On the Strong Convexity of PnP Regularization Using Linear Denoisers
Arghya Sinha, Kunal N. Chaudhury · IEEE Signal Processing Letters · 2024
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 ofanyPnP algorithm derived from classical proximal methods.