Plug-and-Play (PnP) methods are a class of efficient iterative methods that aim to combine data fidelity terms and deep denoisers using classical optimization algorithms, such as ISTA or ADMM. Existing provable PnP methods impose heavy restrictions on the denoiser or fidelity function, such as nonexpansiveness or strict convexity. In this work, we propose a provable PnP method that imposes relatively light conditions based on proximal denoisers, and introduce a quasi-Newton step to greatly accelerate convergence. By specially parameterizing the deep denoiser as a gradient step, we further characterize the fixed-points of the quasi-Newton PnP algorithm as critical points of a possibly non-convex function.

翻译：即插即用（PnP）方法是一类高效的迭代方法，旨在利用经典优化算法（如ISTA或ADMM）将数据保真项与深度降噪器相结合。现有可证明的PnP方法对降噪器或保真函数施加了严格限制，例如非扩张性或严格凸性。本文提出了一种基于近端降噪器的可证明PnP方法，其施加的条件相对宽松，并引入拟牛顿步长以大幅加速收敛。通过将深度降噪器特殊参数化为梯度步长，我们进一步将拟牛顿PnP算法的不动点表征为可能非凸函数的临界点。