Improved misfit function for attenuation and speed reconstruction in ultrasound computed tomography

The reconstruction of acoustic attenuation maps for transmission Ultrasound Computed Tomography (USCT) based on the standard least-squares full wave inversion method requires the accurate knowledge of the sound speed map in the region under study. Any deviation in the reconstructed speed maps creates a very significant bias in the attenuation map, as the standard least-squares misfit function is more sensitive to time misalignments than to amplitude differences of the signals. In this work, we propose a generalized misfit function which includes an additional term that accounts for the amplitude differences between the measured and the estimated signals. The functional gradients used to minimize the proposed misfit function were obtained using an adjoint field formulation and the fractional Laplacian wave equation. The forward and backward wave propagation was obtained with the parallelized GPU version of the software k-Wave and the optimization was performed with a line search method. A numerical phantom simulating breast tissue and synthetic noisy data were used to test the performance of the proposed misfit function. The attenuation was reconstructed based on a converged speed map. An edge-preserving regularization method based on total variation was also implemented. To quantify the quality of the results, the mean values and their standard deviations in several regions of interest were analyzed and compared to the reference values. The proposed generalized misfit function decreases considerably the bias in the attenuation map caused by the deviations in the speed map in all the regions of interest analyzed.