#### DMCA

## BioMed Central Review Review on solving the inverse problem in EEG source analysis (2008)

### Citations

737 |
Rank-Deficient and Discrete Ill-Posed Problems
- Hansen
- 1998
(Show Context)
Citation Context ...es, rotating dipoles or a mixture of both. For the case of a model with fixed orientation dipoles, a signal subspace is first estimated from the data by finding the singular value decomposition (SVD) =-=[8]-=-M = UΣV T and letting U S be the signal subspace spanned by the p first left singular vectors m dip Page 15 of 33 (page number not for citation purposes)Journal of NeuroEngineering and Rehabilitation... |

515 | Markov Random Field Modeling in Computer Vision
- Li
- 1995
(Show Context)
Citation Context ... possible to show that there exists a value 0 <p < 1 for which the solution is maximally sparse. The non-quadratic formulation of the priors may be linked to previous works using Markov Random Fields =-=[18,19]-=-. Experiments in [20] show that the L 1 approach demands more computational effort in comparision with L 2 approaches. It also produced some spurious sources and the source distribution of the solutio... |

398 |
Teukolsky SA, Vetterling WT, Flannery BP (2007) Numerical Recipes: The Art of Scientific Computing
- WH
(Show Context)
Citation Context ...ude the gradient, downhill or standard simplex search methods (such as Nelder-Mead) [43-46], normally including multi-starts, as well as genetic algorithms and very time-consuming simulated annealing =-=[45,47,48]-=-. In these iterative processes, the dipolar source is moved about in the head model while its orientation and magnitude are also changed to obtain the best fit between the recorded EEG and those produ... |

390 |
Computational Methods for Inverse Problems
- Vogel
- 2002
(Show Context)
Citation Context ...er sources by using lead-field normalization. ˆ T T T T − D = W W G ( GW W G + aI ) M FOCUSS| i i i i i where i is the index of the iteration and W i is a diagonal matrix computed using 2 T N N (8) 1 =-=(9)-=- w i diag 1 , j ∈ [1, 2, ..., p] is a diagonal matrix for | G(:, j)|| deeper source compensation. G(:, j) is the jth column of G. The algorithm is initialized with the minimum norm solution ˆD MNE , t... |

262 | Improved localization of cortical activity by combining EEG and MEG with MRI cortical surface reconstruction: a linear approach
- Dale, Sereno
- 1993
(Show Context)
Citation Context ...pole strength D are normally distributed with zero mean and their covariance matrices are proportional to the identity matrix and are denoted by C and R respectively. The inverse solution is given in =-=[14]-=-: ˆ T T −1 D = RG ( GRG + C) M MNE p N Page 7 of 33 (page number not for citation purposes)Journal of NeuroEngineering and Rehabilitation 2008, 5:25 http://www.jneuroengrehab.com/content/5/1/25 Rij c... |

156 | Dynamic statistical parametric mapping: combining fMRI and MEG for high-resolution imaging of cortical activity - Dale, Liu, et al. - 2000 |

95 |
Discovering statistics using SPSS: (and sex and drugs and rock 'n' roll (3rd ed.). Los Angeles: SAGE. (This book is hilarious, given my sense of humor, consider yourself wanred, it also includes SPSS syntax and examples of text for reporting results.
- Field
- 2009
(Show Context)
Citation Context ...in each region were then averaged giving an average error value per region. These were then used to compare the different solutions. Statistical analysis of the data was then carried out through SPSS =-=[76]-=-. To identify whether there are significant differences between the four implemented solutions, ANOVA which is based on the following set of assumptions was used: Table 4: Error measure ED1 for the fo... |

74 | A Bayesian approach to introducing anatomo-functional priors in the EEG /MEG inverse problem
- Baillet, Garnero
- 1997
(Show Context)
Citation Context ...e can be located is affected by a number of factors including head-modelling errors, source-modelling errors and EEG noise (instrumental or biological) [3]. The standard adopted by Baillet et. al. in =-=[4]-=- is that spatial and temporal accuracy should be at least better than 5 mm and 5 ms, respectively. In this primer, we give a review of the inverse problem in EEG source localization. It is intended fo... |

38 | Independent component analysis for EEG source localization
- Zhukov, Weinstein, et al.
- 2000
(Show Context)
Citation Context ...ed by genetic algorithm evolutionary techniques. The minimization operation can be performed in order to localize multiple sources either in the brain [68] or in Independent Component backprojections =-=[69,70]-=-. If component back-projections are used, the correlation between the projected model and the measured one will have to be minimized rather than the energy of the difference. Figure 4 shows how the mi... |

