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.

中文翻译：

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通过混合惩罚的第一光子成像

第一光子成像是一种光子高效的计算成像技术，它通过仅记录每个空间位置的第一光子到达事件，然后优化记录的光子信息来重建图像。优化算法在图像形成中起着至关重要的作用。包含空间相关性的自然场景可以通过受稀疏正则化惩罚约束的所有空间位置的最大似然来重建，不同的惩罚导致不同的重建。小波变换的 l1 范数惩罚重建了主要特征，但模糊了图像的边缘和高频细节。总变分惩罚更好地保留了边缘；然而，它会引起“阶梯效应”，从而降低图像质量。在这项工作中，我们提出了一种混合惩罚来重建更好的边缘特征，同时通过将小波 l1 范数和总变化组合成一个惩罚函数来抑制阶梯效应。数值模拟结果表明，所提出的混合惩罚重建了更好的图像，其平均均方根误差分别比仅使用小波 l1 范数惩罚重建的图像小 12.83%、5.68% 和 10.56%，总变异惩罚，或递归二元分区方法，分别。实验结果与数值结果吻合良好，证明了所提出的混合惩罚的可行性。已在第一光子成像系统中得到验证，所提出的混合惩罚可以应用于其他噪声去除优化问题。