A model function method for determining the regularizing parameter in potential approach for the recovery of scattered wave

Consider the reconstruction of scattered wave from its erroneous far-field pattern data in acoustic wave scattering. The potential scheme proposed by Kirsch and Kress converts this problem into the determination of some density function from a linear integral equation of the first kind. For this ill-posed problem, we apply the model function method to determine the regularizing parameter approximately in the potential scheme. Compared with the standard method which solves the regularizing parameter from the exact discrepancy equation, this paper proposes an implementable numerical approach to determining the regularizing parameter from the equation satisfied by the model function. Applying the proposed scheme to determine the regularizing parameter approximately, we reconstruct the scattered wave with relatively small amount of computation.