Learning Weakly Monotone Operators for Convergent Plug-and-Play PET Reconstruction

This letter extends the capabilities of Plug-and-Play ADMM, a popular algorithm for solving inverse problems while leveraging deep learning priors. Convergence results on PnP ADMM often rely on the Douglas-Rachford (DR) splitting method and require a firmly nonexpansive constraint on the plugged network. Common convolutional architectures do not inherently verify this constraint, and many works are now trying to circumvent it. Building on recent advancements in the DR method for handling weakly monotone operators, we propose a modification of PnP ADMM for low-count Positron Emission Tomography reconstruction, allowing for networks trained on reconstruction-specific tasks with a more general averageness constraint. Our numerical experiments on simulated brain data demonstrate that this flexibility simplifies training and improves reconstruction quality.