{"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/fast-l1-minimization-algorithms-for-robust-1","title":"Fast L1-Minimization Algorithms For Robust Face Recognition","arxiv_id":"1007.3753","date":"2010-07-21","proceeding":null,"authors":["Allen Y. Yang","Zihan Zhou","Arvind Ganesh","S. Shankar Sastry","Yi Ma"],"abstract":"L1-minimization refers to finding the minimum L1-norm solution to an underdetermined linear system b=Ax. Under certain conditions as described in compressive sensing theory, the minimum L1-norm solution is also the sparsest solution. In this paper, our study addresses the speed and scalability of its algorithms. In particular, we focus on the numerical implementation of a sparsity-based classification framework in robust face recognition, where sparse representation is sought to recover human identities from very high-dimensional facial images that may be corrupted by illumination, facial disguise, and pose variation. Although the underlying numerical problem is a linear program, traditional algorithms are known to suffer poor scalability for large-scale applications. We investigate a new solution based on a classical convex optimization framework, known as Augmented Lagrangian Methods (ALM). The new convex solvers provide a viable solution to real-world, time-critical applications such as face recognition. We conduct extensive experiments to validate and compare the performance of the ALM algorithms against several popular L1-minimization solvers, including interior-point method, Homotopy, FISTA, SESOP-PCD, approximate message passing (AMP) and TFOCS. To aid peer evaluation, the code for all the algorithms has been made publicly available.","url_abs":"https://arxiv.org/abs/1007.3753v4","url_pdf":"https://arxiv.org/pdf/1007.3753v4.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":"abstracts"},"code_links":[{"paper_slug":"fast-l1-minimization-algorithms-for-robust-1","repo_url":"https://github.com/vbonifaci/l1opt","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"GPL-3.0"}}],"tasks":[{"task_slug":"compressive-sensing","task_name":"Compressive Sensing"},{"task_slug":"face-recognition","task_name":"Face Recognition"},{"task_slug":"robust-face-recognition","task_name":"Robust Face Recognition"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1007.3753","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}