Stabilizing Deep Reconstruction Operators with Contractive Anchoring

Pretrained deep denoisers can be used to solve a wide range of model-based image reconstruction tasks via Plug-and-Play (PnP) and Regularization-by-Denoising (RED) algorithms, without retraining per task. These denoisers are trained only for single-step denoising. Using them as Image Reconstruction (IR) regularizers in an iterative process can destabilize reconstruction. A common failure mode is the peak-and-collapse behaviour: metrics such as PSNR improve for early iterations and then abruptly degrade, making these algorithms unreliable in practice. We propose a data-driven stabilization framework that (i) formalizes this instability of any IR operator through a local quantity and (ii) prevents collapse by regularizing this quantity adaptively, requiring no retraining or modification of the given pretrained network. Our key idea is to control the potentially unstable IR operator with a contractive operator whose stable iterates act as an anchor and prevent collapse. We further introduce an efficient family of trainable contractive operators that serve as strong anchors while remaining lightweight. Extensive experiments across proximal algorithms, denoiser architectures, noise levels, and imaging tasks show consistent, collapse-free performance and improved reliability of PnP and RED reconstruction.