Efficient Linearized Bregman Iteration for Sparse Adaptive Filters and Kaczmarz Solvers

Michael Lunglmayr; Mario Huemer

doi:10.1109/SAM.2016.7569759

Efficient Linearized Bregman Iteration for Sparse Adaptive Filters and Kaczmarz Solvers

Institute of Signal Processing

Research output: Chapter in Book/Report/Conference proceeding › Conference proceedings › peer-review

Abstract

Linearized Bregman iterations are low complexity and high precision approaches for solving the combined l1 /l2 minimization problem. In this work we give a derivation of the linearized Bregman iteration and show the links to Kaczmarz’s algorithm as well as to sparse least mean squares (LMS) filters. We present a novel extension allowing to perform combined l1 /l2 minimization either in an LMS based adaptive filter or in a Kaczmarz based batch solution. By means of simulations we demonstrate that the performance of our extension is comparable to the original linearized Bregman approaches. Furthermore, we show that with this extension l1/l2 minimization can be performed with less complexity than the corresponding l2 minimization.

Original language	English
Title of host publication	Proceedings of IEEE 9th Sensor Array and Multichannel Signal Processing Workshop (SAM 2016)
Publisher	IEEE
Number of pages	5
ISBN (Electronic)	9781509021031
DOIs	https://doi.org/10.1109/SAM.2016.7569759
Publication status	Published - Jul 2016

Publication series

Name	Proceedings of the IEEE Sensor Array and Multichannel Signal Processing Workshop
ISSN (Print)	2151-870X

Fields of science

202 Electrical Engineering, Electronics, Information Engineering
202015 Electronics
202022 Information technology
202037 Signal processing
202041 Computer engineering

JKU Focus areas

Computation in Informatics and Mathematics
Mechatronics and Information Processing

Access to Document

10.1109/SAM.2016.7569759

Cite this

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title = "Efficient Linearized Bregman Iteration for Sparse Adaptive Filters and Kaczmarz Solvers",

abstract = "Linearized Bregman iterations are low complexity and high precision approaches for solving the combined l1 /l2 minimization problem. In this work we give a derivation of the linearized Bregman iteration and show the links to Kaczmarz{\textquoteright}s algorithm as well as to sparse least mean squares (LMS) filters. We present a novel extension allowing to perform combined l1 /l2 minimization either in an LMS based adaptive filter or in a Kaczmarz based batch solution. By means of simulations we demonstrate that the performance of our extension is comparable to the original linearized Bregman approaches. Furthermore, we show that with this extension l1/l2 minimization can be performed with less complexity than the corresponding l2 minimization.",

author = "Michael Lunglmayr and Mario Huemer",

year = "2016",

month = jul,

doi = "10.1109/SAM.2016.7569759",

language = "English",

series = "Proceedings of the IEEE Sensor Array and Multichannel Signal Processing Workshop",

publisher = "IEEE",

booktitle = "Proceedings of IEEE 9th Sensor Array and Multichannel Signal Processing Workshop (SAM 2016)",

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Efficient Linearized Bregman Iteration for Sparse Adaptive Filters and Kaczmarz Solvers. / Lunglmayr, Michael ; Huemer, Mario.
Proceedings of IEEE 9th Sensor Array and Multichannel Signal Processing Workshop (SAM 2016). IEEE, 2016. 7569759 (Proceedings of the IEEE Sensor Array and Multichannel Signal Processing Workshop).

Research output: Chapter in Book/Report/Conference proceeding › Conference proceedings › peer-review

TY - GEN

T1 - Efficient Linearized Bregman Iteration for Sparse Adaptive Filters and Kaczmarz Solvers

AU - Lunglmayr, Michael

AU - Huemer, Mario

PY - 2016/7

Y1 - 2016/7

N2 - Linearized Bregman iterations are low complexity and high precision approaches for solving the combined l1 /l2 minimization problem. In this work we give a derivation of the linearized Bregman iteration and show the links to Kaczmarz’s algorithm as well as to sparse least mean squares (LMS) filters. We present a novel extension allowing to perform combined l1 /l2 minimization either in an LMS based adaptive filter or in a Kaczmarz based batch solution. By means of simulations we demonstrate that the performance of our extension is comparable to the original linearized Bregman approaches. Furthermore, we show that with this extension l1/l2 minimization can be performed with less complexity than the corresponding l2 minimization.

AB - Linearized Bregman iterations are low complexity and high precision approaches for solving the combined l1 /l2 minimization problem. In this work we give a derivation of the linearized Bregman iteration and show the links to Kaczmarz’s algorithm as well as to sparse least mean squares (LMS) filters. We present a novel extension allowing to perform combined l1 /l2 minimization either in an LMS based adaptive filter or in a Kaczmarz based batch solution. By means of simulations we demonstrate that the performance of our extension is comparable to the original linearized Bregman approaches. Furthermore, we show that with this extension l1/l2 minimization can be performed with less complexity than the corresponding l2 minimization.

UR - http://sam2016.cetuc.puc-rio.br/

U2 - 10.1109/SAM.2016.7569759

DO - 10.1109/SAM.2016.7569759

M3 - Conference proceedings

T3 - Proceedings of the IEEE Sensor Array and Multichannel Signal Processing Workshop

BT - Proceedings of IEEE 9th Sensor Array and Multichannel Signal Processing Workshop (SAM 2016)

PB - IEEE

ER -

Efficient Linearized Bregman Iteration for Sparse Adaptive Filters and Kaczmarz Solvers

Abstract

Publication series

Fields of science

JKU Focus areas

Access to Document

Other files and links

Low Complexity Iterative Signal Processing Methods

Cite this

Efficient Linearized Bregman Iteration for Sparse Adaptive Filters and Kaczmarz Solvers

Abstract

Publication series

Fields of science

JKU Focus areas

Access to Document

Other files and links

Projects

Low Complexity Iterative Signal Processing Methods

Cite this