Electromagnetic Source Localization Research Articles

On bias and its reduction via standardization in discretized electromagnetic source localization problems

In electromagnetic source localization problems stemming from linearized Poisson-type equation, the aim is to locate the sources within a domain that produce given measurements on the boundary. In this type of problem, biasing of the solution is one of the main causes of mislocalization. A technique called standardization was developed to reduce biasing. However, the lack of a mathematical foundation for this method can cause difficulties in its application and confusion regarding the reliability of solutions. Here, we give a rigorous and generalized treatment for the technique using the Bayesian framework to shed light on the technique’s abilities and limitations. In addition, we take a look at the noise robustness of the method that is widely reported in numerical studies. The paper starts by giving a gentle introduction to the problem and its bias and works its way toward standardization.

Spatial Localization of Electromagnetic Radiation Sources by Cascade Neural Network Model with Noise Reduction

Spatial Localization of Electromagnetic Radiation Sources by Cascade Neural Network Model with Noise Reduction

The opening workspace control strategy of a novel manipulator-driven emission source microscopy system

Emission source microscopy (ESM) technique can be utilized for localization of electromagnetic interference sources in the electronic systems, but its accuracy is limited by the typical planar scanning mode. In order to increase the accuracy, this paper presents a novel cylinder-aperture ESM measurement system driven by 6-DOF manipulator, and investigated the control strategy to generate the maximum-area aperture and optimized scanning trajectory. Based on the multiple constraints of the cylinder-aperture ESM measurement, we proposes analyzing the impact of the constraints by steps. This can obtain the analytical solution of the manipulator workspace and support solving the maximum aperture area. Besides, a modified RRT*(Rapidly-exploring Random Trees) algorithm is addressed to optimize the manipulator trajectory. The simulation and tests have proven that this algorithm could obviously reduce the joint mutation and cumulative tracking error. In the experimental section, the near-field scanning (NFS) tests, planar-aperture ESM measurement and proposed cylinder-aperture ESM measurement were conducted to measure one benchmark emission source. The results have demonstrated that the cylinder-aperture ESM measurement has the best convergences on the radiation pattern of the emission source.

Determination of electromagnetic source localization with factorization method

AbstractThe factorization method (FM) is an attractive qualitative inverse scattering technique for the detection of geometrical features of unknown objects. This method depends on the selection of regularization parameters slightingly and has low calculation necessities. The aim of this work is to present a near-field FM for inverse source problems that have many applications. A modified test equation is obtained by converting the far-field term to Hankel's function. A different method has been proposed by manipulating the asymptotic approximation of Hankel's function in order to obtain near-field equations with incident angle and distance parameters. The novelty of this study is an integral equation based on the FM, which consists of multifrequency sparse near-field electric field measurements. We proved that the solution of the proposed integral equation gives information about the location of scatterers. The proposed algorithm is validated with simulation results and the capabilities of the presented method are assessed with several frequency regions and sources. Additionally, the presented method is compared with the direct sampling method in order to understand the performance of the proposed approach over a given scenario. The developed FM provides accurate results for electromagnetic source problems.

Decision and Event-Based Fixed-Time Consensus Control for Electromagnetic Source Localization.

This article deals with the problem of electromagnetic source localization (ESL). An evolutionary particle filter, which is first used to make a decision on the positions of electromagnetic sources, has two characteristics. One characteristic is that the number of particles can be significantly reduced while the other characteristic is that the particle diversity can be well improved. On the basis of the estimated positions of electromagnetic sources, the position and velocity of the virtual leader can be determined. Then, an event-based fixed-time consensus control approach is proposed such that the positions and velocities of robots reach consensus with the virtual leader over a fixed-time interval while saving resource consumption by reducing the communication frequencies and updating times of control inputs. Finally, simulation and experimental results show the effectiveness of the proposed decision and event-based fixed-time consensus control approach for ESL.

