Solution of the EEG inverse problem by random dipole sampling

Created March 19, 2026

Updated on May 14, 2026

approved

Electroencephalography (EEG) source imaging aims to reconstruct brain activity maps from the neuroelectric potential difference measured on the skull. To obtain the brain activity map, we need to solve an ill-posed and ill-conditioned inverse problem that requires regularization techniques to make the solution viable. When dealing with real-time applications, dimensionality reduction techniques can be used to reduce the computational load required to evaluate the numerical solution of the EEG inverse problem. To this end, in this paper we use the random dipole sampling method, in which a Monte Carlo technique is used to reduce the number of neural sources. This is equivalent to reducing the number of the unknowns in the inverse problem and can be seen as a first regularization step. Then, we solve the reduced EEG inverse problem with two popular inversion methods, the weighted Minimum Norm Estimate (wMNE) and the standardized LOw Resolution brain Electromagnetic TomogrAphy (sLORETA). The main result of this paper is the error estimates of the reconstructed activity map obtained with the randomized version of wMNE and sLORETA. Numerical experiments on synthetic EEG data demonstrate the effectiveness of the random dipole sampling method.

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Tags:
EEG Imaging
Inversion Method
Publication - Article
Random Sampling
Underdetermined Inverse Problem
sLORETA
wMNE
Basic
Language
English
MainTitle
Solution of the EEG inverse problem by random dipole sampling
Original ids
https://doi.org/10.1088/1361-6420/ad14a1
Type
publication
bestAccessRight
OPEN
contributors
  • University of Roma ‘La Sapienza’ and Istituto di Scienze Marine—CNR, Roma, Italy;
  • University of Roma ‘La Sapienza’, Roma, Italy;
  • Istituto per le Applicazioni del Calcolo ‘Mauro Picone’—CNR, Roma, Italy
countries
Italy
Creator/Author
Full name
  • Della Cioppa, Lorenzo, orcid: 0000-0001-8222-112x;
  • Tartaglione, Michela, orcid: 0000-0003-0249-6962;
  • Pascarella, Annalisa, orcid: 0000-0001-8795-0815;
  • Pitolli, Francesca, orcid: 0000-0002-7159-0533
Other
Description
Electroencephalography (EEG) source imaging aims to reconstruct brain activity maps from the neuroelectric potential difference measured on the skull. To obtain the brain activity map, we need to solve an ill-posed and ill-conditioned inverse problem that requires regularization techniques to make the solution viable. When dealing with real-time applications, dimensionality reduction techniques can be used to reduce the computational load required to evaluate the numerical solution of the EEG inverse problem. To this end, in this paper we use the random dipole sampling method, in which a Monte Carlo technique is used to reduce the number of neural sources. This is equivalent to reducing the number of the unknowns in the inverse problem and can be seen as a first regularization step. Then, we solve the reduced EEG inverse problem with two popular inversion methods, the weighted Minimum Norm Estimate (wMNE) and the standardized LOw Resolution brain Electromagnetic TomogrAphy (sLORETA). The main result of this paper is the error estimates of the reconstructed activity map obtained with the randomized version of wMNE and sLORETA. Numerical experiments on synthetic EEG data demonstrate the effectiveness of the random dipole sampling method.
Publication Date
2023-12-27
Publisher
IOP Publishing
Subjects
  • EEG imaging, underdetermined inverse problem, random sampling, inversion method, wMNE, sLORETA;
  • Biomedical imaging and signal processing;
  • Randomized algorithms;
  • Random sampling;
  • Inversion method;
  • Monte Carlo methods;
  • 01 natural sciences;
  • 03 medical and health sciences;
  • Underdetermined inverse problem;
  • 0302 clinical medicine;
  • Ill-posedness and regularization problems in numerical linear algebra;
  • 0101 mathematics
isGreen
false
isInDiamondJournal
false
Software
Publication
Name
Inverse Problems
Publication
Article
Starting page
025006
issnOnline
1361-6420
issnPrinted
0266-5611
vol
40
Other Research Product
Detailed informations
system:type
Research Product
Management Info
Author
Catalogue Manager ITINERIS
Version
1
Last Updated
May 14, 2026, 12:43 (UTC)
Created
March 19, 2026, 00:29 (UTC)
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