Abstract
In coherent imaging, speckle is statistically modeled as multiplicative noise, posing a fundamental challenge for image reconstruction. While maximum likelihood estimation (MLE) provides a principled framework for speckle mitigation, its application to coherent imaging system such as digital holography with finite apertures is hindered by the prohibitive cost of high-dimensional matrix inversion, especially at high resolutions. This computational burden has prevented the use of MLE-based reconstruction with physically accurate aperture modeling. In this work, we propose a randomized linear algebra approach that enables scalable MLE optimization without explicit matrix inversions in gradient computation. By exploiting the structural properties of sensing matrix and using conjugate gradient for likelihood gradient evaluation, the proposed algorithm supports accurate aperture modeling without the simplifying assumptions commonly imposed for tractability. We term the resulting method projected gradient descent with Monte Carlo estimation (PGD-MC). The proposed PGD-MC framework (i) demonstrates robustness to diverse and physically accurate aperture models, (ii) achieves substantial improvements in reconstruction quality and computational efficiency, and (iii) scales effectively to high-resolution digital holography. Extensive experiments incorporating three representative denoisers as regularization show that PGD-MC provides a flexible and effective MLE-based reconstruction framework for digital holography with finite apertures, consistently outperforming prior Plug-and-Play model-based iterative reconstruction methods in both accuracy and speed. Our code is available at: this https URL.
Abstract (translated)
在相干成像中，斑点（speckle）被统计建模为乘性噪声，这对图像重建构成了根本性的挑战。最大似然估计（MLE）提供了一种原则化的框架来缓解这种斑点问题，但在具有有限孔径的系统（如数字全息摄影）中的应用却受到高维矩阵求逆成本过高的限制，特别是在高分辨率情况下更是如此。这一计算负担阻碍了物理准确孔径建模下的基于最大似然估计重建方法的应用。 在本文中，我们提出了一种随机线性代数方法，该方法能够在梯度计算过程中不显式使用矩阵求逆的情况下实现可扩展的最大似然优化。通过利用感测矩阵的结构性质，并采用共轭梯度法进行似然梯度评估，所提出的算法支持准确的孔径建模而不需通常为了可处理性而做出的简化假设。我们将该方法称为基于蒙特卡洛估计（Monte Carlo estimation, MC）的投影梯度下降法（projected gradient descent, PGD），简称PGD-MC。 该PGD-MC框架具备以下特点： (i) 对各种物理准确孔径模型具有鲁棒性； (ii) 实现了重建质量和计算效率上的显著改进； (iii) 可以有效地扩展到高分辨率数字全息摄影中。 一系列实验，其中使用了三种代表性的去噪器作为正则化项，展示了PGD-MC为有限孔径数字全息提供了一种灵活且有效的基于最大似然估计的重建框架，并在精度和速度上一直优于以往的Plug-and-Play模型迭代重建方法。我们的代码可在以下链接获取：this https URL.
URL
https://arxiv.org/abs/2602.10344
