Imaging strongly scattering media using a multiple frequency distorted Born iterative method

The distorted Born iterative (DBI) method is a powerful approach for solving the inverse scattering problem for ultrasound tomographic imaging. This method alternates between solving the inverse scattering problem for the scattering function and the forward scattering problem for the total field and the inhomogeneous Green´s function. The algorithm is initialized using the basic Born inverse solution. One fundamental problem is the algorithm diverges for strongly scattering media. This is caused by the limitation of the Born assumption in estimating the initial step of the algorithm. We present a multiple frequency DBI approach to alleviate this problem, thus extending the applicability of the DBI method to the level of dealing with biological tissue. In this multiple frequency approach, a low frequency DBI-based solution, is used to initialize the algorithm at higher frequencies. The low frequency allows convergence of the algorithm to a contrast level that is close to the true level, however, with a poor spatial resolution. The high frequency improves the spatial resolution while preserving convergence because the difference between the true contrast and the initial contrast is relatively small. We present numerical simulations that demonstrate the ability of this method to reconstruct strongly scattering regions.