Performance evaluation of inverse methods for identification and characterization of oscillatory brain sources: Ground truth validation & empirical evidences

Oscillatory brain electromagnetic activity is an established tool to study neurophysiological mechanisms of human behavior using electro-encephalogram (EEG) and magneto-encephalogram (MEG) techniques. Often, to extract source level information in the cortex, researchers have to rely on inverse techniques that generate probabilistic estimation of the cortical activation underlying EEG/ MEG data from sensors located outside the body. State of the art source localization methods such as exact low resolution electromagnetic tomography (eLORETA), Dynamic Imaging of Coherent Sources (DICS) and Linearly Constrained Minimum Variance (LCMV) have over the years been established as the prominent techniques of choice. However, these algorithms produce a distributed map of brain activity underlying sustained and transient responses during neuroimaging studies of behavior. Furthermore, the volume conduction effects and noise of the environment play a considerable role in adding uncertainty to source localization. There are very few comparative analyses that evaluates the “ground truth detection” capabilities of these methods. In this technical note, we compare the aforementioned techniques to estimate sources of spectral event generators in the cortex using a two-pronged approach. First, we simulated EEG data with point dipole (single and two-point), as well as, distributed dipole modelling techniques to validate the accuracy and sensitivity of each one of these methods of source localization. The abilities of the techniques were tested by comparing the centroid error, focal width, reciever operating characteristics (ROC) while detecting already known location of neural activity generators under varying signal to noise ratios and depths of sources from cortical surface. Secondly, we performed source localization on empricial EEG data collected from human participants while they listened to rhythmic tone stimuli binaurally. Inportantly, we found a less-distributed activation map is generated in LCMV and DICS when compared to eLORETA however, control of false positivesis much superior in eLORETA in realistic distributed dipole scenarios. A comprehensive analysis, further, indicate the strengths and drawbacks of each of the methods.


Introduction
Cortical oscillations play an important role in governing basic cognitive functions (Edelman and Mountcastle, 1978;Bressler and Kelso, 2001;Buzsáki and Draguhn, 2004). Several researchers have suggested that electromagnetic brain activity at specific frequency bands carries meaningful information about neural function, e.g. alpha waves at 10 Hz (Bollimunta et al., 2008;Llinás et al., 1999), beta at 15-30 Hz (Brovelli et al., 2004), gamma at 30 Hz and above (Bressler et al., 1993;Varela et al., 2001;Cheyne and Ferrari, 2013). Concurrently, time-locked transient responses have been useful for decades in electrophysiological research, both for understanding basic neurobiological functions as well as in clinical and other applications (Picton et al., 1974;Kutas et al., 1977;Pantev et al., 1995;Clark et al., 1995;Cheyne et al., 2006). Hence, identifying the neural generators of sustained cortical oscillations and task-specific transient neural responses from electro-encephalography/ magneto-encephalography (EEG/ MEG) is an extensive topic of research. Once identified with adequate reliability, the focal localization of sources will eventually reveal the underlying large-scale network governing cognitive tasks.
There are several source localization methods that exist in the literature, commonly known under the umbrella of inverse methods (Hämäläinen and Sarvas, 1989). Most of these techniques are based on fitting single/ multiple dipolar cortical source/sources within a defined cortical volume based on some assumptions about relationships between the sources (Van Veen et al., 1997;Gross et al., 2001;Hillebrand and Barnes, 2003;Liu et al., 2002;Sato et al., 2004). Some methods consider sources to have minimum correlation, e.g. synthetic aperture magnetometry (SAM) , linearly constrained minimum variance spatial filtering (LCMV) (Van Veen et al., 1997;Murzin et al., 2011). There are specialized measures that detect generators of oscillatory brain signals by considering maximum coherence between prospective sources, e.g., dynamic imaging of coherent sources (DICS) (Gross et al., 2001). The aforementioned methods are more popular for MEG, where the possible sources are located closer to brain surface and cost-function optimizations are relatively unambiguous. In EEG, where deeper sources can affect scalp potentials, exact low-resolution brain electromagnetic tomography (eLORETA) (Pascual-Marqui, 2007) has been the method of choice. Though, dynamic statistical parametric mapping (dSPM) (Liu et al., 2002) and sparse Bayesian learning (SBL) (Ramírez et al., 2010) has been developed to improve upon the estimates of spatial filter detection, eLORETA is still by far one of the most robust methods for EEG source localization. eLORETA directly estimates current source density, a biophysically relevant parameter over a grid of plausible cortical locations for both detection of time-locked activity e.g., in event related potentials / fields (EEG/ERF) or frequency-locked activity e.g., spontaneous frequency bursts or steady state oscillatory responses to a periodic stimuli. For example, LCMV is more tuned for detection of ERP/ ERF generators whereas DICS may be considered for spontaneous oscillatory activity that may have large-scale functional connectivity embedded. Nonetheless, the source estimated by all methods are broadly influenced by depth, signal to noise strength of the neural activity in question and redundant informational content of high temporal resolution data. Often these manifest in distributed source activity estimation with diminished statistical power.
The reliability of the location of neural activity along with lower false positives fhould be an important litmus test for any source localization technique. In this article, we evaluate the performance on specificity and sensitivity of the key techniques eLORETA, DICS and LCMV on simulated EEG data. We compared the results from eLORETA and DICS on a paradigm of evoked 40-Hz auditory steady state responses (ASSR) and eLORETA and LCMV for detecting the source of N100 activity when the same data was epoched timelocked to the stimulus onset. Very rigorous comparison metrics e.g. localization error, spatial spread and receiver operating characteristics (ROC) were used to evaluate performance and reliability of results along with a evaluation of the performance of these methods at different depths of dipole placement in the simulated EEG data. The rest of this paper is organized as follows. In Section II, we introduce the simulation framework for testing the three methods (i.e., eLORETA, LCMV, DICS) on synthetic EEG data. We also outline the experimental design used to generate empirical EEG data on which we wish to compare eLORETA, LCMV and DICS. In section III we present the comparative results of applying eLORETA, LCMV and DICS on simulated and empirical EEG data. Finally in section IV we outline comparative benefits and pitfalls of these methods.

