s-SMOOTH: Sparsity and Smoothness Enhanced EEG Brain Tomography
EEG source imaging enables us to reconstruct current density in the brain from the electrical measurements with excellent temporal resolution (~ ). The corresponding EEG inverse problem is an ill-posed one that has infinitely many solutions. This is due to the fact that the number of EEG sensors is...
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| Vydáno v: | Frontiers in neuroscience Ročník 10; s. 543 |
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28.11.2016
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| Abstract | EEG source imaging enables us to reconstruct current density in the brain from the electrical measurements with excellent temporal resolution (~
). The corresponding EEG inverse problem is an ill-posed one that has infinitely many solutions. This is due to the fact that the number of EEG sensors is usually much smaller than that of the potential dipole locations, as well as noise contamination in the recorded signals. To obtain a unique solution, regularizations can be incorporated to impose additional constraints on the solution. An appropriate choice of regularization is critically important for the reconstruction accuracy of a brain image. In this paper, we propose a novel Sparsity and SMOOthness enhanced brain TomograpHy (s-SMOOTH) method to improve the reconstruction accuracy by integrating two recently proposed regularization techniques: Total Generalized Variation (TGV) regularization and ℓ
regularization. TGV is able to preserve the source edge and recover the spatial distribution of the source intensity with high accuracy. Compared to the relevant total variation (TV) regularization, TGV enhances the smoothness of the image and reduces staircasing artifacts. The traditional TGV defined on a 2D image has been widely used in the image processing field. In order to handle 3D EEG source images, we propose a voxel-based Total Generalized Variation (vTGV) regularization that extends the definition of second-order TGV from 2D planar images to 3D irregular surfaces such as cortex surface. In addition, the ℓ
regularization is utilized to promote sparsity on the current density itself. We demonstrate that ℓ
regularization is able to enhance sparsity and accelerate computations than ℓ
regularization. The proposed model is solved by an efficient and robust algorithm based on the difference of convex functions algorithm (DCA) and the alternating direction method of multipliers (ADMM). Numerical experiments using synthetic data demonstrate the advantages of the proposed method over other state-of-the-art methods in terms of total reconstruction accuracy, localization accuracy and focalization degree. The application to the source localization of event-related potential data further demonstrates the performance of the proposed method in real-world scenarios. |
|---|---|
| AbstractList | EEG source imaging enables us to reconstruct current density in the brain from the electrical measurements with excellent temporal resolution (~ms). The corresponding EEG inverse problem is an ill-posed one that has infinitely many solutions. This is due to the fact that the number of EEG sensors is usually much smaller than that of the potential dipole locations, as well as noise contamination in the recorded signals. To obtain a unique solution, regularizations can be incorporated to impose additional constraints on the solution. An appropriate choice of regularization is critically important for the reconstruction accuracy of the brain image. In this paper, we propose a novel Sparsity and SMOOthness enhanced brain TomograpHy (s-SMOOTH) method to improve the reconstruction accuracy by integrating two recently proposed regularization techniques: Total Generalized Variation (TGV) regularization and l_(1-2) regularization. TGV is able to preserve the source edge and recover the spatial distribution of the source intensity with high accuracy. Compared to the relevant total variation (TV) regularization, TGV enhances the smoothness of the image and reduces staircasing artifacts. The traditional TGV defined on a 2D image has been widely used in image processing field. In order to handle 3D EEG source images, we propose a voxel-based TGV (vTGV) regularization that extends the definition of second-order TGV from 2D planar image to 3D irregular surfaces such as cortex surface. In addition, the l_(1-2) regularization is utilized to promote sparsity on the current density itself. We demonstrate that l_(1-2) regularization is able to enhance sparsity and accelerate computations than l_1 regularization. The proposed model is solved by an efficient and robust algorithm based on the difference of convex functions algorithm (DCA) and the alternating direction method of multipliers (ADMM). Numerical experiments using synthetic data demonstrate the advantages of the proposed method over other state-of-the-art methods in terms of total reconstruction accuracy, localization accuracy and focalization degree. The application to the source localization of event-related potential data further demonstrates the performance of the proposed method in real-world scenario. EEG source imaging enables us to reconstruct current density in the brain from the electrical measurements with excellent temporal resolution (~ ). The corresponding EEG inverse problem is an ill-posed one that has infinitely many solutions. This is due to the fact that the number of EEG sensors is usually much smaller than that of the potential dipole locations, as well as noise contamination in the recorded signals. To obtain a unique solution, regularizations can be incorporated to impose additional constraints on the solution. An appropriate choice of regularization is critically important for the reconstruction accuracy of a brain image. In this paper, we propose a novel Sparsity and SMOOthness enhanced brain TomograpHy (s-SMOOTH) method to improve the reconstruction accuracy by integrating two recently proposed regularization techniques: Total Generalized