The Covariance Matrix Analysis and Statistics for Near-field Sources Localization Model

The paper presents the mathematical model of the localization of electromagnetic sources in near-field region based on the sources localization mathematical model valid for the far-field region. The aim of the article is to show similarities and differences between both models with a deeper focus on near-field region model analysis using planar equidistant sensors array. Although both concepts in a high-level mathematical description apparatus look very much the same, in details the near-field region model reconstruction process is more complex with different constrains. Detailed covariance matrix analysis and statistics of the covariance matrix represents the main part of the article. In the conclusion, paper shows some model verification results for the localization of single source, correlated sources and coherent sources.

Passive Intermodulation Source Localization Based on Emission Source Microscopy

Emission source microscopy (ESM) technique can be used for localization and characterization of electromagnetic interference sources by measuring the magnitude and phase of the electromagnetic field in the far-field zone. This article presents a method which uses ESM to locate sources of passive intermodulation (PIM). Compared to the traditional methods of PIM source localization techniques including mechanical manipulation of potential sources and near-field scanning, the proposed ESM-based approach does not require access to the devices under test allowing to detect the PIM sources at relatively large distances. Moreover, the influence of background PIM generated by surrounding environment can be reduced by ESM focusing. The high-quality maps of reconstructed PIM sources can be obtained by using ESM. The feasibility of manual sparse ESM scanning, which is more practical in realistic settings is also demonstrated.

Single-Sensor Source Localization Using Electromagnetic Time Reversal and Deep Transfer Learning: Application to Lightning

Electromagnetic Time Reversal (EMTR) has been used to locate different types of electromagnetic sources. We propose a novel technique based on the combination of EMTR and Machine Learning (ML) for source localization. We show for the first time that ML techniques can be used in conjunction with EMTR to reduce the required number of sensors to only one for the localization of electromagnetic sources in the presence of scatterers. In the EMTR part, we use 2D-FDTD method to generate 2D profiles of the vertical electric field as RGB images. Next, in the ML part, we take advantage of transfer learning techniques by using the pretrained VGG-19 Convolutional Neural Network (CNN) as the feature extractor tool. To the best of our knowledge, this is the first time that the knowledge of pretrained CNNs is applied to simulation-generated images. We demonstrate the skill of the developed methodology in localizing two kinds of electromagnetic sources, namely RF sources with a bandwidth of 0.1–10 MHz and lightning impulses. For the localization of lightning, based on the experimental recordings in the Säntis region, the new approach enables accurate 2D lightning localization using only one sensor, as opposed to current lightning location systems that need at least two sensors to operate.

The individuality index: a measure to quantify the degree of inter-individual, spatial variability in intra-cerebral brain electric and metabolic activity.

Contemporary neuroscience research primarily focuses on the identification of brain activation patterns commonly deviant across participant groups or experimental conditions. This approach inherently underestimates potentially meaningful intra- and inter-individual variability present in brain physiological measures. We propose a parameter referred to as 'individuality index (II)' that takes individual variability into account. It quantifies the degree of individual variance of brain activation patterns for different brain regions and participants. IIs can be computed based on intra-cerebral source strength values such as the ones derived from the exact low resolution electromagnetic tomography source localization software. We exemplary estimated IIs for simulated datasets. Our results illustrate how IIs are affected by different spatial activation patterns across participants and quantify their distributional properties. They suggest that the proposed indices can meaningfully quantify inter- and intra-individuality of brain activation patterns. Their application to realistic datasets will allow the identification of (1) those brain regions that show particularly heterogeneous activation patterns, the contribution of which is particularly likely to be underestimated by conventional group statistics, (2) those brain regions that can alternatively be recruited by different participants for the same tasks, and (3) their associations with potentially decisive behavioral variables such as individually applied mental strategy.

Localization and Frequency Identification of Large-Range Wide-Band Electromagnetic Interference Sources in Electromagnetic Imaging System

The identification and localization of large-range, wide-band electromagnetic interference (EMI) sources have always been both costly and time-consuming. The measurements at different times and places are often required before a typical system can locate a target. In this paper, we proposed a 2D electromagnetic imaging system to localize interference sources and identify the EMI frequency in real time. In this system, an offset paraboloid with a diameter of three meters is designed for large-range EMI imaging, while a multi-channel digital signal acquisition system is developed for wide-band EMI localization. The located interference source is segmented by the maximum entropy method based on particle swarm optimization, and the modified generalized regression neural network (MGRNN) is applied to identify the EMI frequency effectively by excluding misleading effects of outliers. The experiment which has been completed on our dataset indicates that our approach not only increases accuracy by 5% compared with the standard generalized regression neural network approaches for identification, but also exerts a large-range wide-band localization of the EMI source detection method.