Generation of synthetic EEG data:
We used a time-varying sinusoid at 40 Hz, plus normally distributed noise as a model for cortical source dynamics. The magnitude of the dipolar source dynamics in cortical locations are represented by where q i (t) is the electric dipole moment at location i and at time t, is white noise with zero mean and standard deviation σ. We compared 3 conditions with respect to number of sources, by placing single point dipole, twopoints dipoles and distributed dipoles in a MNI brain template according to the Montreal Neurological Institute (Müller and Weisz, 2012). Single point source was placed at around the superior temporal region, in the left hemisphere (MNI coordinates: (−60, −28, 6)). Two sources were placed, one in the left hemisphere (MNI coordinates: (−60, −28, 6)) and the other in the right hemisphere (MNI coordinates: (64, −24, 6)) around the superior temporal region. Approximately, hundred point sources were placed within a spherical volume with radius of 12 mm in the left hemisphere centred around superior temporal region at (−60, −28, 6), according to brain template. Another set of hundred point sources were placed around right hemisphere auditory cortex seed area at (64, −24, 6), defining the distributed source condition. The resolution of the grid chosen for dipole simulation was 5mm and "f t prepare leadf ield.m" code of FieldTrip toolbox was used for this purpose. Dipole moment orientations were assumed to be along the radial direction to retain simplicity. We computed the scalp potentials for EEG at realistic sensor locations by applying a forward model (Mosher et al., 1999;Baillet et al., 2001) with realistic headshape using "f t dipolesimulation.m" of the FieldTrip toolbox (Fig 1).
v r (t) = L T (r, r q ).q(t) where, v is the electric potential at sensor location r, r q represents all source locations, L represents the "lead field kernel", (.) T represents transpose and q(t) is the dipole moment. Synthetic EEG data were generated by varying signal to noise ratio (SNR) at the source space. Physiological SNR was estimated using a statistical measure, 10 log 10 [ s σ b ], where s is peak-to-peak amplitude of EEG data during rhythmic auditory stimulation (see Experimental Methods below) and σ b is the standard deviation of the baseline data. We chose a wide range of SNRs both above and below the estimated physiological SNR level to allow us to evaluate the sensitivity of the all the algorithms. Fig 1 shows simulated EEG activity on scalp surface with bilateral auditory cortical sources. Following (Goldenholz et al., 2009), SNR was computed in decibel(dB) using the following equation.
where U is total sensor count, v is the signal on sensor u ∈ (1, 2, · · · U ) provided by the forward model for a source with unit amplitude. The sensor space variance η 2 u = σ 2 (LL T ) u .

