Light-in-flight imaging enables the visualization and characterization of light propagation, which provides essential information for the study of the fundamental phenomena of light. A camera images an object by sensing the light emitted or reflected from it, and interestingly, when a light pulse itself is to be imaged, the relativistic effects, caused by the fact that the distance a pulse travels between consecutive frames is of the same scale as the distance that scattered photons travel from the pulse to the camera, must be accounted for to acquire accurate space–time information of the light pulse. Here, we propose a computational light-in-flight imaging scheme that records the projection of light-in-flight on a transverse x?y plane using a single-photon avalanche diode camera, calculates z and t information of light-in-flight via an optical model, and therefore reconstructs its accurate (x, y, z, t) four-dimensional information. The proposed scheme compensates the temporal distortion in the recorded arrival time to retrieve the accurate time of a light pulse, with respect to its corresponding spatial location, without performing any extra measurements. Experimental light-in-flight imaging in a three-dimensional space of 375mm×75mm×50mm is performed, showing that the position error is 1.75 mm, and the time error is 3.84 ps despite the fact that the camera time resolution is 55 ps, demonstrating the feasibility of the proposed scheme. This work provides a method to expand the recording and measuring of repeatable transient events with extremely weak scattering to four dimensions and can be applied to the observation of optical phenomena with ps temporal resolution.

First-photon imaging is a photon-efficient, computational imaging technique that reconstructs an image by recording only the first-photon arrival event at each spatial location and then optimizing the recorded photon information. The optimization algorithm plays a vital role in image formation. A natural scene containing spatial correlation can be reconstructed by maximum likelihood of all spatial locations constrained with a sparsity regularization penalty, and different penalties lead to different reconstructions. The l1-norm penalty of wavelet transform reconstructs major features but blurs edges and high-frequency details of the image. The total variational penalty preserves edges better; however, it induces a “staircase effect,” which degrades image quality. In this work, we proposed a hybrid penalty to reconstruct better edge features while suppressing the staircase effect by combining wavelet l1-norm and total variation into one penalty function. Results of numerical simulations indicate that the proposed hybrid penalty reconstructed better images, which have an averaged root mean square error of 12.83%, 5.68%, and 10.56% smaller than those of the images reconstructed by using only wavelet l1-norm penalty, total variation penalty, or recursive dyadic partitions method, respectively. Experimental results are in good agreement with the numerical ones, demonstrating the feasibility of the proposed hybrid penalty. Having been verified in a first-photon imaging system, the proposed hybrid penalty can be applied to other noise-removal optimization problems.