29 |
Linear inverse solutions with optimal resolution kernels applied to electromagnetic tomography. Hum.Brain Mapp
- Menendez, Hauk, et al.
- 1997
(Show Context)
Citation Context ...tor is: where: ' †' denotes the Moore-Penrose pseudoinverse. 3.1.3 The weighted resolution optimization An extension of the Backus-Gilbert method is called the Weighted Resolution Optimization (WROP) =-=[37]-=-. The modification by Grave de Peralta Menendez is cited in [5]. BG GdeP Wg is replaced by W1g where The second part of the functional to be minimzed is replaced by where α GdeP and β GdeP are scalars... |

29 |
Noninvasive localization of electromagnetic epileptic activity: I. Method descriptions and simulations. Brain Topogr 14:131–137.
- R, S, et al.
- 2001
(Show Context)
Citation Context ...owever, when such validation was attempted on epileptic patients, even though there were some inherent limitations in localization of deep temporal structures, the results have been quite encouraging =-=[93,94]-=-. Authors' contributions RG, JM, TC, PX, MZ and VS participated in the literature search and were responsible for writing down the manuscript. TC conducted the experiments for the comparative analysis... |

18 |
Neuromagnetic source imaging with FOCUSS: a recursive weighted minimum norm algorithm
- IF, JS, et al.
- 1995
(Show Context)
Citation Context ...S (Focal underdetermined system solution) This is a recursive procedure of weighted minimum norm estimations, developed to give some focal resolution to linear estimators on distributed source models =-=[5,27,29,30]-=-. Weighting of the columns of G is based on the mag nitudes of the sources of the previous iteration. The Weighted Minimum Norm compensates for the lower gains of deeper sources by using lead-field no... |

14 |
Regularization Tools: A Matlab package for analysis and solution of discrete ill-posed problems. Numerical Algorithms 6
- PC
- 1994
(Show Context)
Citation Context ...or citation purposes)Journal of NeuroEngineering and Rehabilitation 2008, 5:25 http://www.jneuroengrehab.com/content/5/1/25 curve method. The MATLAB toolbox of Christian Hansen was used in this case =-=[21]-=-. Maxima Once the current density estimates were available, the locations and normalized magnitudes of local maxima were found. A voxel was considered to hold a local maximum if the magnitude 28 of it... |

14 |
Drongelen W, Yuchtman M, Suzuki A. Localization of brain electrical activity via linearly constrained minimum variance spatial filtering
- BD, van
- 1997
(Show Context)
Citation Context ...oles at location r having orientation vectors ex, ey and ez respectively, I is the 3 × 3 identity matrix and δ represents a small distance. In linearly constrained minimum variance (LCMV) beamforming =-=[49]-=-, nulls are placed at positions corresponding to interfering sources, i.e. neural sources at locations other than r dip (so δ = 0). The LCMV problem can be written as: min ( C ) W ( r ) G( r ) I Tr su... |

12 | The L-curve and its use in the numerical treatment of inverse problems - PC - 2001 |

11 |
Variable Resolution Electric-Magnetic Tomography
- Valdes-Sosa, Marti, et al.
- 1996
(Show Context)
Citation Context ...density estimate is based only on the measurement noise, in contrast to sLORETA, which takes into account the actual source variance as well. Variable resolution electrical tomography (VARETA) VARETA =-=[34]-=- is a weighted minimum norm solution in which the regularization parameter varies spatially at each point of the solution grid. At points at which the regularization parameter is small, the source is ... |

10 |
Sparse signal reconstruction from limited data using FOCUSS: A re-weighted minimum norm algorithm
- IF, BD
- 1997
(Show Context)
Citation Context ...S (Focal underdetermined system solution) This is a recursive procedure of weighted minimum norm estimations, developed to give some focal resolution to linear estimators on distributed source models =-=[5,27,29,30]-=-. Weighting of the columns of G is based on the mag nitudes of the sources of the previous iteration. The Weighted Minimum Norm compensates for the lower gains of deeper sources by using lead-field no... |

8 |
A recursive algorithm for the three-dimensional imaging of brain electric activity: shrinking LORETA-FOCUSS,”
- Liu, Gao, et al.
- 2004
(Show Context)
Citation Context ...here exists a value 0 <p < 1 for which the solution is maximally sparse. The non-quadratic formulation of the priors may be linked to previous works using Markov Random Fields [18,19]. Experiments in =-=[20]-=- show that the L 1 approach demands more computational effort in comparision with L 2 approaches. It also produced some spurious sources and the source distribution of the solution was very different ... |

8 | Artificial neural networks for source localization in the human brain - Abeyratne, Kinouchi, et al. - 1991 |

8 |
diMichele F: Invariant reversible QEEG effects of anesthetics. Conscious Cogn
- ER, LS, et al.
- 2001
(Show Context)
Citation Context ... results of metabolic imaging techniques. Finally, another application is in the localization of invariant quantitative EEG (QEEG) correlates of the loss and return of consciousness during anesthesia =-=[92]-=-. It should be noted that even though source localization has been used in many different domains, it is difficult to validate the accuracy of the results. However, when such validation was attempted ... |

