximately reformulate as system quasilinear elliptic PDEs, can be numerically solved by weighted quasi-reversibility approach. cost functional for constructed Tikhonov-like involves Carleman Weight Function. Our study shows that, version gradient descent method, one find minimizer without any advanced priori knowledge it.