Source localization methods
The basic goal of any source localization technique is to compute the dipolar source locations and strengths inside the brain from measurements on the scalp (inverse of equation 2). In other words the objective is to estimate the spatial filter W S from the relation where, q(t) is the dipole moment at time t, W S is the spatial filter matrix, and V is vector representation of all sensor time series. Obviously, the system of equations represented by equation 4 is ill-posed as number sensors (dimension of vector V) is finite, but number dipoles are unknown. So, different source localization methods attempt to estimate the W S using diverse constraints posed by anatomy of the brain and functional relationships among brain areas during ongoing task.

LCMV
Linearly constrained minimum variance (LCMV) belongs to the class of "beamformer" methods that enhances a desired signal while suppressing noise and interference at the output array of sensors . LCMV is built upon an adaptive spatial filter whose weights are calculated using covariance matrix of EEG/MEG time series data. A spatial filter computes the variance of the total source power which is allowed to vary but the output of the filtered lead field is kept constant. As a result the beamformer output is maximized for the target source but other source contributions are suppressed. LCMV attempts to minimize the beamformer output power where C is the data covariance matrix. The entries to spatial filter matrix can be expressed as where L is lead field matrix, and following constraint is maintained W S˙L T = 1.

DICS
Dynamic imaging of cortical sources (DICS) beamformer (Gross et al., 2001) works with same constraint assumption of LCMV but extends the computation of spatial filter to the frequency domain. Here, sensor level cross spectral density (CSD) matrix replaces the covariance matrix and the spatial filter is applied to sensor level CSD to reconstruct the source level CSD of all combination of pairwise voxels. Hence, DICS directly estimates the interaction between sources at respective frequencies. The weight function can be written as where 'a' is regularization parameter, + is the Moore-Penrose pseudo-inverse which is equal to the common inverse if the matrix is non-singular. H is also called the centering matrix or the surface Laplacian.
Low resolution imaging results in weak performance for recovering of multiple sources when the point-spread functions of sources overlap. Other methods have also tried to combine surface Laplacian with LCMV (Murzin et al., 2013), to estimate source-level connectivity.

Measurements used for face validity of inverse algorithms:
Using simulated data to test a method provides mechanism for ground truth validation. The exact location of a putative dipolar source is elusive in nature for real data, however, one can certainly set-up simulations when performance of a particular method needs evaluation. We employed three complementary measures to provide face-validity of the eLORETA method with two other methods i.e., LCMV and DICS.
1. Centroid error estimation: Inverse methods estimate a cluster of point dipolar sources. To measure how much error is involved in source localization, we identified the activated voxels in the top 0.5 percentile of all voxel intensities and measured the Euclidean distance between the centroid of the estimated source coordinates and the actual source coordinate, to give us the 'Centroid Error'. This was done for each hemsiphere, separately. Subsequently, the net centroid errors are computed by summing up across two hemispheres and compared for eLORETA, LCMV and DICS.
2. Degree of Focal localization: The size of the cluster in terms of sum of distances of all points from the centroid, gives a measure of focal localization of sources. We computed the total sum of distances of each voxel with significant current density from the centroid location as a measure of the spatial distribution of the estimated source. This gave us a quantitative approach to evaluate the degree of focal source localization. For practical reasons, cluster width computation was done for each hemisphere separately Murzin et al. (2013).
3. Performance evaluation at various depths: The localization of deep sources has been the main factor limiting detection of true sources from M/EEG data. This is highly significant since deep cortical areas constitute 30% of the cortical sources (Hillebrand and Barnes (2002)). We stduied the effects of depth by positioning the dipoles at different distances from the auditory cortical locations mentioned earlier. The depth was varied along the x-axis, from 1 to 20 mm in stepd of 1 mm, towards the center of the brain, in both hemispheres. Further, we computed the centroid error and the focal width of the significant voxels obtained by localizing the dipoles placed at each depth. For the depth analysis, noise was kept to zero to retain simplicity.
4. Receiver Operating Characteristic (ROC) analysis: We compared the "sensitivity" and "specificity" of eLORETA, LCMV and DICS, using receiver operating characteristic (ROC) analysis (Metz, 1978). Here, probability of correct detection, also called 'true positive (TP)' ratios are plotted against a function of probability of incorrectly detecting an activation, also called 'false positive (FP)' ratios. Ideal detection should have enhanced TP while suppressing FP. Hence, a steeply rising ROC curve indicates better performance in terms of sensitivity (higher TP) and specificity (lower FP). We performed ROC analysis on estimated source voxels which are within a certain distance threshold 25 mm (Region Of Interest) from the actual sources (Left and Right Superior Temporal Gyrus). TP is the fraction of significant voxels within the Region of Interest (ROI) at different thresholds ranging from 50 to 95 percentile of all activated voxels. FP is the fraction of significant voxels at the corresponding thresholds that reside outside the ROI.
We also compare the performance of all methods under parametric variation of signal to noise ratio at the source level and different kinds of source configurations, e. g., single point dipole, 2-point dipoles and distributed dipoles.

