Two approaches for tomographic density imaging using inverse scattering

Most acoustic tomography methods neglect density variations in order to obtain speed of sound and attenuation profiles. However, density may provide additional sources of image contrast. In this work, two approaches for density imaging using inverse scattering were explored through simulations in order to evaluate the feasibility of density imaging. The first method consisted of inverting the wave equation by solving for a single functional that depended on both speed of sound and density variations. Density profiles were separated by combining reconstructions at two frequencies (DF-DBIM approach). The second method consisted of solving for two functionals simultaneously: one that depended only on compressibility and one that depended only on density variations. A T-matrix approach was used to relate these functionals to the scattered data. The DF-DBIM approach allowed separation of density and speed of sound profiles at low termination tolerance values and less than an order of magnitude between the largest and smallest frequencies used. However, the convergence of DF-DBIM was compromised even when moderate (around 2%) termination tolerances were used. The T-matrix approach converged when multiple frequency data was used, but required a ka product smaller than one at the lowest frequency. The DF-DBIM requires a very high SNR to obtain reliable quantitative density reconstructions, while the T-matrix approach requires excessively large bandwidths when imaging large targets. These limitations will serve as reference points for further algorithmic improvements required for practical implementation of density imaging on ultrasound tomographic systems.