标题： 收敛的插件式播放与近端去噪器和无约束正则化参数 显示英文标题

标题： Convergent plug-and-play with proximal denoiser and unconstrained regularization parameter

摘要： 在本工作中，我们提出了对插件即用（PnP）算法收敛性的新证明。 PnP方法是用于解决图像逆问题的高效迭代算法，其中正则化通过在邻近算法（如邻近梯度下降（PGD）或多尔弗-拉奇福德分裂（DRS））中插入一个预先训练好的去噪器来实现。 最近的研究通过引入一个精确写成邻近算子形式的去噪器来探索收敛性。 然而，相应的PnP算法则必须使用步长等于$1$的方式运行。 所使用邻近算法的非凸收敛步长条件随之转化为对逆问题正则化参数的严格限制。 这可能会严重降低算法的恢复能力。 在本文中，我们提出了两种解决此限制的方法。 首先，我们为PnP-DRS提供了一个新的收敛证明，该证明不对正则化参数施加任何限制。 其次，我们研究了一种放松版本的PGD算法，该算法在更广泛的正则化参数范围内收敛。 我们在去模糊和超分辨率实验上的实验研究结果表明，这两种解决方案都能提高图像恢复的准确性。 显示英文摘要

摘要： In this work, we present new proofs of convergence for Plug-and-Play (PnP) algorithms. PnP methods are efficient iterative algorithms for solving image inverse problems where regularization is performed by plugging a pre-trained denoiser in a proximal algorithm, such as Proximal Gradient Descent (PGD) or Douglas-Rachford Splitting (DRS). Recent research has explored convergence by incorporating a denoiser that writes exactly as a proximal operator. However, the corresponding PnP algorithm has then to be run with stepsize equal to $1$. The stepsize condition for nonconvex convergence of the proximal algorithm in use then translates to restrictive conditions on the regularization parameter of the inverse problem. This can severely degrade the restoration capacity of the algorithm. In this paper, we present two remedies for this limitation. First, we provide a novel convergence proof for PnP-DRS that does not impose any restrictions on the regularization parameter. Second, we examine a relaxed version of the PGD algorithm that converges across a broader range of regularization parameters. Our experimental study, conducted on deblurring and super-resolution experiments, demonstrate that both of these solutions enhance the accuracy of image restoration.