用于即插即用图像重建的不匹配近端去噪器的域适应
Domain Adaptation of Mismatched Proximal Denoiser for Plug-and-Play Image Reconstruction
浏览论文内容
中文总结 AI 辅助
研究即插即用图像重建中因去噪器部署在训练域外导致的域不匹配问题，定义近端不匹配，推导平稳性界，通过近端匹配适应方法，用两个去噪器家族实验，表明该方法在少样本下显著提升重建质量。
中文摘要 AI 辅助
即插即用近端梯度下降（PnP-PGD）通过使用去噪器作为隐式先验来实现灵活的图像重建。在实际应用中，这些去噪器常常在其训练域之外部署。现有分析在对部署的去噪器的结构假设下建立收敛性，比如要求它是近端映射或收缩映射。然而，它们并未衡量域不匹配如何影响PnP-PGD的收敛。我们将这种影响定义为近端不匹配：部署的去噪器$\widehat{\mathsf D}$与与基础正则化器$R_\star$相关联的目标域参考映射$\mathsf D_\star=\operatorname{prox}_{R_\star}$之间的差异。在这种不匹配情况下，每次去噪更新对于目标目标而言都成为一个不精确的近端步骤。我们进一步推导了一个以$\mathcal{O}(1/K)$的速率衰减的平稳性界，还有一个与平均平方近端不匹配成比例的附加项。这个结果促使通过近端匹配而不是仅基于均方误差的适应方法。我们用两个已有的去噪器家族研究了这种方法：学习近端网络和梯度步去噪器。在大量域偏移下的高斯去模糊和超分辨率实验表明，近端匹配适应比基于均方误差的适应显著提高了重建质量，在少样本情况下获得了最大的数值增益。
英文摘要
Plug-and-play proximal gradient descent (PnP-PGD) enables flexible image reconstruction by using denoisers as implicit priors. In practice, these denoisers are often deployed outside their training domains. Existing analyses establish convergence under structural assumptions on the deployed denoiser, such as requiring it to be a proximal map or a contraction. However, they do not measure how domain mismatch affects convergence of PnP-PGD. We define this effect as \emph{proximal mismatch}: the discrepancy between a deployed denoiser $\widehat{\mathsf D}$ and a target-domain reference map $\mathsf D_\star=\operatorname{prox}_{R_\star}$ associated with the underlying regularizer $R_\star$. Under this mismatch, each denoising update becomes an inexact proximal step for the target objective. We further derive a stationarity bound that decays at a rate of $\mathcal{O}(1/K)$, with an additive term proportional to the average squared proximal mismatch. This result motivates adaptation via proximal matching rather than MSE-based adaptation alone. We study this approach with two established denoiser families: learned proximal networks and gradient-step denoisers. Experiments on Gaussian deblurring and super-resolution under substantial domain shift show that proximal matching adaptation improves reconstruction quality significantly over MSE-based adaptation, yielding the largest numerical gains in the few-shot regime.
发表机构
- School of Mathematics, University of Birmingham（数学系，伯明翰大学）
机构由 AI 辅助整理，请以论文原文为准。