7 |
Bayesian inference applied to the electromagnetic inverse problem. Hum Brain Mapp 7:195–212
- DM, JS, et al.
- 1999
(Show Context)
Citation Context ... expected error and generalized Wiener filtering. Details are given in [12]. Bayesian methods can also be used to estimate a probability distribution of solutions rather than a single 'best' solution =-=[13]-=-. 3.1.1 The Bayesian framework In general, this technique consists in finding an estimator ˆx of x that maximizes the posterior distribution of x given the measurements y [4,12-15]. This estimator can... |

7 | Differential characterization of neural sources with the bimodal truncated SVD pseudo-inverse for EEG and MEG measurements - Gençer, Williamson - 1998 |

7 |
Standardized shrinking LORETA-FOCUSS (SSLOFO): A new algorithm for spatio-temporal EEG source reconstruction
- Liu, Schimpf, et al.
- 2005
(Show Context)
Citation Context ...he L 1 approach and LORETA with FOCUSS. It is also 10 times faster than LORETA with FOCUSS and several hundred times faster than the L 1 approach. Standardized shrinking LORETA-FOCUSS (SSLOFO) SSLOFO =-=[41]-=- combines the features of high resolution (FOCUSS) and low resolution (WMN, sLORETA) methPage 12 of 33 (page number not for citation purposes)Journal of NeuroEngineering and Rehabilitation 2008, 5:25... |

7 | An alternative subspace approach to EEG dipole source localization,”
- Xu, Xu, et al.
- 2004
(Show Context)
Citation Context ...ter methods the projection operator is applied just to the array manifold, rather than to both arguments as in the case of RAP-MUSIC. FINES subspace algorithm An alternative signal subspace algorithm =-=[56]-=- is FINES (First Principal Vectors). This approach, used in order to estimate the source locations, employs projections onto a subspace spanned by a small set of particular vectors (FINES vector set) ... |

6 |
Spatio-temporal EEG source localization using a three dimentional subspace FINE approach in a realistic geometry in homogeneous head model
- Ding, He
- 2006
(Show Context)
Citation Context ...urnal of NeuroEngineering and Rehabilitation 2008, 5:25 http://www.jneuroengrehab.com/content/5/1/25 localization error for a SNR of 14 dB was found to be 1.4 mm and 1.5 mm lower when using FINES. In =-=[75]-=-, He and Ding applied a similar analysis but this time using a realistic head model. The results are consistent with [56] showing that FINES is superior in the noisy scenario. The literature review ab... |

5 | A multiresolution framework to MEG/EEG source imaging
- Gavit, Baillet, et al.
- 2001
(Show Context)
Citation Context ...tor [7,16] (representing the forward solution) and ||.|| is the usual L 2 norm. L(x) may be written as U s (x) + U t (x) where U s (x) introduces spatial (anatomical) priors and U t (x) temporal ones =-=[4,15]-=-. Combining the data attachment term with the prior term, xˆ= min( F ( x)) = min(|| Kx − y|| + aL( x)). x a x This equation reflects a trade off between fidelity to the data and spatial/temporal smoot... |

5 |
CM, Martuzzi R, Gonzalez Andino SL. Electrical neuroimaging based on biophysical constraints. Neuroimage 2004;21:527–39
- R, MM, et al.
(Show Context)
Citation Context ...ess of the inverse solution. Unfortunately, in most approaches, criteria are purely mathematical and do not incorporate biophysical and psychological constraints. LAURA (Local AUtoRegressive Average) =-=[40]-=- attempts to incorporate biophysical laws into the minimum norm solution. According to Maxwell's laws of electromagnetic field, the strength of each source falls off with the reciprocal of the cubic d... |

5 |
A resampling method for estimating the signal subspace of spatio-temporal EEG/MEG data
- Maris
(Show Context)
Citation Context ...//www.jneuroengrehab.com/content/5/1/25 of U. Two other methods of estimating the signal subspace, claimed to be better because they are less affected by spatial covariance in the noise, are given in =-=[52]-=-. The first method involves prewhitening of the data matrix making use of an estimate of the spatial noise covariance matrix. This means that the data matrix M is transformed so that the spatial covar... |

5 |
Electroencephalogram processing using neural networks
- Robert, F, et al.
- 2002
(Show Context)
Citation Context ... find the optimal coordinates and orientation for each dipole – the optimization can be performed with an artificial neural network (ANN) based system. The main advantage of neural network approaches =-=[57]-=- is that once trained, no further iterative process is required. In addition, although iterative methods are shown to be General block diagram for an artificial neural network system used for inverse ... |

4 | Conventional and Reciprocal Approaches to the Inverse Dipole Localization Problem of Electroencephalography - Finke, Gulrajani, et al. |

