{"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/algorithms-for-the-construction-of-incoherent","title":"Algorithms for the Construction of Incoherent Frames Under Various Design Constraints","arxiv_id":"1801.09678","date":"2018-06-20","proceeding":null,"authors":[],"abstract":"Unit norm finite frames are generalizations of orthonormal bases with many\napplications in signal processing. An important property of a frame is its\ncoherence, a measure of how close any two vectors of the frame are to each\nother. Low coherence frames are useful in compressed sensing applications. When\nused as measurement matrices, they successfully recover highly sparse solutions\nto linear inverse problems. This paper describes algorithms for the design of\nvarious low coherence frame types: real, complex, unital (constant magnitude)\ncomplex, sparse real and complex, nonnegative real and complex, and harmonic\n(selection of rows from Fourier matrices). The proposed methods are based on\nsolving a sequence of convex optimization problems that update each vector of\nthe frame. This update reduces the coherence with the other frame vectors,\nwhile other constraints on its entries are also imposed. Numerical experiments\nshow the effectiveness of the methods compared to the Welch bound, as well as\nother competing algorithms, in compressed sensing applications.","url_abs":"http://arxiv.org/abs/1801.09678v2","url_pdf":"http://arxiv.org/pdf/1801.09678v2.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":"algorithms-for-the-construction-of-incoherent","repo_url":"https://github.com/cristian-rusu-research/SIDCO","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"compressed-sensing","task_name":"compressed sensing"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}