Image reconstruction for compressed ultrafast photography based on manifold learning and the alternating direction method of multipliers

Compressed ultrafast photography (CUP) is a high-speed imaging technique with a frame rate of up to ten trillion frames per second (fps) and a sequence depth of hundreds of frames. This technique is a powerful tool for investigating ultrafast processes. However, since the reconstruction process is an ill-posed problem, the image reconstruction will be more difficult with the increase of the number of reconstruction frames and the number of pixels of each reconstruction frame. Recently, various deep-learning-based regularization terms have been used to improve the reconstruction quality of CUP, but most of them require extensive training and are not generalizable. In this paper, we propose a reconstruction algorithm for CUP based on the manifold learning and the alternating direction method of multipliers framework (ML-ADMM), which is an unsupervised learning algorithm. This algorithm improves the reconstruction stability and quality by initializing the iterative process with manifold modeling in embedded space (MMES) and processing the image obtained from each ADMM iterative with a nonlinear modeling based on manifold learning. The numerical simulation and experiment results indicate that most of the spatial details can be recovered and local noise can be eliminated. In addition, a high-spatiotemporal-resolution video sequence can be acquired. Therefore, this method can be applied for CUP with ultrafast imaging applications in the future.