Algorithms for pixel super-resolution phase retrieval

Authors: Yunhui Gao (gyh21@mails.tsinghua.edu.cn) and Liangcai Cao (clc@tsinghua.edu.cn)

HoloLab, Tsinghua University

Introduction

Phase retrieval and pixel super-resolution (PSR) serve as two essential ingredients for high-fidelity and high-resolution holographic imaging. Here, we combine the two as a unified optimization problem and propose a generalized algorithmic framework for pixel super-resolution phase retrieval.

  

Figure 1. PSR phase reconstruction of a resolution target.

  

Figure 2. Comparison of phase reconstruction under varying measurement numbers.

Figure 3. PSR amplitude reconstruction of a biological sample.

Requirements

Matlab 2019a or newer. Older visions may be sufficient but have not been tested.

Quick Start

• PSR phase retrieval using simulated data. Run demo_sim.m with default parameters.
• PSR phase retrieval using experimental data. Run demo_exp.m with default parameters. Experimental data may be obtained from the authors upon reasonable request.

Accelerated Implementations

The basic demo codes provide intuitive and proof-of-concept implementations for beginners, but are far from efficient. To facilitate faster reconstruction, we provide an optimized version based on CPU or GPU, which can be found at demo_sim_fast.m and demo_exp_fast.m for simulated and experimental data, respectively. To enable GPU usage, simply set gpu = true; in the code.

Theories and References

For algorithm derivation and implementation details, please refer to our papers:

• Yunhui Gao and Liangcai Cao, "Generalized optimization framework for pixel super-resolution imaging in digital holography," Opt. Express 29, 28805-28823 (2021). Publication page | Paper (PDF)

• Yunhui Gao, Feng Yang, and Liangcai Cao, "Pixel Super-Resolution Phase Retrieval for Lensless On-Chip Microscopy via Accelerated Wirtinger Flow," Cells 11, 1999 (2022). Publication page | Paper (PDF) | Supplement (PDF).

Citation

@article{gao2021generalized,
  title={Generalized optimization framework for pixel super-resolution imaging in digital holography},
  author={Gao, Yunhui and Cao, Liangcai},
  journal={Optics Express},
  volume={29},
  number={18},
  pages={28805--28823},
  year={2021},
  publisher={Optica Publishing Group}
}

@article{gao2022pixel,
  title={Pixel super-resolution phase retrieval for lensless on-chip microscopy via accelerated Wirtinger flow},
  author={Gao, Yunhui and Yang, Feng and Cao, Liangcai},
  journal={Cells},
  volume={11},
  number={13},
  pages={1999},
  year={2022},
  publisher={MDPI}
}