Feasibility of half-data image reconstruction in 3-D reflectivity tomography with a spherical aperture

Reflectivity tomography is an imaging technique that seeks to reconstruct certain acoustic properties of a weakly scattering object. Besides being applicable to pure ultrasound imaging techniques, the reconstruction theory of reflectivity tomography is also pertinent to hybrid imaging techniques such as thermoacoustic tomography. In this work, assuming spherical scanning apertures, redundancies in the three-dimensional (3-D) reflectivity tomography data function are identified and formulated mathematically. These data redundancies are used to demonstrate that knowledge of the measured data function over half of its domain uniquely specifies the 3-D object function. This indicates that, in principle, exact image reconstruction can be performed using a "half-scan" data function, which corresponds to temporally untruncated measurements acquired on a hemi-spherical aperture, or using a "half-time" data function, which corresponds to temporally truncated measurements acquired on the entire spherical aperture. Both of these minimal scanning configurations have important biological imaging applications. An iterative reconstruction method is utilized for reconstruction of a simulated 3-D object from noiseless and noisy half-scan and half-time data functions.