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This paper addresses the challenge of speckle noise in digital holography by modeling inter-look correlation using a first-order Markov process, which is often overlooked in conventional methods that assume statistical independence among measurements. The authors develop a constrained maximum likelihood estimation approach, employing a projected gradient descent framework enhanced by deep image priors and Monte Carlo techniques for efficient computation. Simulation results reveal that this method effectively reconstructs speckle-free reflectivity even under strong inter-look correlation, significantly outperforming traditional techniques that neglect these dependencies.
Ignoring inter-look correlation can lead to significant performance degradation in holographic reconstruction, but a new Markov-based approach achieves near-ideal results even in challenging conditions.
Multi-look acquisition is a widely used strategy for reducing speckle noise in coherent imaging systems such as digital holography. By acquiring multiple measurements, speckle can be suppressed through averaging or joint reconstruction, typically under the assumption that speckle realizations across looks are statistically independent. In practice, however, hardware constraints limit measurement diversity, leading to inter-look correlation that degrades the performance of conventional methods. In this work, we study the reconstruction of speckle-free reflectivity from complex-valued multi-look measurements in the presence of correlated speckle. We model the inter-look dependence using a first-order Markov process and derive the corresponding likelihood under a first-order Markov approximation, resulting in a constrained maximum likelihood estimation problem. To solve this problem, we develop an efficient projected gradient descent framework that combines gradient-based updates with implicit regularization via deep image priors, and leverages Monte Carlo approximation and matrix-free operators for scalable computation. Simulation results demonstrate that the proposed approach remains robust under strong inter-look correlation, achieving performance close to the ideal independent-look scenario and consistently outperforming methods that ignore such dependencies. These results highlight the importance of explicitly modeling inter-look correlation and provide a practical framework for multi-look holographic reconstruction under realistic acquisition conditions. Our code is available at: https://github.com/Computational-Imaging-RU/MLE-Holography-Markov.
