Plug and Play (PnP) methods achieve remarkable results in the framework of image restoration problems for Gaussian data. Nonetheless, the theory available for the Gaussian case cannot be extended to the Poisson case, due to the non-Lipschitz gradient of the fidelity function, the Kullback-Leibler functional, or the absence of closed-form solution for the proximal operator of such term, leading to employ iterative solvers for the inner subproblem. In this work we extend the idea of PIDSplit+ algorithm, exploiting the Alternating Direction Method of Multipliers, to PnP scheme: this allows to provide a closed form solution for the deblurring step, with no need for iterative solvers. The convergence of the method is assured by employing a firmly non expansive denoiser. The proposed method, namely PnPSplit+, is tested on different Poisson image restoration problems, showing remarkable performance even in presence of high noise level and severe blurring conditions.

翻译：即插即用（PnP）方法在高斯数据框架下的图像复原问题中取得了显著成果。然而，由于保真度函数（即Kullback-Leibler泛函）的梯度非Lipschitz连续，且该函数项的邻近算子缺乏闭式解，导致需要采用迭代求解器处理内部子问题，因此适用于高斯情况的理论无法直接推广至泊松情形。本研究将基于交替方向乘子法的PIDSplit+算法思想拓展至PnP框架：该方法能够为去模糊步骤提供闭式解，从而无需迭代求解器。通过采用严格非扩张的去噪器，确保了算法的收敛性。所提出的方法（称为PnPSplit+）在多种泊松图像复原问题上进行了测试，结果表明即使在强噪声和严重模糊条件下，该方法仍能表现出卓越的性能。