3 |
Evaluation of l1 and l2 minimum norm performances on eeg localizations
- Silva, Maltez, et al.
- 1987
(Show Context)
Citation Context ...contains small and well localized objects as, for example, in the localization of cortical activity by electric measurements. As p is reduced the solutions will become increasingly sparse. When p = 1 =-=[17]-=- the problem can be modified slightly to be recast as a linear program which can be solved by a simplex method. In this case it is the sum of the absolute values of the solution components that is min... |

3 |
Kufta C, Hallett M: An Improved Method for Localizing Electric Brain Dipoles
- Salu, LG, et al.
- 1990
(Show Context)
Citation Context ... to estimate and their initial locations and orientations. Estimates can be obtained as explained below. The optimal dipole In this model, any point inside the sphere has an associated optimal dipole =-=[71]-=-, which fits the observed data better than any other dipole that has the same location but different orientation. The unknown parameters of an optimal dipole are the magnitude components d x , d y and... |

3 |
S (2000) Selection criteria and preoperative investigation of patients with focal epilepsy who lack a localized structural lesion. Epileptic disorders 2
- Duchowny, Jayakar, et al.
(Show Context)
Citation Context ... they are concerned largely with the identification and localization of abnormalities in the EEG [77], and the utilization of this information for neurosurgical interventions in the most severe cases =-=[78,79]-=-. In cognitive neuroscience such techniques have been used to localize the sources of the different frequency bands, to assess the dynamics of different mental states, such as perception, motor prepar... |

3 |
Frequency source analysis in patients with brain lesions
- Harmony, Fernández-Bouzas, et al.
- 1995
(Show Context)
Citation Context ...niques have been used to localize the sources of the different frequency bands, to assess the dynamics of different mental states, such as perception, motor preparation and higher cognitive functions =-=[80,81]-=-. In clinical neuroscience source imaging allows the analysis of EEG changes in psychiatric and neurological patients [82-84] and is extensively used to test and characterize effects of various psycho... |

3 | Congedo M, Askew JH. Low-resolution electromagnetic tomography (LORETA) of cerebral activity in chronic depressive disorder. Int J Psychophysiol 2003;49:175–85 - JF |

3 |
Pascual-Marqui RD, Strik WK, Koenig T, Lehmann D. Frequency domain source localization shows state-dependent diazepam effects
- CM
- 1995
(Show Context)
Citation Context ...nce source imaging allows the analysis of EEG changes in psychiatric and neurological patients [82-84] and is extensively used to test and characterize effects of various psychopharmacological agents =-=[85,86]-=-. Page 29 of 33 (page number not for citation purposes)Journal of NeuroEngineering and Rehabilitation 2008, 5:25 http://www.jneuroengrehab.com/content/5/1/25 However, the main clinical application co... |

3 |
Dipole modeling of scalp electroencephalogram epileptic discharges : correlation with intracerebral fields
- MERLET, GOTMAN
(Show Context)
Citation Context ...owever, when such validation was attempted on epileptic patients, even though there were some inherent limitations in localization of deep temporal structures, the results have been quite encouraging =-=[93,94]-=-. Authors' contributions RG, JM, TC, PX, MZ and VS participated in the literature search and were responsible for writing down the manuscript. TC conducted the experiments for the comparative analysis... |

2 |
De Clercq W, Vergult A, D'Asseler Y, Camilleri KP, Fabri SG, Van Huffel S, Lemahieu I: Review on solving the forward problem in EEG source analysis
- Hallez, Vanrumste, et al.
(Show Context)
Citation Context ...oblem; this is calculated or derived only once or several times depending on the approach used in the inverse problem and has been discussed in the corresponding review on solving the forward problem =-=[2]-=-. Then, in conjunction with the actual EEG data measured at specified positions of (usually less than 100) electrodes on the scalp, it can be used to work back and estimate the sources that fit these ... |

2 |
Veen BD, Wakai RT. Statistical performance analysis of signal variance-based dipole models for MEG/EEG source localization and detection
- Rodriguez-Rivera, Van
(Show Context)
Citation Context ...dipole at each grid point) but with a set of constraints. As regards dipole moment constraints, which may be necessary to limit the search space for meaningful dipole sources, Rodriguez-Rivera et al. =-=[11]-=- discuss four dipole models with different dipole moment constraints. These are (i) constant unknown dipole moment; (ii) fixed known dipole moment orientation and variable moment magnitude; (iii) fixe... |

2 |
3-Dimensional Brain Source Imaging by Means of Laplacian Weighted Minimum Norm Estimate in a Realistic Geometry Head Model
- Ding, He
(Show Context)
Citation Context ...his approach can be adopted to both continuous and discrete regularization. P(α) = ||Ax(α)||.||Kx(α) - y δ || Another well known regularization method is the Generalized Cross Validation (GCV) method =-=[21,25]-=- which is based on the assumption that y is affected by normally distributed noise. The optimum alpha for GCV is that corresponding to the minimum value for the function G: Methods to estimate the reg... |