Characterization of cortical source generators based on electroencephalography during tonic pain.

ObjectiveThe aim of the present study was to characterize the cortical source generators evoked by experimental tonic pain.MethodsElectroencephalography (EEG) was recorded on two separate days during rest and with immersion of the hand in ice water for 2 minutes (cold pressor test). Exact low-resolution brain electromagnetic tomography source localization was performed in 31 healthy volunteers to characterize the cortical source generators.ResultsReliability was high in all eight frequency bands during rest and cold pressor conditions (intraclass coefficients =0.47–0.83 in the cingulate and insula). Tonic pain increased cortical activities in the delta (1–4 Hz), theta (4–8 Hz), beta1 (12–18 Hz), beta2 (18–24 Hz), beta3 (24–32 Hz), and gamma (32–60 Hz) bands (all P<0.011) in widespread areas mainly in the limbic system, whereas decreased cortical activities were found in cingulate and pre- and postcentral gyri in the alpha2 (10–12 Hz) band (P=0.007). The pain intensity was correlated with cingulate activity in the beta2, beta3, and gamma bands (all P<0.04).ConclusionSource localization of EEG is a reliable method to estimate cortical source generators. Activities in different brain regions, mainly in the limbic system, showed fluctuations in various frequency bands. Cingulate changes were correlated with pain intensity.SignificanceThis method might add information to the objective assessment of the cortical pain response in future experimental pain studies.

SEEG dipole source localization based on an empirical Bayesian approach taking into account forward model uncertainties

Electromagnetic brain source localization consists in the inversion of a forward model based on a limited number of potential measurements. A wide range of methods has been developed to regularize this severely ill-posed problem and to reduce the solution space, imposing spatial smoothness, anatomical constraint or sparsity of the activated source map. This last criteria, based on physiological assumptions stating that in some particular events (e.g., epileptic spikes, evoked potential) few focal area of the brain are simultaneously actives, has gained more and more interest. Bayesian approaches have the ability to provide sparse solutions under adequate parametrization, and bring a convenient framework for the introduction of priors in the form of probabilistic density functions. However the quality of the forward model is rarely questioned while this parameter has undoubtedly a great influence on the solution. Its construction suffers from numerous approximation and uncertainties, even when using realistic numerical models. In addition, it often encodes a coarse sampling of the continuous solution space due to the computational burden its inversion implies. In this work we propose an empirical Bayesian approach to take into account the uncertainties of the forward model by allowing constrained variations around a prior physical model, in the particular context of SEEG measurements. We demonstrate on simulations that the method enhance the accuracy of the source time-course estimation as well as the sparsity of the resulting source map. Results on real signals prove the applicability of the method in real contexts.

Sparse Emission Source Microscopy for Rapid Emission Source Imaging

Emission source microscopy (ESM) technique can be utilized for the localization of electromagnetic interference sources in complex and large systems. This paper presents a sparse and nonuniform sampling technique for ESM. Compared with the traditional way of acquiring abundant and uniformly distributed scanning points on the scanning plane using a robotic scanning system, the proposed method is much more time-efficient in identifying the major radiation sources, even though the image quality is sacrificed. The feasibility of sparse sampling is mathematically proved, and it is shown that increasing number of scanning points increases the signal-to-noise ratio of reconstructed images. Besides, a nearest neighbor interpolation method is applied in the real-time processing to estimate the radiated power through the scanning plane. Thus, back-propagated images and estimated radiated power can be obtained in the real-time measurement process, which can efficiently and instantaneously provide the locations and the radiation strength of the most significant emission sources.

Current use of imaging and electromagnetic source localization procedures in epilepsy surgery centers across Europe.

