Three-dimensional image reconstruction in variable density acoustic tomography

Diffraction tomography (DT) is an established imaging technique for use with diffracting wavefields, which represents a generalized form of x-ray tomography. In this work, we revisit the three-dimensional reconstruction problem of DT for variable density acoustic media. Novel reconstruction algorithms are developed for reconstructing separate images that depict a weakly scattering object's compressibility and density variations. If tomographic measurement data are acquired at four distinct temporal frequencies, we demonstrate that the effects of object dispersion can be accounted for completely by use of analytic reconstruction formulas. Computer-simulation studies are conducted to demonstrate the developed image reconstruction methods.