A new generalized projection and its application to acceleration of audio declipping

A new generalized projection and its application to acceleration of audio declipping

Článek WoS

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.

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.

projection; optimization; generalization; box constraints; declipping; desaturation; proximal splitting; sparsity

projection; optimization; generalization; box constraints; declipping; desaturation; proximal splitting; sparsity

RAJMIC, P.; ZÁVIŠKA, P.; VESELÝ, V.; MOKRÝ, O.

2020

19.09.2019

MDPI

Basel

2075-1680

Axioms

8

3

Švýcarská konfederace

1

20

20

https://www.mdpi.com/2075-1680/8/3/105

http://hdl.handle.net/11012/180691

axioms-08-00105