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.

翻译：即插即用（PnP）方法是一类高效的迭代方法，旨在通过经典优化算法（如ISTA或ADMM）结合数据保真项和深度去噪器。现有可证明的PnP方法对去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。本文提出一种基于近端去噪器的可证明PnP方法，仅需相对宽松的条件，并引入拟牛顿步以大幅加速收敛。通过将深度去噪器参数化为梯度步，我们进一步刻画了拟牛顿PnP算法的固定点特性。