Domain Adaptation of Mismatched Proximal Denoiser for Plug-and-Play Image Reconstruction

What the math gives to ML

The paper provides a useful way to measure deployment-domain shift for denoisers: not by output MSE alone, but by how far the denoiser is from the proximal map that the reconstruction algorithm implicitly needs. This turns denoiser adaptation into an operator-matching problem and yields an optimization-relevant error term, because the average squared proximal mismatch appears as an additive stationarity floor in PnP iterations. The most transferable construction is a proximal-consistency fine-tuning loss for denoising or generative restoration modules, evaluated on the actual noisy iterates produced by the downstream inverse solver rather than only on clean-image pairs.