In 2014 the European Union-funded E-PILEPSY project was launched to improve awareness of, and accessibility to, epilepsy surgery across Europe. We aimed to investigate the current use of neuroimaging, electromagnetic source localization, and imaging postprocessing procedures in participating centers. A survey on the clinical use of imaging, electromagnetic source localization, and postprocessing methods in epilepsy surgery candidates was distributed among the 25 centers of the consortium. A descriptive analysis was performed, and results were compared to existing guidelines and recommendations. Response rate was 96%. Standard epilepsy magnetic resonance imaging (MRI) protocols are acquired at 3 Tesla by 15 centers and at 1.5 Tesla by 9 centers. Three centers perform 3T MRI only if indicated. Twenty-six different MRI sequences were reported. Six centers follow all guideline-recommended MRI sequences with the proposed slice orientation and slice thickness or voxel size. Additional sequences are used by 22 centers. MRI postprocessing methods are used in 16 centers. Interictal positron emission tomography (PET) is available in 22 centers; all using 18F-fluorodeoxyglucose (FDG). Seventeen centers perform PET postprocessing. Single-photon emission computed tomography (SPECT) is used by 19 centers, of which 15 perform postprocessing. Four centers perform neither PET nor SPECT in children. Seven centers apply magnetoencephalography (MEG) source localization, and nine apply electroencephalography (EEG) source localization. Fourteen combinations of inverse methods and volume conduction models are used. We report a large variation in the presurgical diagnostic workup among epilepsy surgery centers across Europe. This diversity underscores the need for high-quality systematic reviews, evidence-based recommendations, and harmonization of available diagnostic presurgical methods.

Feature Extraction for BCIs Based on Electromagnetic Source Localization and Multiclass Filter Bank Common Spatial Patterns.

Brain-Computer Interfaces (BCIs) provide means for communication and control without muscular movement and, therefore, can offer significant clinical benefits. Electrical brain activity recorded by electroencephalography (EEG) can be interpreted into software commands by various classification algorithms according to the descriptive features of the signal. In this paper we propose a novel EEG BCI feature extraction method employing EEG source reconstruction and Filter Bank Common Spatial Patterns (FBCSP) based on Joint Approximate Diagonalization (JAD). The proposed method is evaluated by the commonly used reference EEG dataset yielding an average classification accuracy of 77.1 ± 10.1 %. It is shown that FBCSP feature extraction applied to reconstructed source components outperforms conventional CSP and FBCSP feature extraction methods applied to signals in the sensor domain.

Electromagnetic Time Reversal Algorithms and Source Localization in Lossy Dielectric Media

The problem of reconstructing the spatial support of an extended radiating electric current source density in a lossy dielectric medium from transient boundary measurements of the electric fields is studied. A time reversal algorithm is proposed to localize a source density from loss-less wave-held measurements. Further, in order to recover source densities in a lossy medium, we first build attenuation operators thereby relating loss-less waves with lossy ones. Then based on asymptotic expansions of attenuation operators with respect to attenuation parameter, we propose two time reversal strategies for localization. The losses in electromagnetic wave propagation are incorporated using the Debye's complex permittivity, which is well-adopted for low frequencies (radio and microwave) associated with polarization in dielectrics.

The Phase of Thalamic Alpha Activity Modulates Cortical Gamma-Band Activity: Evidence from Resting-State MEG Recordings

Recent findings have implicated thalamic alpha oscillations in the phasic modulation of cortical activity. However, the precise relationship between thalamic alpha oscillations and neocortical activity remains unclear. Here we show in a large sample of healthy human participants (n = 45) using spatial filtering techniques and measures of phase amplitude coupling that the amplitude of gamma-band activity in posterior medial parietal cortex is modulated by the phase of thalamic alpha oscillations during eyes-closed resting-state recordings. In addition, our findings show that gamma-band activity in visual cortex was not modulated by thalamic alpha oscillations but coupled to the phase of strong cortical alpha activity. To overcome the limitations of electromagnetic source localization we estimated conduction delays using transfer entropy and found nonspurious information transfer from thalamus to cortex. The present findings provide novel evidence for magneto-encephalography-measured phase coupling between cortical gamma-band activity and thalamic alpha oscillations, which highlight the role of phasic inhibition in the coordination of cortical activity.

