An improved method for tomographic density imaging using a multiple frequency inverse scattering approach

Current inverse scattering methods for quantitative density imaging have limitations that keep them from practical experimental implementations. In this work an improved approach, termed the multiple frequency distorted Born iterative method (MF-DBIM) algorithm, was developed for imaging density variations. The MF-DBIM approach consists of inverting the wave equation by solving for a single functional that depends on both sound speed and density variations at multiple frequencies. Density information was isolated by using a linear combination of the reconstructed single-frequency profiles. The results were compared to reconstructions using methods currently available in the literature, i.e., the dual frequency DBIM (DF-DBIM) and T-matrix approaches. The performance of the MF-DBIM was assessed by reconstructing cylindrical targets of different radii, speed of sound and density contrasts. The MF-DBIM required the use of frequency hopping in order to converge to a proper solution. Useful density reconstructions, i.e., root mean square errors (RMSEs) less than 30%, were obtained even with 2% Gaussian noise in the simulated data and using frequency ranges spanning less than an order of magnitude. Therefore, the MF-DBIM approach largely outperformed both the DF-DBIM method (which has problems converging with noise even an order of magnitude smaller) and the T-matrix method (which requires a ka factor close to unity in order to achieve convergence). The MF-DBIM performance degraded severely when the angular coverage on reception was less than 180°. Although the MF-DBIM performance also degraded as the frequency jump magnitude increased, the RMSEs were not largely affected when the frequency jump was smaller than 5% of the maximum frequency used for the reconstructions.