WEEP: A Differentiable Nonconvex Sparse Regularizer via Weakly-Convex Envelope
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918296139333632 |
|---|---|
| author | Furuhashi, Takanobu Hontani, Hidekata Zhao, Qibin Yokota, Tatsuya |
| author_facet | Furuhashi, Takanobu Hontani, Hidekata Zhao, Qibin Yokota, Tatsuya |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_20447 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | WEEP: A Differentiable Nonconvex Sparse Regularizer via Weakly-Convex Envelope Furuhashi, Takanobu Hontani, Hidekata Zhao, Qibin Yokota, Tatsuya Machine Learning Computer Vision and Pattern Recognition 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. |
| title | WEEP: A Differentiable Nonconvex Sparse Regularizer via Weakly-Convex Envelope |
| topic | Machine Learning Computer Vision and Pattern Recognition |
| url | https://arxiv.org/abs/2507.20447 |