2 |
Biscay R, Valdes-Sosa P. A solution to the dynamical inverse problem of EEG generation using spatiotemporal Kalman filtering. Neuroimage 2004;23:435–53
- Galka, Yamashita, et al.
(Show Context)
Citation Context ...G G + a( + bP P ) D = G M Δ t T x t x T x =−∇B ∇ ∇ −∇ ∇ T x y T y t B y T t ⊥ Pt−1 is the projector onto . Spatio-temporal modelling Apart from imposing temporal smoothness constraints, Galka et. al. =-=[35]-=- solved the inverse problem by recasting it as a spatio-temporal state space model which they solve by using Kalman filtering. The computational complexity of this approach that arises due to the high... |

2 |
Hämäaläinen M, Salmelin R: Global Optimization in the Localization of Neuromagnetic Sources
- Uutela
- 1998
(Show Context)
Citation Context ...ude the gradient, downhill or standard simplex search methods (such as Nelder-Mead) [43-46], normally including multi-starts, as well as genetic algorithms and very time-consuming simulated annealing =-=[45,47,48]-=-. In these iterative processes, the dipolar source is moved about in the head model while its orientation and magnitude are also changed to obtain the best fit between the recorded EEG and those produ... |

2 |
Lewis PS, Leahy RM: Multiple Dipole Modeling and Localization from Spatio-Temporal MEG Data
- JC
- 1992
(Show Context)
Citation Context ...bust since they can take into consideration the signal noise when performing dipole localization. Multiple-signal Classification algorithm (MUSIC) The multiple-signal Classification algorithm (MUSIC) =-=[6,51]-=- is a version of the spatio-temporal approach. The dipole model can consist of fixed orientation dipoles, rotating dipoles or a mixture of both. For the case of a model with fixed orientation dipoles,... |

2 |
Leahy RM: Recursive MUSIC: A framework for EEG and MEG source localization
- JC
- 1998
(Show Context)
Citation Context ...C metric becomes difficult as the dimension of the source space increases. Problems also arise when the subspace correlation is computed at only a finite set of grid points. Recursive MUSIC (R-MUSIC) =-=[53]-=- automates the MUSIC search, extracting the location of the sources through a recursive use of subspace projection. It uses a modified source representation, referred to as the spatio-temporal indepen... |

2 | Sclabassi RJ. The forward EEG solutions can be computed using Artificial neural networks - Sun |

2 | Nagashino H, Kinoushi Y. Single dipole source localization from conventional EEG using BP neural networks - Zhang, Yuasa - 1998 |

2 | Localization of multiple deep epileptic sources in a realistic head model via independent component analysis
- Weinstein, Zhukov, et al.
- 1999
(Show Context)
Citation Context ...ed by genetic algorithm evolutionary techniques. The minimization operation can be performed in order to localize multiple sources either in the brain [68] or in Independent Component backprojections =-=[69,70]-=-. If component back-projections are used, the correlation between the projected model and the measured one will have to be minimized rather than the energy of the difference. Figure 4 shows how the mi... |

2 |
Yagyu T, Kinoshita T, Sasada K. Source localization of EEG activity during hypnotically induced anxiety and relaxation. Int J Psychophysiol 2001;41:143–53
- Isotani, Tanaka, et al.
(Show Context)
Citation Context ...niques have been used to localize the sources of the different frequency bands, to assess the dynamics of different mental states, such as perception, motor preparation and higher cognitive functions =-=[80,81]-=-. In clinical neuroscience source imaging allows the analysis of EEG changes in psychiatric and neurological patients [82-84] and is extensively used to test and characterize effects of various psycho... |

2 | L-0 , Dierks T, Julin P, Winblad B, Jelic V. Discrimination of Alzheimer's disease and mild cognitive impairment by equivalent EEG sources: a cross-sectional and longitudinal study. Clin Neurophysiology 2000; 111 - Huang, Wahlund |

2 |
Pascual-Marqui RD, Lehmann D, Hell D, Vollenweider FX: Localization of MDMA-induced brain activity in healthy volunteers using low resolution brain electromagnetic tomography (LORETA). Human Brain Mapping 2001
- Frei, Gamma
(Show Context)
Citation Context ...nce source imaging allows the analysis of EEG changes in psychiatric and neurological patients [82-84] and is extensively used to test and characterize effects of various psychopharmacological agents =-=[85,86]-=-. Page 29 of 33 (page number not for citation purposes)Journal of NeuroEngineering and Rehabilitation 2008, 5:25 http://www.jneuroengrehab.com/content/5/1/25 However, the main clinical application co... |

1 |
Dijk BW, Spekreijse H: Mathematical Dipoles are Adequate to Describe Realistic Generators of Human Brain Activity
- JC, Van
- 1988
(Show Context)
Citation Context ...locations on the scalp (in the order of microvolts (μV)) and then applies signal processing techniques to estimate the current sources inside the brain that best fit this data. It is well established =-=[1]-=- that neural activity can be modelled by currents, with activity during fits being wellapproximated by current dipoles. The procedure of source localization works by first finding the scalp potentials... |

