  In this research, we reveal the inborn but hitherto ignored properties of
quantitative differential phase contrast (qDPC) imaging: the phase transfer
function being an edge detection filter. Inspired by this, we highlighted the
duality of qDPC between optics and pattern recognition, and propose a simple
and effective qDPC reconstruction algorithm, termed Pupil-Driven qDPC
(pd-qDPC), to facilitate the phase reconstruction quality for the family of
qDPC-based phase reconstruction algorithms. We formed a new cost function in
which modified L0-norm was used to represent the pupil-driven edge sparsity,
and the qDPC convolution operator is duplicated in the data fidelity term to
achieve automatic background removal. Further, we developed the iterative
reweighted soft-threshold algorithms based on split Bregman method to solve
this modified L0-norm problem. We tested pd-qDPC on both simulated and
experimental data and compare against state-of-the-art (SOTA) methods including
L2-norm, total variation regularization (TV-qDPC), isotropic-qDPC, and Retinex
qDPC algorithms. 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. In general, the pd-qDPC enables the high-quality qDPC reconstruction
without any modification of the optical system. It simplifies the system
complexity and benefits the qDPC community and beyond including but not limited
to cell segmentation and PTF learning based on the edge filtering property.