Variation (TGV) regularization and ℓ regularization. TGV is able to preserve the source edge and recover the spatial distribution of the source intensity with high accuracy. Compared to the relevant total variation (TV) regularization, TGV enhances the smoothness of the image and reduces staircasing artifacts. The traditional TGV defined on a 2D image has been widely used in the image processing field. In order to handle 3D EEG source images, we propose a voxel-based Total Generalized Variation (vTGV) regularization that extends the definition of second-order TGV from 2D planar images to 3D irregular surfaces such as cortex surface. In addition, the ℓ regularization is utilized to promote sparsity on the current density itself. We demonstrate that ℓ regularization is able to enhance sparsity and accelerate computations than ℓ regularization. The proposed model is solved by an efficient and robust algorithm based on the difference of convex functions algorithm (DCA) and the alternating direction method of multipliers (ADMM). Numerical experiments using synthetic data demonstrate the advantages of the proposed method over other state-of-the-art methods in terms of total reconstruction accuracy, localization accuracy and focalization degree. The application to the source localization of event-related potential data further demonstrates the performance of the proposed method in real-world scenarios. EEG source imaging enables us to reconstruct current density in the brain from the electrical measurements with excellent temporal resolution (~ ms). The corresponding EEG inverse problem is an ill-posed one that has infinitely many solutions. This is due to the fact that the number of EEG sensors is usually much smaller than that of the potential dipole locations, as well as noise contamination in the recorded signals. To obtain a unique solution, regularizations can be incorporated to impose additional constraints on the solution. An appropriate choice of regularization is critically important for the reconstruction accuracy of a brain image. In this paper, we propose a novel Sparsity and SMOOthness enhanced brain TomograpHy (s-SMOOTH) method to improve the reconstruction accuracy by integrating two recently proposed regularization techniques: Total Generalized Variation (TGV) regularization and ℓ1−2 regularization. TGV is able to preserve the source edge and recover the spatial distribution of the source intensity with high accuracy. Compared to the relevant total variation (TV) regularization, TGV enhances the smoothness of the image and reduces staircasing artifacts. The traditional TGV defined on a 2D image has been widely used in the image processing field. In order to handle 3D EEG source images, we propose a voxel-based Total Generalized Variation (vTGV) regularization that extends the definition of second-order TGV from 2D planar images to 3D irregular surfaces such as cortex surface. In addition, the ℓ1−2 regularization is utilized to promote sparsity on the current density itself. We demonstrate that ℓ1−2 regularization is able to enhance sparsity and accelerate computations than ℓ1 regularization. The proposed model is solved by an efficient and robust algorithm based on the difference of convex functions algorithm (DCA) and the alternating direction method of multipliers (ADMM). Numerical experiments using synthetic data demonstrate the advantages of the proposed method over other state-of-the-art methods in terms of total reconstruction accuracy, localization accuracy and focalization degree. The application to the source localization of event-related potential data further demonstrates the performance of the proposed method in real-world scenarios. EEG source imaging enables us to reconstruct current density in the brain from the electrical measurements with excellent temporal resolution (~ ms). The corresponding EEG inverse problem is an ill-posed one that has infinitely many solutions. This is due to the fact that the number of EEG sensors is usually much smaller than that of the potential dipole locations, as well as noise contamination in the recorded signals. To obtain a unique solution, regularizations can be incorporated to impose additional constraints on the solution. An appropriate choice of regularization is critically important for the reconstruction accuracy of a brain image. In this paper, we propose a novel Sparsity and SMOOthness enhanced brain TomograpHy (s-SMOOTH) method to improve the reconstruction accuracy by integrating two recently proposed regularization techniques: Total Generalized Variation (TGV) regularization and ℓ1-2 regularization. TGV is able to preserve the source edge and recover the spatial distribution of the source intensity with high accuracy. Compared to the relevant total variation (TV) regularization, TGV enhances the smoothness of the image and reduces staircasing artifacts. The traditional TGV defined on a 2D image has been widely used in the image processing field. In order to handle 3D EEG source images, we propose a voxel-based Total Generalized Variation (vTGV) regularization that extends the definition of second-order TGV from 2D planar images to 3D irregular surfaces such as cortex surface. In addition, the ℓ1-2 regularization is utilized to promote sparsity on the current density itself. We demonstrate that ℓ1-2 regularization is able to enhance sparsity and accelerate computations than ℓ1 regularization. The proposed model is solved by an efficient and robust algorithm based on the difference of convex functions algorithm (DCA) and the alternating direction method of multipliers (ADMM). Numerical experiments using synthetic data demonstrate the advantages of the proposed method over other state-of-the-art methods in terms of total reconstruction accuracy, localization accuracy and focalization degree. The application to the source localization of event-related potential data further demonstrates the performance of the proposed method in real-world scenarios.EEG source imaging enables us to reconstruct current