Empirical EEG recordings
Participants 10 healthy volunteers (8 males, 2 females) aged between 22 − 39 years (mean age 28 years) participated in the study after giving informed consent, following the guidelines approved by Institutional Human Ethics Board at National Brain Research Centre. All participants were self-declared normal individuals with no history of hearing impairments, had either correct or corrected-to-normal vision and no history of neurological disorders.

Stimuli
Volunteers had to remain stationary in a seated position within a sound-proof room and hear auditory stimuli through 10 Ohm insert earphones with disposable foam ear-tips, binaurally for 200 seconds while fixating at a visual cross. Additionally they had a baseline block where they fixated at the visual cross for 200 seconds without any sounds being played. Sounds were pure tones of 1000 Hz frequency and 25 millisecond time duration, with 5% rise and fall and were repeated with a frequency of 40 Hz during an On block of 1 second duration interspersed between 2 Off blocks where no auditory stimuli were presented. Stimuli was made using in STIM2 stimulus system with audio box P/N 1105 at 85 dB.

Data Collection and Pre-processing
EEG data was acquired in an acoustically shielded room with 64 channels NeuroScan (SynAmps2) system with 1 KHz sampling rate. Brain Products abrasive electrolyte gel (EASYCAP) was used to make contact with scalp surface and the impedance was maintained at values less than 5kΩ for all volunteers. Baseline EEG data was recorded for 200 seconds with eyes open, no tone, and a fixation cross on a monitor in front of the participants. Baseline and binaural stimuli were presented while participants were asked to maintain fixation on the cross all along to reduce eye movements. A Polhemus Fastrak system was used to track the location of sensors on the EEG cap.
Recorded raw data was re-referenced to linked mastoids (M1 and M2) and was detrended to remove linear trends from the signal. Epochs of 5 second duration were constructed after removing an initial 50 seconds of the 200 seconds long session to capture auditory steady state response (ASSR). Data was band pass filtered with cutoff frequencies 5-48 Hz, to concentrate on sources underlying ASSR.
For an evoked waveform analysis, after re-referencing to linked mastoids (M1 and M2), epochs of 1 second duration during were extracted from the raw data during stimulus condition, then filtered with cut-off frequencies 0.5-48Hz, detrended and averaged across trials to generate the evoked potential. Thresholds of −100µV and 100µV were used to reject blink-corrupted trials, meaning if at any point within the epoch, the voltage exceeded the threshold values, the entire trial was deleted from the subsequent analysis.
Individual sensor locations from the EEG cap (Polhemus) was acquired for each subject. Structural T1weighted MPRAGE scan was performed on the volunteers using a 3T Philips Achieva MRI scanner for coregistration with the sensor locations for accurate source localization. A forward model for each volunteer was computed using Boundary Element Method (BEM) from their respective T1-image. After computing the lead field intensities in each volunteer, the individual grids were interpolated and finally normalized to a Montreal Neurological Institute (MNI) template. The normalized grid locations where the lead field intensities were exceeding the top 99.5 percentile across all grid locations were characterized as significant sources of brain activity.

Simulated EEG data
Simulated EEG data was computed by placing electric dipolar sources at auditory cortical locations, according to single dipole condition, two-points dipoles condition and distributed dipole condition, using equation 1 and projecting the source activity at realistic sensor locations of a Neuroscan (Compumedics Inc, USA) EEG cap using a realistic head model (equation 2, Baillet et al., 2001). We considered two types of temporal profiles for source activity, a sinusoidal signal mimicking the band-specific frequency response observed in typical EEG signal such as auditory steady state response (ASSR) and a mixture of Gaussian pulses representing the time-locked event related potentials (ERP). Baseline data set was generated separately by placing sources at the right frontal lobe (10, -69, 36) and the left parietal lobe (-47, 21, 36)  Simulated EEG data for each SNR scenarios were analyzed with LCMV, DICS and eLORETA. Fig 2 illustrates combined results from eLORETA, DICS and LCMV algorithms on a brain surface rendered by the MNI brain at SNR 26.8 dB for the distributed dipole model. We applied eLORETA and DICS to perform frequency-locked source analysis on the sinusoidal source data. eLORETA and LCMV were employed for localizing the sources of the peak negative response on the gaussian signaal, by selecting a time segment constituting of points ±25 ms around the peak (Fig 1b). We considered 5 % regularization for each method. Identical inverse filters were used for localizing the oscillatory signal as well as the baseline data. The top 0.5 percentile of the voxels having the highest power ratios were considered significant. For plotting activations, the source locations in the 3-D voxel space was projected to a surface plot using customized MATLAB codes (coord2surf.m in GitHub location).

