Robust X-Ray Phase Ptycho-Tomography

Synchrotron-based soft X-ray ptychography has enabled the reconstruction of both the phase and attenuation projections of samples relevant to the physical and biological sciences. The phase projection images typically have higher fidelity and hence are used for tomographic reconstruction. In practice, three-dimensional tomographic reconstruction can be challenging because the measurements may have outliers, a fluctuating background and may be restricted to a limited angular range of sample rotations. Thus, conventional reconstruction algorithms such as filtered back projection can result in reconstructions with strong artifacts. In this paper, we present a robust model-based iterative reconstruction algorithm for X-ray ptychography-based phase tomography. Our method casts the reconstruction as a regularized inverse problem, involving a novel data fitting term that accounts for noise, the fluctuating background as well as outliers, combined with an image model term that enforces regularity on the volume to be reconstructed. We use a majorization-minimization strategy to find a minimum of the formulated cost function. Reconstructions on a simulated as well as a real dataset show that it is possible to acquire high-quality phase reconstructions compared to the typically used filtered-back projection algorithm as well as conventional regularized inversion approaches.