Iterative projection meets sparsity regularization: towards practical single-shot quantitative phase imaging with in-line holography

Holography provides access to the optical phase. The emerging compressive phase retrieval approach can achieve in-line holographic imaging beyond the information-theoretic limit or even from a single shot by exploring the signal priors. However, iterative projection methods based on physical knowledge of the wavefield suffer from poor imaging quality, whereas the regularization techniques sacrifice robustness for fidelity. In this work, we present a unified compressive phase retrieval framework for in-line holography that encapsulates the unique advantages of both physical constraints and sparsity priors. In particular, a constrained complex total variation (CCTV) regularizer is introduced that explores the well-known absorption and support constraints together with sparsity in the gradient domain, enabling practical high-quality in-line holographic imaging from a single intensity image. We developed efficient solvers based on the proximal gradient method for the non-smooth regularized inverse problem and the corresponding denoising subproblem. Theoretical analyses further guarantee the convergence of the algorithms with prespecified parameters, obviating the need for manual parameter tuning. As both simulated and optical experiments demonstrate, the proposed CCTV model can characterize complex natural scenes while utilizing physically tractable constraints for quality enhancement. This new compressive phase retrieval approach can be extended, with minor adjustments, to various imaging configurations, sparsifying operators, and physical knowledge. It may cast new light on both theoretical and empirical studies.