Accuracy:
Frequency analyses using eLORETA and DICS yielded similar centroid errors for 1-point dipole condition at all SNR levels (Fig 3a). For 2-point and distributed dipoles condition, DICS seems to perform slightly better in high noise scanrios but eLORETA performance was improved when SNR became more favourable (Fig 3b,c).
For 1-dipole source, increasing SNR improved detection accuracy but no such benefit is practically observed for 2-dipole though in, distributed dipole condition eLORETA performance got better with increasing SNR.
In time domain analysis, LCMV yielded a lower centroid error for point dipoles (single and 2-point sources) as well as distributed dipoles compared to eLORETA in physiologically realistic SNRs (Fig 3). Interestingly, LCMV performance seemed to be least affected by SNR changes based on the centroid error metric.

Localization Spread:
To measure the degree of focal localization of sources we computed the distance between centroid of estimated source cluster and each significant voxel point contained within the cluster. The average sum of distance across all voxels gives us a measure of focal source localization performance for eLORETA, DICS and LCMV algorithms (Fig 4). eLORETA clearly performs favorably (more focal localization) than DICS and LCMV for most noise settings for single dipole localization. For physiologically relevant noise settings in 2-dipoles and distributed dipoles scenario the performance difference between eLORETA and DICS in frequency domain and eLORETA and LCMV in time domain, were somewhat comparable but overall, eLORETA can claim a more favourable performance.

Depth:
To The centroid error for DICS and LCMV is observed to decline to a greater extent, compared to eLORETA, as we increase the depth of the simulated dipoles. However, the focal width of significant voxels increases with increase in depth of the dipoles. Further, the focal width of sources computed by eLORETA are lesser than that of DICS and LCMV for most depths. Since, no noise was added to the simulated sinusoidal signal or the gaussian pulse, eLORETA can be credited to have a higher degree of focal localization in comparison to LCMV and DICS at zero noise condition.

Sensitivity and Specificity:
To evaluate sensitivity, we computed the Receiver Operating Characteristics (ROC) curves (Fig 6) after applying DICS, LCMV and eLORETA methods in different SNR scenarios across different dipole conditions.
The region of interest (ROI) for assigning true positives was fixed at 25 mm (see section 2.3 for details). The leadfield intensity thresholds were chosen from 50th to 95th percentile of the intensities observed (absolute value was used at steps of 5), to calculate the true positive fraction. Correspondingly, the false positive fraction was determined by the ratio of the significant voxels outside the ROI and total voxels outside the ROI.
A steeper ROC curve is associated with optimal performance as reflected by lower false positives and higher true positives. We observe that eLORETA performance improves with SNR levels, i.e, eLORETA performs better at low noise settings. Interestingly, eLORETA performance improved for distributed dipoles in frequency analysis and time-lock analysis, whereas for DICS and LCMV the performance deteriorated. For point dipole conditions, LCMV performed better than eLORETA for lower SNR values, but eLORETA was way ahead at higher SNR values. An important observation was that the LCMV performance was least affected by SNR in point dipole conditions which is in line with the results from other metrics of accuracy and localization.

