数字全息中的蒙特卡洛最大似然重建与散射
Monte Carlo Maximum Likelihood Reconstruction for Digital Holography with Speckle
AI总结：
本文提出了一种基于随机线性代数的PGD-MC方法，用于有限孔径数字全息中的最大似然重建，实现了高精度和高效能的重建效果。
摘要：
在相干成像中，散射被统计建模为乘性噪声，这对图像重建提出了根本性的挑战。尽管最大似然估计（MLE）提供了一个系统的方法来减轻散射，但将其应用于如有限孔径的数字全息系统时，高维矩阵求逆的计算成本是一个障碍，尤其是在高分辨率情况下。这种计算负担已阻止了基于MLE的重建在物理上准确的孔径建模中的应用。在本文中，我们提出了一种随机线性代数方法，使能够扩展的MLE优化在梯度计算中不需要显式的矩阵求逆。通过利用传感矩阵的结构特性，并使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，而无需通常用于可处理性的简化假设。我们称这种结果的方法为投影梯度下降与蒙特卡洛估计（PGD-MC）。所提出的PGD-MC框架（i）展示了对多样且物理上准确的孔径模型的鲁棒性，（ii）在重建质量和计算效率上实现了显著改进，（iii）能够有效扩展到高分辨率数字全息。广泛的实验结合了三种代表性的去噪器作为正则化项，显示PGD-MC为有限孔径的数字全息提供了灵活且有效的MLE基于重建框架，一致地在准确性和速度上优于先前的Plug-and-Play模型基于迭代重建方法。我们的代码可在：https://github.com/Computational-Imaging-RU/MC_Maximum_Likelihood_Digital_Holography_Speckle。
英文摘要：
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: https://github.com/Computational-Imaging-RU/MC_Maximum_Likelihood_Digital_Holography_Speckle.
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