Please use this identifier to cite or link to this item: https://doi.org/10.3934/ipi.2013.7.1075
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dc.titleA fast modified Newton's method for curvature based denoising of 1D signals
dc.contributor.authorYip, A.M.
dc.contributor.authorZhu, W.
dc.date.accessioned2014-10-28T02:28:04Z
dc.date.available2014-10-28T02:28:04Z
dc.date.issued2013-08
dc.identifier.citationYip, A.M., Zhu, W. (2013-08). A fast modified Newton's method for curvature based denoising of 1D signals. Inverse Problems and Imaging 7 (3) : 1075-1097. ScholarBank@NUS Repository. https://doi.org/10.3934/ipi.2013.7.1075
dc.identifier.issn19308337
dc.identifier.urihttp://scholarbank.nus.edu.sg/handle/10635/102642
dc.description.abstractWe propose a novel fast numerical method for denoising of 1D signals based on curvature minimization. Motivated by the primal-dual formulation for total variation minimization introduced by Chan, Golub, and Mulet, the proposed method makes use of some auxiliary variables to reformulate the stiff terms presented in the Euler-Lagrange equation which is a fourth-order differential equation. A direct application of Newton's method to the resulting system of equations often fails to converge. We propose a modified Newton's iteration which exhibits local superlinear convergence and global convergence in practical settings. The method is much faster than other existing methods for the model. Unlike all other existing methods, it also does not require tuning any additional parameter besides the model parameter. Numerical experiments are presented to demonstrate the effectiveness of the proposed method. © 2013 American Institute of Mathematical Sciences.
dc.description.urihttp://libproxy1.nus.edu.sg/login?url=http://dx.doi.org/10.3934/ipi.2013.7.1075
dc.sourceScopus
dc.subjectDenoising
dc.subjectMean curvature
dc.subjectNewton's method
dc.subjectTotal variation
dc.subjectVariational method
dc.typeArticle
dc.contributor.departmentMATHEMATICS
dc.description.doi10.3934/ipi.2013.7.1075
dc.description.sourcetitleInverse Problems and Imaging
dc.description.volume7
dc.description.issue3
dc.description.page1075-1097
dc.identifier.isiut000324405200023
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