Efficient First-Order Algorithms for Adaptive Signal Denoising

Dmitrii Ostrovskii, Zaid Harchaoui
Proceedings of the 35th International Conference on Machine Learning, PMLR 80:3946-3955, 2018.

Abstract

We consider the problem of discrete-time signal denoising, focusing on a specific family of non-linear convolution-type estimators. Each such estimator is associated with a time-invariant filter which is obtained adaptively, by solving a certain convex optimization problem. Adaptive convolution-type 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 first-order 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v80-ostrovskii18a, title = {Efficient First-Order Algorithms for Adaptive Signal Denoising}, author = {Ostrovskii, Dmitrii and Harchaoui, Zaid}, booktitle = {Proceedings of the 35th International Conference on Machine Learning}, pages = {3946--3955}, year = {2018}, editor = {Dy, Jennifer and Krause, Andreas}, volume = {80}, series = {Proceedings of Machine Learning Research}, month = {10--15 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v80/ostrovskii18a/ostrovskii18a.pdf}, url = {https://proceedings.mlr.press/v80/ostrovskii18a.html}, abstract = {We consider the problem of discrete-time signal denoising, focusing on a specific family of non-linear convolution-type estimators. Each such estimator is associated with a time-invariant filter which is obtained adaptively, by solving a certain convex optimization problem. Adaptive convolution-type 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 first-order 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.} }
Endnote
%0 Conference Paper %T Efficient First-Order Algorithms for Adaptive Signal Denoising %A Dmitrii Ostrovskii %A Zaid Harchaoui %B Proceedings of the 35th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2018 %E Jennifer Dy %E Andreas Krause %F pmlr-v80-ostrovskii18a %I PMLR %P 3946--3955 %U https://proceedings.mlr.press/v80/ostrovskii18a.html %V 80 %X We consider the problem of discrete-time signal denoising, focusing on a specific family of non-linear convolution-type estimators. Each such estimator is associated with a time-invariant filter which is obtained adaptively, by solving a certain convex optimization problem. Adaptive convolution-type 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 first-order 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.
APA
Ostrovskii, D. & Harchaoui, Z.. (2018). Efficient First-Order Algorithms for Adaptive Signal Denoising. Proceedings of the 35th International Conference on Machine Learning, in Proceedings of Machine Learning Research 80:3946-3955 Available from https://proceedings.mlr.press/v80/ostrovskii18a.html.

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