Single-Shot Phase Retrieval Via Gradient-Sparse Non-Convex Regularization Integrating Physical Constraints

Measurements of light typically capture amplitude information, often overlooking crucial phase details. This oversight underscores the importance of phase retrieval (PR), essential in biomedical imaging, X-ray crystallography, and microscopy, for reconstructing complex signals from intensity-only measurements. Traditional methods frequently fall short, especially in noisy conditions or when restricted to single-shot measurements. To address these challenges, we introduce a novel model that combines non-convex regularization with physical constraints. The model adopts the smoothly clipped absolute deviation (SCAD) function as a sparsity regularization term for gradients, incorporating fundamental constraints on support and absorption to establish an inverse model. Using the alternating direction method of multipliers (ADMM), we break down the problem into manageable sub-problems, implementing SCAD shrinkage in the complex domain and applying Wirtinger gradient projection methods. A thorough convergence analysis validates the stability and robustness of the algorithm. Extensive simulations confirm significant improvements in reconstruction quality compared to existing methods, with evaluations demonstrating superior performance across various noise levels and parameter settings.