Improving the image reconstruction quality of compressed ultrafast photography via an augmented Lagrangian algorithm

Compressed ultrafast photography (CUP) has been shown to be a powerful tool to measure ultrafast dynamic scenes. In previous studies, CUP used a two-step iterative shrinkage/thresholding (TwIST) algorithm to reconstruct three-dimensional image information. However, the image reconstruction quality greatly depended on the selection of the penalty parameter, which caused the reconstructed images to be unable to be correctly determined if the ultrafast dynamic scenes were unknown in advance. Here, we develop an augmented Lagrangian (AL) algorithm for the image reconstruction of CUP to overcome the limitation of the TwIST algorithm. Our numerical simulations and experimental results show that, compared to the TwIST algorithm, the AL algorithm is less dependent on the selection of the penalty parameter, and can obtain higher image reconstruction quality. This study solves the problem of the image reconstruction instability, which may further promote the practical applications of CUP.