Efficient FirstOrder Algorithms for Adaptive Signal Denoising
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Proceedings of the 35th International Conference on Machine Learning, PMLR 80:39463955, 2018.
Abstract
We consider the problem of discretetime signal denoising, focusing on a specific family of nonlinear convolutiontype estimators. Each such estimator is associated with a timeinvariant filter which is obtained adaptively, by solving a certain convex optimization problem. Adaptive convolutiontype estimators were demonstrated to have favorable statistical properties, see (Juditsky & Nemirovski, 2009; 2010; Harchaoui et al., 2015b; Ostrovsky et al., 2016). Our first contribution is an efficient implementation of these estimators via the known firstorder proximal algorithms. Our second contribution is a computational complexity analysis of the proposed procedures, which takes into account their statistical nature and the related notion of statistical accuracy. The proposed procedures and their analysis are illustrated on a simulated data benchmark.
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