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Bibliographic Details
Main Authors: Furuhashi, Takanobu, Hontani, Hidekata, Zhao, Qibin, Yokota, Tatsuya
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2507.20447
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Table of Contents:
  • 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.