Efficient multilook coherent imaging with temporally dependent speckle noise

Speckle noise is a persistent challenge in coherent imaging systems, significantly impacting image acquisition quality. When multiple looks are captured, recent theoretical and algorithmic advances have demonstrated the potential of maximum likelihood estimation (MLE)-based algorithms to effectively mitigate speckle noise and achieve state-of-the-art performance. However, key challenges remain in (1) addressing the temporal dependencies of speckle noise across looks in applications such as digital holography, which further degrades the performance, and (2) reducing the high computational complexity of MLE-based recovery algorithms. In this work, we propose a novel framework to address both challenges. First, we introduce a Markov model to capture temporal correlations in speckle noise across multiple looks and formulate the corresponding MLE optimization problem. Second, we extend previously developed solution strategies, based on Randomized Numerical Linear Algebra, to efficiently solve this more complex optimization. Specifically, our algorithm leverages Monte Carlo sampling and the conjugate gradient method to scale the MLE-based recovery to high-dimensional imaging data. We demonstrate the effectiveness of our framework through experiments in digital holography, showing improved reconstruction quality and computational efficiency.