1 |
Connolly JF, Finley A: Effects of dipole position, orientation and noise on the accuracy of EEG source localization
- Whittingstall, Stroink, et al.
(Show Context)
Citation Context ...inverse problem. The accuracy with which a source can be located is affected by a number of factors including head-modelling errors, source-modelling errors and EEG noise (instrumental or biological) =-=[3]-=-. The standard adopted by Baillet et. al. in [4] is that spatial and temporal accuracy should be at least better than 5 mm and 5 ms, respectively. In this primer, we give a review of the inverse probl... |

1 |
AM, Belliveau JW: Monte Carlo Simulation
- AK, Dale
(Show Context)
Citation Context ...ined below, there are other approaches for deriving the linear inverse operators which will be described, such as minimization of expected error and generalized Wiener filtering. Details are given in =-=[12]-=-. Bayesian methods can also be used to estimate a probability distribution of solutions rather than a single 'best' solution [13]. 3.1.1 The Bayesian framework In general, this technique consists in f... |

1 |
Pullan AJ: Comparison of Potential- and Activation-Based Formulations for the Inverse Problem of Electrocardiology
- LK, JM
(Show Context)
Citation Context ...( Tr( I−KT)) 2 while the denominator measures the discrepancy of matrix KT from the identity matrix. The regularization parameter as estimated by the Composite Residual and Smoothing Operator (CRESO) =-=[23,24]-=- is that which maximizes the derivative of the difference between the residual norm and the semi-norm i.e. the derivative of B(α): B(α) = α 2||Ax(α)|| 2 - ||Kx(α) - y δ|| 2 (7) Unlike the other descri... |

1 |
BP: A New Method for Implementaion of Regularization
- Lian, Yao, et al.
- 1998
(Show Context)
Citation Context ...ethod is discrete, the L-curve is also discrete and is then typically represented by a spline curve in order to find the corner of the curve. Similar to the L-curve method, the Minimal Product method =-=[24]-=- aims at minimizing the upper bound of the solution and the residual simultaneously (Figure 2b). In this case the optimum regularization parameter is that corresponding to the minimum value of functio... |

1 |
Gonzalez-Andino SL: A Critical Analysis of Linear Inverse Solutions to the Neuroelectromagnetic Inverse Problem
- RG
- 1998
(Show Context)
Citation Context ...d in the description of the forward problem in Section ??, the Bayesian methods find an estimate ˆD of D such that where Dˆ= min( U( D)) 2 R a U( D) =|| M − GD|| + L( D). d x ad ( ) As an example, in =-=[26]-=- one finds that the linear operator A in Equation (5) is taken to be a matrix A whose rows represent the averages (linear combinations) of the true sources. One choice of the matrix A is given by A In... |

1 |
Toward Functional Brain Imaging of Cortical Electrophysiology Markovian Models for Magneto and Electroencephalogram Source Estimation and Experimental Assessments
- Baillet
- 1998
(Show Context)
Citation Context ... → 0 and w j = 1 the minimum norm solution described below is obtained. In the next subsections we review some of the most common choices for L(D). Minimum norm estimates (MNE) Minimum norm estimates =-=[5,27,28]-=- are based on a search for the solution with minimum power and correspond to Tikhonov regularization. This kind of estimate is well suited to distributed source models where the dipole activity is lik... |

1 |
Yaoqin X: A new algorithm for EEG source reconstruction based on LORETA by contracting the source region
- Xin, Xinshan
(Show Context)
Citation Context ... be impressively improved in comparison to MNE. However, localization of deeper sources cannot be properly estimated. In addition to Minimum Norm, FOCUSS has also been used in conjunction with LORETA =-=[31]-=- as discussed below. Low resolution electrical tomography (LORETA) LORETA [5,27] combines the lead-field normalization with the Laplacian operator, thus, gives the depth-compensated inverse solution u... |

1 |
Oharriz Y: Explicit Backus and Gilbert EEG Inverse Solution for Spherical Symmetry
- JJ, PA, et al.
(Show Context)
Citation Context ...priate dynamical models, better solutions than those obtained by the instantaneous inverse solutions (such as LORETA) are obtained. uvg u T g 3.1.2 The Backus-Gilbert method The Backus-Gilbert method =-=[5,7,36]-=- consists of finding an approximate inverse operator T of G that projects the EEG data M onto the solution space in such a way that the estimated primary current density ˆD BG = TM, is closest to the ... |

