提出可微分的稀疏正则化方法，解决优化兼容性难题
WEEP: A Differentiable Nonconvex Sparse Regularizer via Weakly-Convex Envelope
- 基于弱凸包络构造可微分正则项，保持稀疏性
- 在压缩感知与图像去噪任务中优于经典凸与非凸方法
- 适合需梯度优化的稀疏建模场景，如深度学习
稀疏正则化在信号处理与特征提取中至关重要，但常依赖不可微分的惩罚项，与基于梯度的优化器冲突。本文提出 WEEP（分段惩罚的弱凸包络），一种基于弱凸包络框架的新可微分正则化方法。WEEP 提供可调、无偏的稀疏性，具有简单的闭式近端算子，同时保持完全可微性和 L-光滑性，确保与梯度法和近端算法兼容。该方法解决了统计性能与计算可实现性的权衡。在挑战性的压缩感知与图像去噪任务中，其性能显著优于已有的凸与非凸稀疏正则化方法。
原文摘要 · Abstract (English)
Sparse regularization is fundamental in signal processing and feature extraction but often relies on non-differentiable penalties, conflicting with gradient-based optimizers. We propose WEEP (Weakly-convex Envelope of Piecewise Penalty), a novel differentiable regularizer derived from the weakly-convex envelope framework. WEEP provides tunable, unbiased sparsity and a simple closed-form proximal operator, while maintaining full differentiability and L-smoothness, ensuring compatibility with both gradient-based and proximal algorithms. This resolves the tradeoff between statistical performance and computational tractability. We demonstrate superior performance compared to established convex and non-convex sparse regularizers on challenging compressive sensing and image denoising tasks.
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