Stabilizing Deep Reconstruction Operators with Contractive Anchoring

Pretrained deep denoisers can be used to solve a wide rangeof model-based image reconstruction tasks via Plug-and-Play (PnP) andRegularization-by-Denoising (RED) algorithms, without retraining pertask. These denoisers are trained only for single-step denoising. Usingthem as Image Reconstruction (IR) regularizers in an iterative processcan destabilize reconstruction. A common failure mode is the peak-and-collapse behaviour: metrics such as PSNR improve for early iterations andthen abruptly degrade, making these algorithms unreliable in practice.We propose a data-driven stabilization framework that (i) formalizes thisinstability of any IR operator through a local quantity and (ii) preventscollapse by regularizing this quantity adaptively, requiring no retrainingor modification of the given pretrained network. Our key idea is tocontrol the potentially unstable IR operator with a contractive operatorwhose stable iterates act as an anchor and prevent collapse. We furtherintroduce an efficient family of trainable contractive operators that serve asstrong anchors while remaining lightweight. Extensive experiments acrossproximal algorithms, denoiser architectures, noise levels, and imagingtasks show consistent, collapse-free performance and improved reliabilityof PnP and RED reconstruction.