Retrieving Scattering Matrices With Gaussian Regularized Adaptive Statistical Prior

Wavefront shaping has revolutionized the control of light propagation through scattering media, transforming disordered speckles into highly focused optical spots. This breakthrough depends on the accurate and efficient retrieval of scattering matrices, which promises to unlock new possibilities in optical imaging, communication, and sensing. However, a major challenge persists: retrieving scattering matrices from direct intensity measurements, often hindered by the lack of effective prior knowledge or regularization constraints. In this study, we introduce the Gaussian-regularized adaptive statistical prior fast iterative shrinkage-thresholding algorithm (GRASP-FISTA), a novel method designed to overcome this challenge in phase retrieval for scattering media. By exploiting the statistical properties of scattering matrix elements—specifically their circular Gaussian distribution—we impose a robust statistical prior that enhances retrieval accuracy. Integrated with the Plug-and-Play FISTA framework, known for its rapid convergence, GRASP-FISTA offers an efficient and reliable solution to phase retrieval. Experimental validation on multimode fibers, ground glass, and chicken breast tissue demonstrates that GRASP-FISTA reduces iteration counts by 2–3 times, increases robustness against Gaussian noise, and improves reconstruction accuracy. By incorporating statistical constraints into gradient-descent-based methods, GRASP-FISTA significantly broadens the scope of phase retrieval, paving the way for new applications across diverse scattering processes.