A New Convergence Analysis of Plug-and-Play Proximal Gradient Descent Under Prior Mismatch
This work addresses a theoretical gap in optimization methods for inverse problems, but it appears incremental as it builds on existing plug-and-play frameworks.
The paper tackles the problem of convergence analysis for plug-and-play proximal gradient descent when the denoiser is trained on a mismatched data distribution, providing the first convergence proof under such conditions and removing restrictive assumptions.
In this work, we provide a new convergence theory for plug-and-play proximal gradient descent (PnP-PGD) under prior mismatch where the denoiser is trained on a different data distribution to the inference task at hand. To the best of our knowledge, this is the first convergence proof of PnP-PGD under prior mismatch. Compared with the existing theoretical results for PnP algorithms, our new results removed the need for several restrictive and unverifiable assumptions.