Why linear sampling really seems to work (Q953801)

The author provides a qualitative and quantitative analysis of the linear sampling method, and give an interpretation of the obtained results for cases where the fatorization methods is also known to work. To this end the author formally restrict his treatment to the specific case of acoustic scattering by sound-soft obstacles. The analysis of the author, however, extends to other cases of interest, as it only exploits general techniques from the theory of linear ill-posed problems. Moreover, the main tool of the author is a careful investigation of the Tikhonov regularization method and the discrepancy principle for linear operator equations with inconsistent right-hand sides and, possibly, perturbed operators.