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

Abstract

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.

Coded aperture snapshot spectral imaging fundus camera

“…Given the measurement y and matrix 𝜱, there are two optimization frameworks to predict the original spectral scene 𝒇 : the penalty function method and the augmented Lagrangian (AL) method. Because the AL method outperforms the penalty function method, as shown in the previous studies [24][25][26], we use the AL method to solve the above inverse problem:…”

Punching holes in light: recent progress in single-shot coded-aperture optical imaging

“…The solution to this minimization problem can be stably and accurately recovered, even with a highly compressed measurement [187]. In practice, equation (5-4) can be solved by various methods, including the two-step iterative shrinkage/thresholding algorithm [188], alternating direction method of multipliers algorithm [189], and augmented Lagrangian algorithm [190]. For the first-generation CUP system, the reconstruction produced up to 350 frames in a movie, with an imaging speed of up to 100 billion fps.…”

Single-shot compressed ultrafast photography: a review

“…One example is optimizing the search path to seek a better CS algorithm, which has resulted in the proposed use of the augmented Lagrangian (AL) algorithm. 36 In addition, an alternative scheme is confining the search path within a certain scope, which is called the space-and intensityconstrained (SIC) reconstruction method. 37…”

“…To further validate the improvement in the image reconstruction quality, a superluminal propagation of noninformation was recorded in Ref. 36. As shown in Fig.…”