{"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/towards-optimal-nonlinearities-for-sparse","title":"Towards optimal nonlinearities for sparse recovery using higher-order statistics","arxiv_id":"1605.08201","date":"2016-05-26","proceeding":null,"authors":["Steffen Limmer","Sławomir Stańczak"],"abstract":"We consider machine learning techniques to develop low-latency approximate\nsolutions to a class of inverse problems. More precisely, we use a\nprobabilistic approach for the problem of recovering sparse stochastic signals\nthat are members of the $\\ell_p$-balls. In this context, we analyze the\nBayesian mean-square-error (MSE) for two types of estimators: (i) a linear\nestimator and (ii) a structured estimator composed of a linear operator\nfollowed by a Cartesian product of univariate nonlinear mappings. By\nconstruction, the complexity of the proposed nonlinear estimator is comparable\nto that of its linear counterpart since the nonlinear mapping can be\nimplemented efficiently in hardware by means of look-up tables (LUTs). The\nproposed structure lends itself to neural networks and iterative\nshrinkage/thresholding-type algorithms restricted to a single iterate (e.g. due\nto imposed hardware or latency constraints). By resorting to an alternating\nminimization technique, we obtain a sequence of optimized linear operators and\nnonlinear mappings that converge in the MSE objective. The result is attractive\nfor real-time applications where general iterative and convex optimization\nmethods are infeasible.","url_abs":"http://arxiv.org/abs/1605.08201v2","url_pdf":"http://arxiv.org/pdf/1605.08201v2.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":"towards-optimal-nonlinearities-for-sparse","repo_url":"https://github.com/stli/MLSP2016_OptNonlin","is_official":1,"mentioned_in_paper":1,"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}