Coherent Plug-and-Play: Digital Holographic Imaging Through Atmospheric Turbulence Using Model-Based Iterative Reconstruction and Convolutional Neural Networks

Abstract

In order to image a distant object through atmospheric turbulence, it is necessary to correct for the phase errors that would otherwise cause rapidly varying spatial blur in a conventionally focused image. One approach to solving this problem is to illuminate an object with coherent light and to use a digital holography (DH) receiver to form a coherent measurement. The associated amplitude and phase can then be used with model-based iterative reconstruction (MBIR) frameworks to estimate and correct for atmospheric phase errors from single-shot DH data (i.e., one sensor measurement). In this work, we present a new approach for the reconstruction of optically-coherent images from single-shot DH data in the presence of atmospheric turbulence, referred to as Coherent Plug-and-Play (C-PnP). Our algorithm integrates a convolutional neural network (CNN) image model with physics-based models for image reconstruction from DH data corrupted by atmospheric phase errors. C-PnP combines the modeling power of deep neural networks with the accuracy of existing physics models. Based on an extension of the plug-and-play framework, C-PnP uses multi-agent consensus equilibrium to balance the influence of these models. When compared with an existing approach using a simple image model, C-PnP improves image quality by a factor of $2.2\times$ and phase-error correction by a factor of $2.9\times$ , on average. We obtain these results by considering a wide range of images, signal levels, and phase-error strengths.