Bandwidth-optimized regularization for low-frequency recovery in quantitative phase imaging

We propose the expanded matrix solution of the transport of intensity equation (EMS-TIE), introducing a tunable parameter (th) to the Tikhonov regularization term. This design addresses the limitation of conventional Tikhonov solvers, where the filter's bandwidth is strictly coupled to the cutoff frequency. By decoupling these parameters, the proposed design allows for tuning the filter shape to optimize signal recovery. Simulations and experiments demonstrate that increasing passband width significantly reduces retrieval error and enhances low-frequency phase recovery, outperforming standard Tikhonov-based methods.