Underwater single-photon imaging is challenging, as the transmitting path presents turbulence and strong backscattering noise; both facts degrade the image, thus hindering its applications in real world. However, current studies on underwater single-photon modeling have generally overlooked the potential impact of water turbulence on imaging performance. This oversight may result in an inaccurate characterization of the optical propagation process in realistic imaging environment. This letter proposed a joint denoising and deblurring method with regularization by denoising (JDD-RED) for underwater single-photon image that include the modeling of turbulence and the tailored restoration model, improving the performance by considering blurring mechanism, as well as advanced signal processing method. This method is validated on numerical experiments by employing joint deblurring and denoising tasks. Compared with the PICK-3-D algorithm, the JDD-RED reconstruction results demonstrate that more detailed information can be retained while denoising. In addition, the results show an average improvement of 1.48 dB in peak signal-to-noise ratio (PSNR) and 60% in structural similarity (SSIM), proving the superior performance of the JDD-RED algorithm.

This paper presents a new algorithm for the learning of spatial correlation and non-local restoration of single-photon 3-Dimensional Lidar images acquired in the photon starved regime (fewer or less than one photon per pixel) or with a reduced number of scanned spatial points (pixels). The algorithm alternates between three steps: (i) extract multi-scale information, (ii) build a robust graph of non-local spatial correlations between pixels, and (iii) the restoration of depth and reflectivity images. A non-uniform sampling approach, which assigns larger patches to homogeneous regions and smaller ones to heterogeneous regions, is adopted to reduce the computational cost associated with the graph. The restoration of the 3D images is achieved by minimizing a cost function accounting for the multi-scale information and the non-local spatial correlation between patches. This minimization problem is efficiently solved using the alternating direction method of multipliers (ADMM) that presents fast convergence properties. Various results based on simulated and real Lidar data show the benefits of the proposed algorithm that improves the quality of the estimated depth and reflectivity images, especially in the photon-starved regime or when containing a reduced number of spatial points.