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Title: A fast modified Newton's method for curvature based denoising of 1D signals
Authors: Yip, A.M. 
Zhu, W.
Keywords: Denoising
Mean curvature
Newton's method
Total variation
Variational method
Issue Date: Aug-2013
Citation: Yip, 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.
Abstract: We 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.
Source Title: Inverse Problems and Imaging
ISSN: 19308337
DOI: 10.3934/ipi.2013.7.1075
Appears in Collections:Staff Publications

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