Performance of Fast Inverse Scattering Solutions for the Exact Helmholtz Equation Using Multiple Frequencies and Limited Views

Abstract

We have previously reported fast algorithms for imaging by acoustical inverse scattering using the exact (not linearized) Helmholtz wave equation [1]. We now report numerical implementations of these algorithms which allow the reconstruction of quantitative images of speed of sound, density, and absorption from either transmission or reflection data. We also demonstrate the application of our results to larger grids (up to 64 × 64 pixels) and compare our results with analytically derived data, which are known to be highly accurate, for scattering from right circular cylindrical objects. We report on the performance of our algorithms for both transmission and reflection data and for the simultaneous solution of scattering components corresponding to speed of sound and absorption. We have further examined the performance of our methods with various amounts of random noise added to the simulated data. We also report on the performance of one technique we have devised to extract quantitative density images from our algorithms.