A fast modified Newton's method for curvature based denoising of 1D signals
Andy M. Yip, Wei Dong Zhu · Inverse Problems and Imaging · 2013
We propose a novel fast numerical method for denoising of 1D signalsbased on curvature minimization. Motivated by theprimal-dual formulation for total variation minimizationintroduced by Chan, Golub, and Mulet, the proposed method makesuse of some auxiliary variables to reformulate the stiff terms presentedin the Euler-Lagrange equation which is a fourth-orderdifferential equation. A direct application of Newton's methodto the resulting system of equations often fails to converge.We propose a modified Newton's iteration whichexhibits 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 additionalparameter besides the model parameter.Numerical experiments are presented to demonstrate theeffectiveness of the proposed method.