An SVD Free Construction of an Indicator Function as an Imaging Algorithm

作者：Kim K^*; Leem K H; Pelekanos G

来源：Journal of Computational Analysis and Applications, 2014, 16(4): 731-739.

• factorization method
• Helmholtz equation
• inverse problems
• singular value decomposition

A novel SVD free method is presented to reconstruct the shape of a sound-soft obstacle from the knowledge of the time harmonic incident electromagnetic wave and the far field pattern of the scattered wave. The approach presented is based on Kirsch%26apos;s factorization method and constructs a simple indicator function which is used to visualize the scattering profile. The method is baptized as Singular Value Decomposition Free Indicator (SVDFI) and its performance is evaluated by comparing our reconstructions with those obtained via Morozov%26apos;s discrepancy principle (MDP). Numerical results that illustrate the effectiveness of SVDFI on reconstruction problems involving both simulated and real data are reported and analyzed.