Statistically optimal image reconstruction in propagation-based phase-contrast tomography

Propagation-based phase-contrast tomography is a coherent imaging method that seeks to reconstruct the three-dimensional complex-valued refractive index distribution of an object. Measurements of the transmitted wavefield intensities on two parallel detector-planes at each tomographic view angle are utilized to determine the wavefield's complex amplitude, which represent the projection data utilized for tomographic reconstruction. The mathematical formulas employed to determine the complex amplitude contain Fourier domain singularities that can result in greatly amplified noise levels in the reconstructed images. In this article, statistically optimal reconstruction methods that employ multiple (> 2) detector-planes are developed that mitigate the noise amplification effects due to singularities in the reconstruction formulas. These reconstruction methods permit exploitation of statistically complementary information in a collection of in-line holographic measurement data, resulting in images that can have dramatically reduced noise levels. Computer-simulation studies are conducted to demonstrate and investigate quantitatively the developed reconstruction methods.