Combined Analysis-L1 and Total Variation ADMM with Applications to MEG Brain Imaging and Signal Reconstruction

Rui Gao; Filip Tronarp; Simo Särkkä

doi:10.23919/EUSIPCO.2018.8553122

Combined Analysis-L1 and Total Variation ADMM with Applications to MEG Brain Imaging and Signal Reconstruction

Rui Gao^*, Filip Tronarp, Simo Särkkä

^*Corresponding author for this work

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

8 Citations (Scopus)

Abstract

In this article, we propose an efficient method for solving analysis-l1-TV regularization problems with a multi-step alternating direction method of multipliers (ADMM) approach as the fast solver. Additionally, we apply it to a real-data magnetoencephalography (MEG) brain imaging problem as well as to signal reconstruction. In our approach, the inverse problem arising in MEG or signal reconstruction is formulated as an optimization problem which we regularize using a combination of analysis-l1 prior together with a total variation (TV) regularization term. We then formulate an optimization algorithm based on ADMM which can effectively be used to solve the optimization problems. The performance of the algorithm is illustrated in practical scenarios.

Original language	English
Title of host publication	Proceedings of the 26th European Signal Processing Conference, EUSIPCO 2018
Publisher	IEEE
Pages	1930-1934
Number of pages	5
ISBN (Print)	978-90-827970-1-5
DOIs	https://doi.org/10.23919/EUSIPCO.2018.8553122
Publication status	Published - 2018
MoE publication type	A4 Conference publication
Event	European Signal Processing Conference - Rome, Italy Duration: 3 Sept 2018 → 7 Sept 2018 Conference number: 26

Publication series

Name	European Signal Processing Conference
Publisher	IEEE COMPUTER SOC
ISSN (Print)	2076-1465

Conference

Conference	European Signal Processing Conference
Abbreviated title	EUSIPCO
Country/Territory	Italy
City	Rome
Period	03/09/2018 → 07/09/2018

Funding

Thanks to Academy of Finland for funding.

Keywords

Analysis-l1-TV-norm
total variation (TV)
alternating direction method of multipliers (ADMM)
magnetoencephalography (MEG)
image reconstruction
algorithm

Access to Document

10.23919/EUSIPCO.2018.8553122

Cite this

@inproceedings{b2785a81aa6c402489fca5439599ed68,

title = "Combined Analysis-L1 and Total Variation ADMM with Applications to MEG Brain Imaging and Signal Reconstruction",

abstract = "In this article, we propose an efficient method for solving analysis-l1-TV regularization problems with a multi-step alternating direction method of multipliers (ADMM) approach as the fast solver. Additionally, we apply it to a real-data magnetoencephalography (MEG) brain imaging problem as well as to signal reconstruction. In our approach, the inverse problem arising in MEG or signal reconstruction is formulated as an optimization problem which we regularize using a combination of analysis-l1 prior together with a total variation (TV) regularization term. We then formulate an optimization algorithm based on ADMM which can effectively be used to solve the optimization problems. The performance of the algorithm is illustrated in practical scenarios.",

keywords = "Analysis-l1-TV-norm, total variation (TV), alternating direction method of multipliers (ADMM), magnetoencephalography (MEG), image reconstruction, algorithm",

author = "Rui Gao and Filip Tronarp and Simo S{\"a}rkk{\"a}",

year = "2018",

doi = "10.23919/EUSIPCO.2018.8553122",

language = "English",

isbn = "978-90-827970-1-5",

series = "European Signal Processing Conference",

publisher = "IEEE",

pages = "1930--1934",

booktitle = "Proceedings of the 26th European Signal Processing Conference, EUSIPCO 2018",

address = "United States",

note = "European Signal Processing Conference, EUSIPCO ; Conference date: 03-09-2018 Through 07-09-2018",

}

Gao, R, Tronarp, F & Särkkä, S 2018, Combined Analysis-L1 and Total Variation ADMM with Applications to MEG Brain Imaging and Signal Reconstruction. in Proceedings of the 26th European Signal Processing Conference, EUSIPCO 2018. European Signal Processing Conference, IEEE, pp. 1930-1934, European Signal Processing Conference, Rome, Italy, 03/09/2018. https://doi.org/10.23919/EUSIPCO.2018.8553122

Combined Analysis-L1 and Total Variation ADMM with Applications to MEG Brain Imaging and Signal Reconstruction. / Gao, Rui; Tronarp, Filip; Särkkä, Simo.
Proceedings of the 26th European Signal Processing Conference, EUSIPCO 2018. IEEE, 2018. p. 1930-1934 (European Signal Processing Conference).

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

TY - GEN

T1 - Combined Analysis-L1 and Total Variation ADMM with Applications to MEG Brain Imaging and Signal Reconstruction

AU - Gao, Rui

AU - Tronarp, Filip

AU - Särkkä, Simo

N1 - Conference code: 26

PY - 2018

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N2 - In this article, we propose an efficient method for solving analysis-l1-TV regularization problems with a multi-step alternating direction method of multipliers (ADMM) approach as the fast solver. Additionally, we apply it to a real-data magnetoencephalography (MEG) brain imaging problem as well as to signal reconstruction. In our approach, the inverse problem arising in MEG or signal reconstruction is formulated as an optimization problem which we regularize using a combination of analysis-l1 prior together with a total variation (TV) regularization term. We then formulate an optimization algorithm based on ADMM which can effectively be used to solve the optimization problems. The performance of the algorithm is illustrated in practical scenarios.

AB - In this article, we propose an efficient method for solving analysis-l1-TV regularization problems with a multi-step alternating direction method of multipliers (ADMM) approach as the fast solver. Additionally, we apply it to a real-data magnetoencephalography (MEG) brain imaging problem as well as to signal reconstruction. In our approach, the inverse problem arising in MEG or signal reconstruction is formulated as an optimization problem which we regularize using a combination of analysis-l1 prior together with a total variation (TV) regularization term. We then formulate an optimization algorithm based on ADMM which can effectively be used to solve the optimization problems. The performance of the algorithm is illustrated in practical scenarios.

KW - Analysis-l1-TV-norm

KW - total variation (TV)

KW - alternating direction method of multipliers (ADMM)

KW - magnetoencephalography (MEG)

KW - image reconstruction

KW - algorithm

UR - https://www.scopus.com/pages/publications/85059804897

U2 - 10.23919/EUSIPCO.2018.8553122

DO - 10.23919/EUSIPCO.2018.8553122

M3 - Conference article in proceedings

SN - 978-90-827970-1-5

T3 - European Signal Processing Conference

SP - 1930

EP - 1934

BT - Proceedings of the 26th European Signal Processing Conference, EUSIPCO 2018

PB - IEEE

T2 - European Signal Processing Conference

Y2 - 3 September 2018 through 7 September 2018

ER -

Combined Analysis-L1 and Total Variation ADMM with Applications to MEG Brain Imaging and Signal Reconstruction

Abstract

Publication series

Conference

Funding

Keywords

Access to Document

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Cite this