用图拉普拉斯正则化构建可解释的轻量级图像去噪网络。
Constructing an Interpretable Deep Denoiser by Unrolling Graph Laplacian Regularizer
- 通过展开共轭梯度法，将图正则化去噪问题转化为神经网络层。
- 参数量远少于同类模型，且在分布偏移下仍保持稳定性能。
- 适合需要可解释性与低资源部署的图像修复场景。
图像去噪器可通过插拔式（PnP）架构应用于多种复原任务。本文提出一种通用框架，通过展开最大后验（MAP）问题求解过程，构建基于图拉普拉斯正则化（GLR）的可解释深度去噪器（GDD）。基于近期定理：任意（伪）线性去噪器Ψ，在温和条件下可映射为使用GLR正则化的MAP问题解，我们首先通过Ψ⁻¹的截断泰勒展开初始化图拉普拉斯矩阵L。随后，将共轭梯度（CG）算法的迭代过程展开为前馈神经网络的多层结构，实现参数可调。所提GDD网络具有图结构可解释性、参数量低、初始化简便等优势。实验表明，其去噪性能媲美现有方法，但参数显著减少，且对协变量偏移更具鲁棒性。
原文摘要 · Abstract (English)
An image denoiser can be used for a wide range of restoration problems via the Plug-and-Play (PnP) architecture. In this paper, we propose a general framework to build an interpretable graph-based deep denoiser (GDD) by unrolling a solution to a maximum a posteriori (MAP) problem equipped with a graph Laplacian regularizer (GLR) as signal prior. Leveraging a recent theorem showing that any (pseudo-)linear denoiser $\boldsymbol Ψ$, under mild conditions, can be mapped to a solution of a MAP denoising problem regularized using GLR, we first initialize a graph Laplacian matrix $\mathbf L$ via truncated Taylor Series Expansion (TSE) of $\boldsymbol Ψ^{-1}$. Then, we compute the MAP linear system solution by unrolling iterations of the conjugate gradient (CG) algorithm into a sequence of neural layers as a feed-forward network -- one that is amenable to parameter tuning. The resulting GDD network is "graph-interpretable", low in parameter count, and easy to initialize thanks to $\mathbf L$ derived from a known well-performing denoiser $\boldsymbol Ψ$. Experimental results show that GDD achieves competitive image denoising performance compared to competitors, but employing far fewer parameters, and is more robust to covariate shift.
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