Simultaneous Scatterer Shape Estimation and Partial Aperture Far-Field Pattern Denoising

Abstract

We study the inverse problem of recovering the scatterer shape from the far-field pattern(FFP) in the presence of noise. Furthermore, only a discrete partial aperture is usually known. This problem is ill-posed and is frequently addressed using regularization. Instead, we propose to use a direct approach denoising the FFP using a filtering technique. The effectiveness of the technique is studied on a scatterer with the shape of the ellipse with a tower. The forward scattering problem is solved using the finite element method (FEM). The numerical FFP is additionally corrupted by Gaussian noise. The shape parameters are found based on a least-square error estimator. If ũ_∞ is a perturbation of the FFP then we attempt to find Γ, the scatterer shape, which minimizes ‖ u_∞−ũ_∞ ‖ using the conjugate gradient method for the denoised FFP.