1 |
Gonzalez-Andino SL: Comparison of algorithms for the localization of focal sources: evaluation with simulated data and analysis of experimental data
- RG
(Show Context)
Citation Context ... of correct localization in 3D space. The WROP method is a family of linear distributed solutions including all weighted minimum norm solutions. As particular cases of the WROP family there are LAURA =-=[26,38]-=-, a local autoregressive average which includes physical constraints into the solutions and EPI-FOCUS [38] which is a linear inverse (quasi) solution, especially suitable for single, but not necessari... |

1 |
De Peralta RG: EEG source imaging. Clinical Neurophysiology 2004
- CM, MM, et al.
(Show Context)
Citation Context ...uasi) solution, especially suitable for single, but not necessarily point-like generators in realistic head models. EPIFOCUS has demonstrated a remarkable robustness against noise. LAURA As stated in =-=[39]-=- in a norm minimization approach we make several assumptions in order to choose the optimal mathematical solution (since the inverse problem is underdetermined). Therefore the validity of the assumpti... |

1 | Haueisen J: Efficient Electromagnetic Source Imaging With Adaptive Standardized LORETA/FOCUSS - PH, Liu, et al. |

1 |
Hese P, D'Havé M
- Vanrumste, Hoey, et al.
(Show Context)
Citation Context ...ant difference in accuracy for radial or tangential dipoles is to be expected. As the noise increases, localization errors increase, particularly for deep sources of radial orientation. Similarly, in =-=[46]-=- it was found that the importance of the realistic head model over the spherical head model reduces by increasing the noise level. It has also been found that solutions for multiple-assumed sources ha... |

1 |
Darcey TM: Source Localization Using a Current-Density Minimization Approach
- MI, TE
(Show Context)
Citation Context ...ude the gradient, downhill or standard simplex search methods (such as Nelder-Mead) [43-46], normally including multi-starts, as well as genetic algorithms and very time-consuming simulated annealing =-=[45,47,48]-=-. In these iterative processes, the dipolar source is moved about in the head model while its orientation and magnitude are also changed to obtain the best fit between the recorded EEG and those produ... |

1 |
Poeppe D, Miyashita Y: Reconstrusting Spatio-Temporal Activities of Neural Sources from Magnetoencephalographic Data Using a Vector Beamformer
- Sekihara, Nagarajan
(Show Context)
Citation Context ... neural activity index: Var ˆ ( rdip) Var ˆ N( rdip) = Tr{[ G T ( rdip) Q −1 G( rdip)] −1 } where Q is the noise covariance matrix estimated from data that is known to be source free. Sekihara et. al =-=[50]-=- proposed an 'eigenspace projection' beamformer technique in order to reconstruct source activities at each instant in time. It is assumed that, for a general beamformer, the matrix W = [w x , w y , w... |

1 |
Leahy RM: Source Localization Using Recursively Applied and
- JC
- 1999
(Show Context)
Citation Context ...ather than an individual current dipole. It recursively builds up the IT model and compares this full model to the signal subspace. In the recursively applied and projected MUSIC (RAPMUSIC) extension =-=[54,55]-=-, each source is found as a global maximizer of a different cost function. Assuming g(r, e) = h(r)e, the first source is found as the source location that maximizes the metric rˆ= arg max( subcorr( h(... |

1 |
Huang M, Leahy RM: Paired MEG Data Set Source Localization Using Recursively Applied and Projected (RAP) MUSIC
- JJ, JC
(Show Context)
Citation Context ...ather than an individual current dipole. It recursively builds up the IT model and compares this full model to the signal subspace. In the recursively applied and projected MUSIC (RAPMUSIC) extension =-=[54,55]-=-, each source is found as a global maximizer of a different cost function. Assuming g(r, e) = h(r)e, the first source is found as the source location that maximizes the metric rˆ= arg max( subcorr( h(... |

1 |
NT, Guanglan Z, Abeyratne UR, Saratchandran P: RBF networks for source localization in quantitative electrophysiology
- AK, Lye
(Show Context)
Citation Context ...rnal of NeuroEngineering and Rehabilitation 2008, 5:25 http://www.jneuroengrehab.com/content/5/1/25 better in noise free environments, ANN performs best in environments with low signal to noise ratio =-=[58]-=-. Therefore ANNs seem to be more noise robust. In any case, many research works [59-67] claim a localization error in ANN methods of less than 5%. A general ANN system for EEG source localization is i... |

1 | Saratchandran P: EEG source localization: a comparative study of classical and neural network methods - Abeyratne, Zhang |

1 | Sonmez M, Sun M: EEG source localization: a neural network approach - RJ |

1 |
De Clercq J, Vanrumste B, Walle R Van de, Lemahieu I, DHave M, Boon P: EEG dipole source localization using artificial neural networks
- Hoey
(Show Context)
Citation Context ...e robust. In any case, many research works [59-67] claim a localization error in ANN methods of less than 5%. A general ANN system for EEG source localization is illustrated in Figure 3. According to =-=[65]-=-, the number of neurons in the input layer is equal to the number of electrodes and the features at the input can be directly the values of the measured voltage. The network also consists of one or tw... |

