Generalized optimization framework for pixel super-resolution imaging in digital holography

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 two essential ingredients for high-fidelity and high-resolution 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. As an example, the Wirtinger gradient descent algorithm for pixel-super-resolved phase retrieval, termed as Wirtinger-PSR, is proposed and compared with the classical error-reduction algorithm. The Wirtinger-PSR algorithm is verified with both simulated and experimental data. The proposed framework generalizes well to various physical settings and helps bridging the gap between empirical studies and theoretical analyses.