Near-Field Localization of Partially Polarized Sources with a Cross-Dipole Array

The problem of near-field partially polarized electromagnetic source localization using an array of cross-dipoles, each of which consists of one x-axis dipole and one y-axis dipole, is addressed. The maximum likelihood (ML) algorithm for estimating the angle and range parameters is developed. This algorithm requires no search over the polarization parameters. We also show that the ML algorithm can be implemented by processing the x-axis dipole data and the y-axis dipole data separately. In addition, a subspace-based algorithm, which is based on the ideas of MUSIC and generalized ESPRIT, is presented. This algorithm decouples the two-dimensional (2D) search into two successive one-dimensional (1D) searches, where the angle and range parameters are estimated in succession. The deterministic Cramer-Rao bound (CRB), for the problem under consideration, is also derived. The performance of the subspace-based algorithm is evaluated and compared with that of the ML algorithm and the CRB.

Anisotropic partial volume CSF modeling for EEG source localization

Electromagnetic source localization (ESL) provides non-invasive evaluation of brain electrical activity for neurology research and clinical evaluation of neurological disorders such as epilepsy. Accurate ESL results are dependent upon the use of patient specific models of bioelectric conductivity. While the effects of anisotropic conductivities in the skull and white matter have been previously studied, little attention has been paid to the accurate modeling of the highly conductive cerebrospinal fluid (CSF) region. This study examines the effect that partial volume errors in CSF segmentations have upon the ESL bioelectric model. These errors arise when segmenting sulcal channels whose widths are similar to the resolution of the magnetic resonance (MR) images used for segmentation, as some voxels containing both CSF and gray matter cannot be definitively assigned a single label. These problems, particularly prevalent in pediatric populations, make voxelwise segmentation of CSF compartments a difficult problem. Given the high conductivity of CSF, errors in modeling this region may result in large errors in the bioelectric model. We introduce here a new approach for using estimates of partial volume fractions in the construction of patient specific bioelectric models. In regions where partial volume errors are expected, we use a layered gray matter-CSF model to construct equivalent anisotropic conductivity tensors. This allows us to account for the inhomogeneity of the tissue within each voxel. Using this approach, we are able to reduce the error in the resulting bioelectric models, as evaluated against a known high resolution model. Additionally, this model permits us to evaluate the effects of sulci modeling errors and quantify the mean error as a function of the change in sulci width. Our results suggest that both under and over-estimation of the CSF region leads to significant errors in the bioelectric model. While a model with fixed partial volume fraction is able to reduce this error, we see the largest improvement when using voxel specific partial volume estimates. Our cross-model analyses suggest that an approximately linear relationship exists between sulci error and the error in the resulting bioelectric model. Given the difficulty of accurately segmenting narrow sulcal channels, this suggests that our approach may be capable of improving the accuracy of patient specific bioelectric models by several percent, while introducing only minimal additional computational requirements.

Electromagnetic source imaging: Backus–Gilbert resolution spread function‐constrained and functional MRI‐guided spatial filtering

Electromagnetic source imaging techniques are usually limited by their low spatial resolution, even though these techniques have high temporal resolution. Our heuristic analysis shows that the spatial ambiguity of electromagnetic source localization arises from interference from other sources. In this paper, we suggest a new inverse solution based on the principle of spatial filtering to effectively suppress the interference from other sources, especially from the far sources. By means of this approach, functional MRI information can also be effectively integrated into the inverse solution to further improve spatial accuracy of source localization. Most importantly, the results of source localization by this approach are not significantly biased by incompatible fMRI information. Our simulations and experimental results using electroencephalography based on a realistic head model show that the Backus-Gilbert resolution spread function-constrained and functional MRI-guided spatial filtering suggested in this paper provide high spatial accuracy and resolution of source localization, even in the presence of multiple simultaneously active sources.