Metropolis-SSD: Symmetric Stochastic Denoisers for Convergent Image Reconstruction

Denoiser-driven methods have become a powerful approach to iterative image reconstruction. Deep denoisers can achieve excellent reconstruction quality, but convergence of the resulting iterations is difficult to guarantee. Such guarantees typically require global properties such as nonexpansiveness, which are difficult to enforce for nonlinear denoisers. Linear denoisers offer a more tractable alternative, as their spectral properties can be analyzed and controlled directly. Their limited expressive power, however, can restrict reconstruction quality. A recent approach, NECTR, bridges this gap by separating nonlinear weight prediction from linear pixel aggregation, using a pretrained network to predict the weights. For quadratic data fidelity, NECTR guarantees convergence by enforcing the resulting linear denoiser ensuring that the resulting linear denoiser is stochasticity can easily be enforced by normalizing the predicted weights, imposing symmetry simultaneously is more challenging. We introduce Metro-SSD, which uses a simple Metropolis-type normalization to enforce both symmetry and stochasticity. Metro-SSD admits an exact matrix free implementation requiring only two aggregation passes, making it practical for large scale problems. Under a mild condition on the imaging forward model, we establish convergence guarantees for Metro-SSD with PnP-HQS and PnP-DRS. Using an attention-based network to predict the aggregation weights, Metro-SSD outperforms or matches the performance of state-of-the-art baselines in deblurring, superresolution and MRI.