  Differential phase contrast (DPC) imaging plays an important role in the
family of quantitative phase measurement. However, the reconstruction algorithm
for quantitative DPC (qDPC) imaging is not yet optimized, as it does not
incorporate the inborn properties of qDPC imaging. In this research, we propose
a simple but effective image prior, the dark-field sparse prior (DSP), to
facilitate the phase reconstruction quality for all DPC-based phase
reconstruction algorithms. The DSP is based on the key observation that most
pixel values for an idea differential phase contrast image are zeros since the
subtraction of two images under anti-symmetric illumination cancels all
background components. With this DSP prior, we formed a new cost function in
which L0-norm was used to represent the DSP. Further, we developed two
different algorithms based on (1) the Half Quadratic Splitting, and (2) the
Richardson-Lucy deconvolution to solve this NP-hard L0-norm problem. We tested
our new model on both simulated and experimental data and compare against
state-of-the-art methods including L2-norm and total variation regularizations.
Results show that our proposed model is superior in terms of phase
reconstruction quality and implementation efficiency, in which it significantly
increases the experimental robustness, while maintaining the data fidelity.
