Shape reconstruction of the multi-scale rough surface from multi-frequency phaseless data. (6th June 2016) - Bao, Gang; Zhang, Lei
Abstract: We consider the problem of reconstructing the shape of multi-scale sound-soft large rough surfaces from phases measurements of the scattered field generated by tapered waves with multiple frequencies impinging on a rough surface. To overcome both the ill-posedness and nonlinearity of this problem for a single frequency, the Landweber regularization method based on the adjoint of the nonlinear objective functional is used. When the multi-frequency data is available, an approximation method is introduced to estimate the large-scale structure of the rough surface using the data measurements at the lowest frequency. The obtained estimate serves as an initial guess for a recursive linearization algorithm in frequency, which is used to capture the small scale structure of the rough surface. Numerical experiments are presented to illustrate the effectiveness of the method.