Reconstruction algorithms for interior and exterior spherical radon transform-based ultrasound imaging

This work is concerned with the numerical implementation of a reconstruction algorithm developed to recover a function from its spherical means over spheres centered on a circle. The algorithm is experimentally verified by simulations using numerical phantoms. In the scheme of tomography, acoustic waves are generated by illuminating an object with a short burst of radio-frequency waves. In applications, like breast cancer imaging, which use modalities like photo-acoustic tomography (PAT) that model the acoustic pressures as spherical means, data are measured on the detectors located in a circle surrounding the object. This is then used to reconstruct the absorption density inside the object. In contrast, applications like bore hole tomography and improved Intravascular Ultra Sound (IVUS) imaging for prostate cancer, which use modalities like Radial Reflection Diffraction Tomography (RRDT), a ring of detectors placed exterior to the object, collect the acoustic waves as back-scattered field. This work uses a single algorithm to reconstruct functions from data collected using these two different techniques ? one, by placing the object inside the ring of detectors, and the other, by placing the object exterior to the ring of detectors. The algorithm then draws a comparison between the two reconstructions. The case of bistatic ultrasound imaging, where the elliptical Radon transform is appropriate, is also discussed.