A New Generalized Projection and Its Application to Acceleration of Audio Declipping
1
Signal Processing Laboratory, Brno University of Technology, 616 00 Brno, Czech Republic
2
Faculty of Mechanical Engineering, Brno University of Technology, 616 69 Brno, Czech Republic
*
Author to whom correspondence should be addressed.
†
Current address: Technická 12, 616 00 Brno, Czech Republic.
Axioms 2019, 8(3), 105; https://doi.org/10.3390/axioms8030105
Received: 6 March 2019
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Revised: 9 September 2019
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Accepted: 10 September 2019
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Published: 19 September 2019
(This article belongs to the Special Issue Harmonic Analysis and Applications)
In convex optimization, it is often inevitable to work with projectors onto convex sets composed with a linear operator. Such a need arises from both the theory and applications, with signal processing being a prominent and broad field where convex optimization has been used recently. In this article, a novel projector is presented, which generalizes previous results in that it admits to work with a broader family of linear transforms when compared with the state of the art but, on the other hand, it is limited to box-type convex sets in the transformed domain. The new projector is described by an explicit formula, which makes it simple to implement and requires a low computational cost. The projector is interpreted within the framework of the so-called proximal splitting theory. The convenience of the new projector is demonstrated on an example from signal processing, where it was possible to speed up the convergence of a signal declipping algorithm by a factor of more than two.
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Keywords:
projection; optimization; generalization; box constraints; declipping; desaturation; proximal splitting; sparsity
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MDPI and ACS Style
Rajmic, P.; Záviška, P.; Veselý, V.; Mokrý, O. A New Generalized Projection and Its Application to Acceleration of Audio Declipping. Axioms 2019, 8, 105. https://doi.org/10.3390/axioms8030105
AMA Style
Rajmic P, Záviška P, Veselý V, Mokrý O. A New Generalized Projection and Its Application to Acceleration of Audio Declipping. Axioms. 2019; 8(3):105. https://doi.org/10.3390/axioms8030105
Chicago/Turabian StyleRajmic, Pavel, Pavel Záviška, Vítězslav Veselý, and Ondřej Mokrý. 2019. "A New Generalized Projection and Its Application to Acceleration of Audio Declipping" Axioms 8, no. 3: 105. https://doi.org/10.3390/axioms8030105
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