P4D-4 Image Reconstruction of Moderate Contrast Targets Using the Distorted Born Iterative Method

Ultrasonic tomography using inverse scattering, i.e., the distorted Born iterative method (DBIM), allows for the quantitative image reconstruction of mechanical properties of materials. The use of multi-frequency information has been proposed to avoid convergence issues for targets with moderate speed of sound contrasts Deltac (i.e., targets for which the excess phase Deltaphi when propagating through the object is larger than pi) but not validated experimentally. Furthermore, DBIM has to be regularized due to its ill-conditioning. To experimentally validate DBIM for use in ultrasonic tomography, a systematic procedure to choose the regularization parameter based on the Rayleigh quotient iteration was developed and images of objects with moderate Deltac were reconstructed. The performance of DBIM using the developed regularization scheme was studied through: 1) Simulations of a two dimensional (2D) phantom (Deltaphi= 2.14pi) with inclusions smaller than a wavelength, 2) Experiments with a balloon phantom with high Deltac with scattered data collected at 0.64 MHz (Deltaphi=0.84pi) and 1.2 MHz (Deltaphi=1.6pi), and 3) Three dimensional (3D) reconstruction of a moderate contrast sphere (Deltaphi=1.32pi). The 2D and 3D multi-frequency DBIM simulations were successfully stabilized by the proposed regularization scheme as evidenced by the low reconstruction mean square errors (MSEs) (Deltac MSE=9% for 2D and 15% for 3D) and the detection of the sub-wavelength inclusions in the 2D reconstruction. In experiments, the measured scattered fields agreed well with the predicted scattered fields from the phantom model (MSE=4% for 0.64 MHz and MSE=7.8% for 1.2 MHz). The MSE of the reconstructed image using only the experimental data at 0.64 MHz was 19%. Using the experimental data at 1.2 MHz to refine the 0.64 MHz reconstruction allowed the MSE to be reduced to 12%, and improved the spatial resolution as evidenced by the reduced edge blurring.