Properties of Limit Points in Plug-and-Play Iterations

Characterize the properties of limit points generated by Plug-and-Play Prior iterations that use black-box denoisers, especially in settings where no corresponding explicit regularizer exists, including identifying appropriate optimality or stationarity conditions those limit points satisfy.

Background

Even when PnP iterations are studied under restrictive assumptions, the absence of an explicit regularizer tied to the denoiser leaves the status of limit points theoretically unclear. This undermines interpretability and the ability to draw conclusions about optimality or stationarity of the resulting reconstructions.

Clarifying the mathematical nature of these limit points—including data-consistency and relationships to any implicit potentials—would strengthen theoretical foundations and practical trust in PnP methods.