{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/a-novel-regularization-based-on-the-error","title":"A Novel Regularization Based on the Error Function for Sparse Recovery","arxiv_id":"2007.02784","date":"2020-07-06","proceeding":null,"authors":["Weihong Guo","Yifei Lou","Jing Qin","Ming Yan"],"abstract":"Regularization plays an important role in solving ill-posed problems by adding extra information about the desired solution, such as sparsity. Many regularization terms usually involve some vector norm, e.g., $L_1$ and $L_2$ norms. In this paper, we propose a novel regularization framework that uses the error function to approximate the unit step function. It can be considered as a surrogate function for the $L_0$ norm. The asymptotic behavior of the error function with respect to its intrinsic parameter indicates that the proposed regularization can approximate the standard $L_0$, $L_1$ norms as the parameter approaches to $0$ and $\\infty,$ respectively. Statistically, it is also less biased than the $L_1$ approach. We then incorporate the error function into either a constrained or an unconstrained model when recovering a sparse signal from an under-determined linear system. Computationally, both problems can be solved via an iterative reweighted $L_1$ (IRL1) algorithm with guaranteed convergence. A large number of experimental results demonstrate that the proposed approach outperforms the state-of-the-art methods in various sparse recovery scenarios.","url_abs":"https://arxiv.org/abs/2007.02784v1","url_pdf":"https://arxiv.org/pdf/2007.02784v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"a-novel-regularization-based-on-the-error","repo_url":"https://github.com/yflouucla/ErrorFunction4Sparsity","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}