Regularized tomographic density imaging using multiple frequency information

Inverse scattering methods for density imaging have limitations in terms of required signal-to-noise ratio and band width that keep them from being experimentally implemented. The multiple frequency distorted Born iterative method (MF-DBIM), has been previously proposed to overcome some of these limitations. The objective of this work is to study the convergence of MF-DBIM through both simulations and experiments. Simulations were conducted by reconstructing circular cylinders of radii 1, 2, and 4 wavelengths, and ratios of density Δρ to sound speed Δc contrasts between -3 and 2. Experiments were performed using a balloon phantom filled with saline and frequencies between 1.5 and 3 MHz. Two methods for stabilizing MF-DBIM were studied: total variation regularization (TVR), and weighted TVR giving emphasis to the variation of the pixels around the edges of the imaging target. In simulations, the convergence of MF-DBIM was found to be dependent on the imaging target. For cylinders with Δρ/Δc <; 0 reconstruction errors were typically below 30%. The errors were significantly higher (i.e., up to 70% minimum reconstruction error) for cylinders with Δρ/Δc >; 0. The degraded performance of MF-DBIM was related to the limited spatial bandwidth of the inverse scattering problem. In experiments, calibration errors did not allow reconstruction of useful density tomograms when using MF-DBIM. Density tomograms with 56% reconstruction errors were obtained with MF-DBIM and TVR, but only for a very narrow range of regularization parameters. In contrast, reconstruction errors between 55% and 60% were obtained with MF-DBIM and weighted TVR for regularization parameter values spanning more than an order of magnitude. Therefore, preliminary experimental results presented here suggest auxiliary techniques such as weighted TVR may help extending the convergence of tomographic density imaging algorithms.