AI 中文总结
该研究提出基于PnP-split的\textbf{GSDsplit}方法，以输入凸神经网络参数化的松弛梯度步去噪器替代通用去噪块，提升泊松逆问题重建的稳定性并降低对ADMM参数的敏感性。
AI 中文摘要
Plug&Play方法将经典变分模型与学习到的去噪器相结合，在成像逆问题中取得了优异的结果。它们的收敛性已针对高斯数据进行了广泛研究，而泊松模型由于非二次Kullback-Leibler保真项需要额外注意。本研究引入了\textbf{GSDsplit}，一种基于\textbf{PnP-split}的分裂方法，其中通用去噪块被替换为松弛梯度步去噪器。所得方法保留了显式泊松保真度更新。该去噪器通过由输入凸神经网络（Input Convex Neural Network）参数化的学习凸势的梯度定义，其架构和训练同时促进盲去噪能力和足以保证 firm nonexpansiveness 的平滑性条件。使用经验平滑度估计选择与\textbf{PnP-split}收敛假设兼容的松弛参数。数值实验提供证据表明，训练后的去噪器在考虑的验证数据上以与FNE兼容的机制运行。\textbf{GSDsplit}在经验支持范围之外也能产生稳定的重建，对ADMM参数的敏感性显著降低，同时对不同模糊算子和泊松噪声水平仍保持有效。
英文摘要
Plug and Play methods combine classical variational models with learned denoisers and have achieved strong results in imaging inverse problems. Their convergence has been widely studied for Gaussian data, whereas Poisson models require additional care because of the nonquadratic Kullback-Leibler fidelity. This work introduces GSDSplit+ , a splitting method built upon PnPSplit+, in which the generic denoising block is replaced by a relaxed Gradient Step Denoiser. The resulting method retains explicit Poisson fidelity updates. The denoiser is defined through the gradient of a learned convex potential parameterized by an Input Convex Neural Network. Its architecture and training promote both blind denoising capability and a smoothness condition sufficient for firm nonexpansiveness. Empirical smoothness estimates are used to select a relaxation parameter compatible with the convergence assumptions of PnPSplit+. Numerical experiments provide evidence that the trained denoiser operates in an FNE-compatible regime on the considered validation data. GSDSplit+ also yields stable reconstructions outside the empirically supported range and shows substantially lower sensitivity to the ADMM parameter, while remaining effective for different blur operators and Poisson noise levels.
