High-fidelity image reconstruction for compressed ultrafast photography via an augmented- Lagrangian and deep-learning hybrid algorithm

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., AL + DL) algorithm to realize high-fidelity image reconstruction for CUP. The AL + 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 AL + DL algorithm in image fidelity over conventional AL and TwIST algorithms, where the peak signalto- 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.