标题： 关于使用线性去噪器的PnP正则化的强凸性 显示英文标题

标题： On the Strong Convexity of PnP Regularization Using Linear Denoisers

摘要： 在插件和播放（PnP）方法中，去噪器被用作经典邻近算法中的正则化器，用于图像重建。 已知一类广泛的线性去噪器可以表示为凸正则化器的邻近算子。 因此，相关的PnP算法可以与凸优化问题$\mathcal{P}$相关联。 对于这样的线性去噪器，我们证明$\mathcal{P}$在线性逆问题中表现出强凸性。 具体而言，我们表明$\mathcal{P}$的强凸性可以用于验证由经典邻近方法派生的任何PnP算法的目标和迭代收敛性。 显示英文摘要

摘要： In the Plug-and-Play (PnP) method, a denoiser is used as a regularizer within classical proximal algorithms for image reconstruction. It is known that a broad class of linear denoisers can be expressed as the proximal operator of a convex regularizer. Consequently, the associated PnP algorithm can be linked to a convex optimization problem $\mathcal{P}$. For such a linear denoiser, we prove that $\mathcal{P}$ exhibits strong convexity for linear inverse problems. Specifically, we show that the strong convexity of $\mathcal{P}$ can be used to certify objective and iterative convergence of any PnP algorithm derived from classical proximal methods.