Direct imaging methods for inverse scattering problem of biharmonic wave with phased and phaseless data

Abstract This paper investigates the inverse biharmonic scattering problems of identifying the shape and location of the obstacle with phased and phaseless measurement data. Direct imaging methods based on reverse time migration are proposed for reconstructing the extended obstacle with one of four types of boundary conditions on the obstacle. The newly developed imaging functions are constructed by utilizing merely one of various measurement data, including the scattered field, its normal derivative, the bending moment, the transverse force, its far-field and the phaseless total field. Our resolution analysis demonstrates that these imaging functions have a contrast when sampling points are near or far from the boundary of the obstacle. Numerical experiments with the clamped boundary condition are further presented to show the algorithms’ effectiveness to accurately reconstruct complex scatter geometries and its robustness to noise.