1 | Nagashino H, Kinouchi Y: EEG source localization for two dipoles by neural networks - Yuasa, Zhang |

1 |
Akhtari M, Sutherling WW: Multiple source localization using genetic algorithms
- McNay, Michielssen, et al.
- 1996
(Show Context)
Citation Context ... potential and the measured potentials is minimized by genetic algorithm evolutionary techniques. The minimization operation can be performed in order to localize multiple sources either in the brain =-=[68]-=- or in Independent Component backprojections [69,70]. If component back-projections are used, the correlation between the projected model and the measured one will have to be minimized rather than the... |

1 |
Dewald JPA: Evaluation of different cortical source localization methods using simulated and experimental EEG data
- Yao
(Show Context)
Citation Context ...er source. s n1 can be chosen in the following way: s n1 ⎧ bd = ⎨ ⎩ and similarly for s n2 using d n1 . p ∑ | D( n)|( s d + s d ) n1 n1 n2 n2 ( where b > 0), for dn < some number 1, otherwise n2 2 In =-=[72]-=-, Yao and Dewald used three indicators to determine the accuracy of the inverse solution: 1. the error distance (ED) which is the distance between the true and estimated sources defined as N I 1 1 NI ... |

1 |
R Jr, Simpson G, Ruchkin D: A test of brain electrical source analysis (BESA): a simulation study. Electroenceph Clin Neurophysiol
- Miltner, Braun, et al.
- 1994
(Show Context)
Citation Context ...oblem which was mentioned in Section 3.2.1 is BESA. This technique is very sensitive to the initial guess of the number of dipoles and therefore is highly dependent on the level of user expertise. In =-=[74]-=- it is shown that the grand average location error of 9 subjects who were familiar with evoked potential data was 1.4 cm with a standard deviation of 1 cm. Rather than finding all possible sources sim... |

1 |
Hunjan A, Sharma R, Rutka JT, Chuang SH, Kamijo K, Yamazaki T, Snead OC: Dipole localization for identification of neuronal generators in independent neighboring interictal EEG spike foci
- Ochi, Otsubo, et al.
(Show Context)
Citation Context ...alyses for clinical settings differ from those used for research in the developmental neurosciences, as they are concerned largely with the identification and localization of abnormalities in the EEG =-=[77]-=-, and the utilization of this information for neurosurgical interventions in the most severe cases [78,79]. In cognitive neuroscience such techniques have been used to localize the sources of the diff... |

1 |
OC: Surgical treatment of medical refractory epilepsy
- Snead
(Show Context)
Citation Context ... they are concerned largely with the identification and localization of abnormalities in the EEG [77], and the utilization of this information for neurosurgical interventions in the most severe cases =-=[78,79]-=-. In cognitive neuroscience such techniques have been used to localize the sources of the different frequency bands, to assess the dynamics of different mental states, such as perception, motor prepar... |

1 | Strik WK, Maurer K: Electrical brain activity in schizophrenia described by equivalent dipoles of FFT-data. Schizophr Res - Dierks - 1995 |

1 | D'Hav M, Vandekerckhove T, Achten E, Adam C, Clmenceau S, Baulac M, Goosens L, Calliauw L, De Reuck J: Dipole modelling and intracranial EEG recording: Correlation between dipole and ictal onset zone. Acta Neurochir - Boon - 1997 |

1 | Chiappa KH, Cocchius JI, Connolly S, Cosgrove GR: Accuracy of EEG dipole source localization using implanted sources in the human brain. Clinical Neurophysiology - Krings - 1999 |

1 |
Blomstedt G, Jousmaki V, Korkman M: Magnetoencephalography in presurgical evaluation of children with Landau-Kleffner syndrome. Epilepsia
- Paetau, Granstrom
- 1999
(Show Context)
Citation Context ...g surgical decisions. More specifically, it has been validated for the presurgical evaluation of adult patients suffering from refractory epilepsy [87-89] and in children with LandauKleffner syndrome =-=[90]-=-. Source localization is even feasible in neonates [91]. It allows the epileptogenic area to be located and comparisons to be made with clinical information, magnetic resonance imaging (MRI) anatomica... |

1 |
Gondry-Jouet C, Dmpelmann M, Grebe R, Wallois F: High-resolution electroencephalography and source localization in neonates. Human Brain Mapping 2007:40
- Roche-Labarbe, Aarabi, et al.
(Show Context)
Citation Context ...lidated for the presurgical evaluation of adult patients suffering from refractory epilepsy [87-89] and in children with LandauKleffner syndrome [90]. Source localization is even feasible in neonates =-=[91]-=-. It allows the epileptogenic area to be located and comparisons to be made with clinical information, magnetic resonance imaging (MRI) anatomical data, and the results of metabolic imaging techniques... |