A Message-Passing Perspective on Ptychographic Phase Retrieval

We introduce a probabilistic approach to ptychographic reconstruction in computational imaging. Ptychography is an imaging method where the complex amplitude of an object is estimated from a sequence of diffraction measurements. We formulate this reconstruction as a Bayesian inverse problem and derive an inference algorithm, termed "Ptycho-EP," based on belief propagation and Vector Approximate Message Passing from information theory. Prior knowledge about the unknown object can be integrated into the probabilistic model, and the Bayesian framework inherently provides uncertainty quantification of the reconstruction. Numerical experiments demonstrate that, when the probe's illumination function is known, our algorithm accurately retrieves the object image at a sampling ratio approaching the information theoretic limit. In scenarios where the illumination function is unknown, both the object and the probe can be jointly reconstructed via an Expectation-Maximization algorithm. We evaluate the performance of our algorithm against conventional methods, highlighting its superior convergence speed.