Compressed ultrafast photography (CUP) is the fastest single-shot passive ultrafast optical imaging technique, which has shown to be a powerful tool in recording self-luminous or non-repeatable ultrafast phenomena. However, the low fidelity of image reconstruction based on the conventional augmented-Lagrangian (AL) and two-step iterative shrinkage/thresholding (TwIST) algorithms greatly prevents practical applications of CUP, especially for those ultrafast phenomena that need high spatial resolution. Here, we develop a novel AL and deep-learning (DL) hybrid (i.e., $\mathrm{AL}+\mathrm{DL}$) algorithm to realize high-fidelity image reconstruction for CUP. The $\mathrm{AL}+\mathrm{DL}$ algorithm not only optimizes the sparse domain and relevant iteration parameters via learning the dataset but also simplifies the mathematical architecture, so it greatly improves the image reconstruction accuracy. Our theoretical simulation and experimental results validate the superior performance of the $\mathrm{AL}+\mathrm{DL}$ algorithm in image fidelity over conventional AL and TwIST algorithms, where the peak signal-to-noise ratio and structural similarity index can be increased at least by 4 dB (9 dB) and 0.1 (0.05) for a complex (simple) dynamic scene, respectively. This study can promote the applications of CUP in related fields, and it will also enable a new strategy for recovering high-dimensional signals from low-dimensional detection.

中文翻译：

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通过增强的拉格朗日深度学习混合算法对压缩超快摄影进行高保真图像重建

压缩超快摄影（CUP）是最快的单次被动超快光学成像技术，已证明是记录自发光或不可重复的超快现象的有力工具。但是，基于常规的增强拉格朗日（AL）和两步迭代收缩/阈值（TwIST）算法的图像重建低保真度极大地阻止了CUP的实际应用，尤其是对于那些需要高空间分辨率的超快现象。在这里，我们开发了一种新颖的AL和深度学习（DL）混合体（即，$铝+\mathrm{DL}$）算法以实现CUP的高保真图像重建。的$铝+\mathrm{DL}$该算法不仅通过学习数据集优化了稀疏域和相关的迭代参数，而且简化了数学结构，极大地提高了图像重建的准确性。我们的理论仿真和实验结果验证了该系统的优越性能。$铝+\mathrm{DL}$在图像保真度方面优于传统的AL和TwIST算法，对于复杂（简单）的动态场景，峰值信噪比和结构相似性指数至少可以提高4 dB（9 dB）和0.1（0.05），分别。这项研究可以促进银联在相关领域的应用，也将为从低维检测中恢复高维信号提供一种新的策略。