density in the brain from the electrical measurements with excellent temporal resolution (~ ms). The corresponding EEG inverse problem is an ill-posed one that has infinitely many solutions. This is due to the fact that the number of EEG sensors is usually much smaller than that of the potential dipole locations, as well as noise contamination in the recorded signals. To obtain a unique solution, regularizations can be incorporated to impose additional constraints on the solution. An appropriate choice of regularization is critically important for the reconstruction accuracy of a brain image. In this paper, we propose a novel Sparsity and SMOOthness enhanced brain TomograpHy (s-SMOOTH) method to improve the reconstruction accuracy by integrating two recently proposed regularization techniques: Total Generalized Variation (TGV) regularization and ℓ1-2 regularization. TGV is able to preserve the source edge and recover the spatial distribution of the source intensity with high accuracy. Compared to the relevant total variation (TV) regularization, TGV enhances the smoothness of the image and reduces staircasing artifacts. The traditional TGV defined on a 2D image has been widely used in the image processing field. In order to handle 3D EEG source images, we propose a voxel-based Total Generalized Variation (vTGV) regularization that extends the definition of second-order TGV from 2D planar images to 3D irregular surfaces such as cortex surface. In addition, the ℓ1-2 regularization is utilized to promote sparsity on the current density itself. We demonstrate that ℓ1-2 regularization is able to enhance sparsity and accelerate computations than ℓ1 regularization. The proposed model is solved by an efficient and robust algorithm based on the difference of convex functions algorithm (DCA) and the alternating direction method of multipliers (ADMM). Numerical experiments using synthetic data demonstrate the advantages of the proposed method over other state-of-the-art methods in terms of total reconstruction accuracy, localization accuracy and focalization degree. The application to the source localization of event-related potential data further demonstrates the performance of the proposed method in real-world scenarios. |
| Author | Hsin, Yue-Loong Qin, Jing Li, Ying Osher, Stanley Liu, Wentai |
| AuthorAffiliation | 3 Department of Neurology, Chung Shan Medical University Taichung, Taiwan 5 California NanoSystems Institute, University of California, Los Angeles Los Angeles, CA, USA 1 Biomimetic Research Lab, Department of Bioengineering, University of California, Los Angeles Los Angeles, CA, USA 2 Department of Mathematical Sciences, Montana State University Bozeman, MT, USA 4 Department of Mathematics, University of California, Los Angeles Los Angeles, CA, USA |
| AuthorAffiliation_xml | – name: 5 California NanoSystems Institute, University of California, Los Angeles Los Angeles, CA, USA – name: 3 Department of Neurology, Chung Shan Medical University Taichung, Taiwan – name: 1 Biomimetic Research Lab, Department of Bioengineering, University of California, Los Angeles Los Angeles, CA, USA – name: 2 Department of Mathematical Sciences, Montana State University Bozeman, MT, USA – name: 4 Department of Mathematics, University of California, Los Angeles Los Angeles, CA, USA |
| Author_xml | – sequence: 1 givenname: Ying surname: Li fullname: Li, Ying – sequence: 2 givenname: Jing surname: Qin fullname: Qin, Jing – sequence: 3 givenname: Yue-Loong surname: Hsin fullname: Hsin, Yue-Loong – sequence: 4 givenname: Stanley surname: Osher fullname: Osher, Stanley – sequence: 5 givenname: Wentai surname: Liu fullname: Liu, Wentai |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/27965529$$D View this record in MEDLINE/PubMed |
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| CitedBy_id | crossref_primary_10_1016_j_apm_2022_01_027 crossref_primary_10_1137_18M121993X crossref_primary_10_1016_j_jvcir_2022_103588 crossref_primary_10_1109_TBDATA_2017_2756664 crossref_primary_10_1109_TCYB_2022_3173336 crossref_primary_10_3390_a15050169 |
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| Copyright | 2016. This work is licensed under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. Copyright © 2016 Li, Qin, Hsin, Osher and Liu. 2016 Li, Qin, Hsin, Osher and Liu |
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| Keywords | difference of convex functions algorithm (DCA) ℓ1−2 regularization inverse problem alternating direction method of multipliers (ADMM) total generalized variation (TGV) EEG source imaging |
| Language | English |
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| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 content type line 23 Edited by: Alexandre Gramfort, CNRS LTCI, Télécom ParisTech, Université Paris-Saclay, France Reviewed by: Stefan Haufe, Technische Universität Berlin, Germany; Alberto Sorrentino, University of Genoa, Italy This article was submitted to Brain Imaging Methods, a section of the journal Frontiers in Neuroscience |
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). The... EEG source imaging enables us to reconstruct current density in the brain from the electrical measurements with excellent temporal resolution (~ms). The... EEG source imaging enables us to reconstruct current density in the brain from the electrical measurements with excellent temporal resolution (~ ms). The... |
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| SubjectTerms | Accuracy Algorithms Alternating direction method of multipliers (ADMM) Alzheimer's disease Contamination Cortex (temporal) difference of convex functions algorithm (DCA) Dimensional analysis EEG EEG source imaging Electroencephalography Event-related potentials Image processing inverse problem Inverse problems l_(1-2) regularization Localization Medical imaging Neuroimaging Neuroscience Optimization techniques Regularization methods Schizophrenia Sparsity Spatial distribution Tomography Total Generalized Variation (TGV) |
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