Numerical algorithms for pixel super-resolution holographic imaging

The imaging quality of in-line digital holography is challenged by the twin-image and aliasing effects because sensors only respond to intensity and pixels are of finite size. As a result, phase retrieval and pixel super-resolution techniques serve as the two essential ingredients for high-fidelity holographic imaging. In this work, we combine the two as a unified optimization problem, and propose a generalized algorithmic framework for pixel-super-resolved phase retrieval. In particular, we introduce the iterative projection algorithms and gradient descent algorithms for solving this problem. The basic building blocks, namely the projection operator and the Wirtinger gradient, are derived and analyzed. The algorithms are verified with both simulated and experimental data. The proposed framework generalizes well to various physical settings, and is compatible with many state-of-the-art optimization algorithms.