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  • Received: Oct. 25, 2019

    Accepted: Dec. 24, 2019

    Posted: Jan. 3, 2020

    Published Online: Feb. 14, 2020

    The Author Email: Ming-Jie Sun (

    DOI: 10.1364/PRJ.381516

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    Xiao Peng, Xin-Yu Zhao, Li-Jing Li, Ming-Jie Sun. First-photon imaging via a hybrid penalty[J]. Photonics Research, 2020, 8(3): 03000325

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Photonics Research, Vol. 8, Issue 3, 03000325 (2020)

First-photon imaging via a hybrid penalty

Xiao Peng1,†, Xin-Yu Zhao1,†, Li-Jing Li, and Ming-Jie Sun*

Author Affiliations

  • School of Instrumentation and Optoelectronic Engineering, Beihang University, Beijing 100191, China


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.