Empirical EEG data
Source localization underlying 40Hz EEG activity The Fourier spectrum of each EEG channel time series were computed by multi-taper method with number of tapers = 2, using Fieldtrip function ft freqanalysis.m. Power spectral density of empirical EEG data and the event related potential (ERP) time locked to the onset of a single tone stimulus are shown in Fig 7. Fig 7 a Lead field intensity was computed using eLORETA and DICS by co-registration of Polhemus data and structural MR image, for each participant, which was later normalized to a MNI template (see Methods for details). We considered 5 % regularization for all methods. The ratio of source power between stimulus and baseline condition was calculated in each voxel. The averaged lead field intensities across all participants were evaluated using non-parametric statistics and top 0.5% voxels were identified as sources. In Fig 8a,  Acknowledging the absence of ground truth concerning true sources that exist in empirical data, we assumed that the voxels identified as overlapping sources by both the methods i.e., eLORETA and DICS (marked yellow in Fig 8a), to be the "true sources". 7 such clusters and their respective centroids were identified. In parallel, we performed a k-means clustering on all the voxels identified from two methods in question, and identified the cluster of voxels that contained the "true sources". The Euclidean distance between the centroid of the "true source" assigned earlier were computed from each point of this cluster. The normalized sum of distances expresses the focal width of the corresponding method and gives a measure of uncertainty from the method under investigation. The focal width of 7 such clusters and their respective locations are tabulated in Table 2a.
Overall, DICS yielded lower cluster widths in comparison to eLORETA Source localization of N100 response In Fig 7b) we show the ERP responses to the binaural tone and the ERPs in Off blocks (baseline condition), averaged across all trials and participants (grand average). A negative peak around 100 ms post onset of tone stimulus (N100) was observed in the binaural condition with a latency of around 110 ms. The topoplot represents the spatial map of the difference in relative changes of amplitude between ERPs from the the binaural and baseline conditions across all channels and trials.
Next, we computed the underlying source activation during the N100 response using LCMV and eLORETA.
In Fig 8b) we plot the source activations (top 0.5% voxels similar to 40Hz case) in epochs of duration 50 ms, within which the 25th ms corresponds to the peak of N100. 7 clusters were observed where both methods agreed about the location of sources (yellow regions of Fig 8b). The locations of these clusters and the focal width obtained from both methods eLORETA and LCMV, following the same lines of reasoning as in 40 Hz, are tabulated in table 2b.

Discussion
Currently, multiple source localizing algorithms exist and many more studies have reported the underlying neural generators of temporally fixed events or the plausible networks governing the control of the frequency response observed in the signals of different complexities. However, different inverse methods provide different solutions leading to no agreement of which algorithm is the 'best method'. Therefore, we compared the popular beamformer methods through metrics, to approach this issue.
We compared three methods, eLORETA (Pascual-Marqui, 2007), LCMV (Van Veen et al., 1997) and DICS (Gross et al., 2001) using the metrics (Centroid error, Focal width, ROC) explained in section 2.3 across three dipolar models (single, two-point and distributed model) for the simulated sinusoidal signal (mimicking the steady state 40 Hz) and a mixture of Gaussian pulses (representing the time locked potential). The models were simplistic, however, since we knew the exact location of dipole/s, ground truth validation was possible.
Moreover, the study was conducted across different SNRs to test the each method's sensitivity to noise. In addition, for testing the inverse methods with respect to dipolar depth, we computed centroid error and focal width of significant sources of distributed dipoles placed at different depths for both types of signals, at zero noise condition. Also, we conducted source localization by collecting empirical EEG data exhibiting 40 Hz auditory steady state response, Fig 7. DICS and eLORETA were used to compute the sources underlying the 40 Hz activity and LCMV and eLORETA were used to compute the sources underlying the N100 response, shown in Fig 8. A general consensus emerges from comparing the algorithms that there is no clear winner (Table 1). DICS performs better than eLORETA in single and two-point dipole conditions, even at lower SNR. The centroid error and focal width of both the algorithms are comparable across all models, but eLORETA shows significant control on the false positive ratio in the distributed dipole condition, proving to be the method of choice for estimating sources underlying frequency response. For time-locked localization, LCMV proved to be a better option when dealing with noisy data. Performance of DICS and especially, LCMV were observed to be inert to varying SNRs, as opposed to eLORETA. However, it can be inferred that localizing more number of dipoles leads to a reduction in the true positive fraction of LCMV and DICS. On localizing deeper sources, focal width of the cluster increased, but overall, eLORETA proves to be more focal than the other two algorithms in zero noise conditions. Although, since eLORETA is susceptible to noise, cluster analysis on empirical dataset suggests that the presence of noise in EEG can affect the focal localization of eLORETA.
Inspite of the kind of tests we have conducted, the choice of method of localization also depends heavily on the what kind of response needs to be localized i.e. different algorithms may be used for localizing coherent signals, subtle signals or band of frequency. Therefore, even if source localizing algorithms have better performance using several metrics, other methods can be used exploratory fashion. Although, with many localizing options on the shelf, it can be essential to find the overlap of anatomical regions using different algorithms, in order to verify cortical sources. Additionally, studies employing methods such as synchronous EEG/fMRI may predict the neural generators with a better accuracy.

SNR (in dB) SNR (in dB) Centroid Error (in mm)
Centroid