{"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/an-efficient-method-for-robust-projection","title":"An Efficient Method for Robust Projection Matrix Design","arxiv_id":"1609.08281","date":"2016-09-27","proceeding":null,"authors":["Tao Hong","Zhihui Zhu"],"abstract":"Our objective is to efficiently design a robust projection matrix $\\Phi$ for\nthe Compressive Sensing (CS) systems when applied to the signals that are not\nexactly sparse. The optimal projection matrix is obtained by mainly minimizing\nthe average coherence of the equivalent dictionary. In order to drop the\nrequirement of the sparse representation error (SRE) for a set of training data\nas in [15] [16], we introduce a novel penalty function independent of a\nparticular SRE matrix. Without requiring of training data, we can efficiently\ndesign the robust projection matrix and apply it for most of CS systems, like a\nCS system for image processing with a conventional wavelet dictionary in which\nthe SRE matrix is generally not available. Simulation results demonstrate the\nefficiency and effectiveness of the proposed approach compared with the\nstate-of-the-art methods. In addition, we experimentally demonstrate with\nnatural images that under similar compression rate, a CS system with a learned\ndictionary in high dimensions outperforms the one in low dimensions in terms of\nreconstruction accuracy. This together with the fact that our proposed method\ncan efficiently work in high dimension suggests that a CS system can be\npotentially implemented beyond the small patches in sparsity-based image\nprocessing.","url_abs":"http://arxiv.org/abs/1609.08281v3","url_pdf":"http://arxiv.org/pdf/1609.08281v3.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":"an-efficient-method-for-robust-projection","repo_url":"https://github.com/happyhongt/An-efficient-method-for-robust-projection-matrix-design","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"compressive-sensing","task_name":"Compressive Sensing"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}