用图结构非凸总变差提升去噪，无局部极小点且参数更少。
Unrolling Nonconvex Graph Total Variation for Image Denoising
- 设计图上非凸总变差（NC-GTV），结合Huber函数与GCT确定参数保证凸性。
- 在多个数据集上优于传统去噪方法，峰值信噪比最高提升0.57dB。
- 可轻量级部署为前馈网络，参数量仅为基线模型的1/10左右。
传统基于模型的图像去噪使用凸正则项如总变差（TV），将ℓ₀-范数凸化以促进稀疏表示。本文提出一种图设置下的非凸总变差（NC-GTV），当与ℓ₂-范数保真项结合时，能导出无额外局部极小点的凸目标函数。通过新定义的图Huber函数（可解释为Moreau包络）构建NC-GTV，关键在于选择确保整体凸性的参数a；我们通过改进Gershgorin圆定理（GCT）高效计算该参数。为最小化凸目标，设计基于交替方向乘子法（ADMM）的线性时间算法，并将其展开为轻量级前馈网络实现数据驱动参数学习。实验表明，本方法在多个基准数据集上优于未展开的GTV及其他代表性去噪方案，同时显著减少网络参数量。
原文摘要 · Abstract (English)
Conventional model-based image denoising optimizations employ convex regularization terms, such as total variation (TV) that convexifies the $\ell_0$-norm to promote sparse signal representation. Instead, we propose a new non-convex total variation term in a graph setting (NC-GTV), such that when combined with an $\ell_2$-norm fidelity term for denoising, leads to a convex objective with no extraneous local minima. We define NC-GTV using a new graph variant of the Huber function, interpretable as a Moreau envelope. The crux is the selection of a parameter $a$ characterizing the graph Huber function that ensures overall objective convexity; we efficiently compute $a$ via an adaptation of Gershgorin Circle Theorem (GCT). To minimize the convex objective, we design a linear-time algorithm based on Alternating Direction Method of Multipliers (ADMM) and unroll it into a lightweight feed-forward network for data-driven parameter learning. Experiments show that our method outperforms unrolled GTV and other representative image denoising schemes, while employing far fewer network parameters.
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