Shape reconstruction of the multi-scale rough surface from multi-frequency phaseless data (Q2820670)

The paper is devoted to study the 2D inverse scattering problem of recovering the shape of an unknown multi--scale rough surface in a homogeneous medium from phaseless scattering measurements with time harmonic tapered incident wave. The propagation domain is \(\Omega_f=\{ (x,z) \in \mathbb R^2: z>f(x) \}\) with a bounded \(C^2\) function \(f\). The problem is to reconstruct the function \(f\) from the scattering data \(| \Psi^s(x,H)|\), \(H>\max_{x\in R} \{ 0, f(x) \}\), where \(\Delta \Psi^s+k^2 \Psi=0\) in \(\Omega_f\) and \(\Psi^s+\Psi^{\mathrm{inc}}=0\) on \(\partial \Omega_f\). For solving the problem, the authors use a Landweber type iterative process. Numerical experiments are presented to illustrate the effectiveness of the method.