Full Aperture Reconstruction of the Acoustic Far-Field Pattern from Few Measurements (Communications in Computational Physics, 2020)
We propose a numerical procedure to extend to full aperture the acoustic far-field pattern (FFP) when measured in only few observation angles. The reconstructionprocedure is a multi-step technique that combines a total variation regularized iterative method with the standard Tikhonov regularized pseudo-inversion. The proposedapproach distinguishes itself from existing solution methodologies by using an exactrepresentation of the total variation which is crucial for the stability and robustnessof Newton algorithms. We present numerical results in the case of two-dimensionalacoustic scattering problems to illustrate the potential of the proposed procedure forreconstructing the full aperture of the FFP from very few noisy data such as backscattering synthetic measurements.