MUSIC for Extended Scatterers as an Instance of the Factorization Method

Source abstract

Recent work of Luke and Devaney showed that there exists an implementation of a modified linear sampling method that is equivalent to a MUSIC algorithm for scattering from sound-soft obstacles. The correspondence is independent of the size of the scatterer or the wavelength of the incident field. As the proof was not constructive, an explicit implementation could not be justified. In the present work, we show that MUSIC is an instance of the factorization method applied to any nonabsorbing scatterer, thus providing a justification for the MUSIC algorithm at arbitrary illuminating frequency for arbitrary nonabsorbing scatterers. These results are also extended to scattering from cracks. With explicit constructions in hand, we are also able to provide error and stability estimates for practical implementations in noisy environments with limited data and to explain a curious behavior of the factorization method in the case of noisy data.