Regularized tomographic density imaging using multiple frequencyinformation

Inverse scattering methods for density imaging have limitations in terms ofrequired signal-to-noise ratio and bandwidth that keep them from beingexperimentally implemented. The multiple frequency distorted Born iterativemethod (MF-DBIM), has been previously proposed to overcome some of theselimitations. The objective of this work is to study the convergence of MF-DBIMthrough both simulations and experiments. Simulations were conducted byreconstructing circular cylinders of radii 1, 2, and 4 wavelengths, and ratiosof density δp to sound speed δc contrasts between 3 and 2.Experiments were performed using a balloon phantom filled with saline andfrequencies between 1.5 and 3 MHz. Two methods for stabilizing MF-DBIM werestudied: total variation regularization (TVR), and weighted TVR giving emphasisto the variation of the pixels around the edges of the imaging target. Insimulations, the convergence of MF-DBIM was found to be dependent on the imagingtarget. For cylinders with δp/δc < 0 reconstruction errors weretypically below 30%. The errors were significantly higher (i.e., up to 70%minimum reconstruction error) for cylinders with δp/δc > 0. Thedegraded performance of MF-DBIM was related to the limited spatial bandwidth ofthe inverse scattering problem. In experiments, calibration errors did not allowreconstruction of useful density tomograms when using MF-DBIM. Densitytomograms with 56% reconstruction errors were obtained with MF-DBIM and TVR, butonly for a very narrow range of regularization parameters. In contrast,reconstruction errors between 55% and 60% were obtained with MF-DBIM andweighted TVR for regularization parameter values spanning more than an order ofmagnitude. Therefore, preliminary experimental results presented here suggestauxiliary techniques such as weighted TVR may help extending the convergence oftomographic density imaging algorithms.