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We study the effect of the head shape variations on the EEG/magnetoencephalography (MEG) forward and inverse problems. We build a random head model such that each sample represents the head shape of a different individual and solve the forward problem assuming this random head model, using a polynomial chaos expansion. The random solution of the forward problem is then used to quantify the effect of the geometry when the inverse problem is solved with a standard head model. The results derived with this approach are valid for a continuous family of head models, rather than just for a set of cases. The random model consists of three random surfaces that define layers of different electric conductivity, and we built an example based on a set of 30 deterministic models from adults. Our results show that for a dipolar source model, the effect of the head shape variations on the EEG/MEG inverse problem due to the random head model is slightly larger than the effect of the electronic noise present in the sensors. The variations in the EEG inverse problem solutions are due to the variations in the shape of the volume conductor, while the variations in the MEG inverse problem solutions, larger than the EEG ones, are caused mainly by the variations of the absolute position of the sources in a coordinate system based on anatomical landmarks, in which the magnetometers have a fixed position. Index Terms--EEG/magnetoencephalography (MEG) average head model, polynomial chaos expansion (PCE), sparse grids, stochastic modeling.

Electroencephalography (EEG) is an important tool for studying the brain functions and is becoming popular in clinical practice. In this paper, we develop four parametric EEG models to estimate current sources that are spatially distributed on a surface. Our models approximate the source shape and extent explicitly and can be applied to localize extended sources which are often encountered, e.g., in epilepsy diagnosis. We assume a realistic head model and solve the EEG forward problem using the boundary element method. We present the source models with increasing degrees of freedom, provide the forward solutions, and derive the maximum-likelihood estimates as well as Cramer-Rao bounds of the unknown source parameters. In order to evaluate the applicability of the proposed models, we first compare their estimation performances with the dipole model's using several known source distributions. We then discuss the conditions under which we can distinguish between the proposed extended sources and the focal dipole using the generalized likelihood ratio test. We also apply our models to the electric measurements obtained from a phantom body in which an extended electric source is imbedded. We observe that the proposed model can capture the source extent information satisfactorily and the localization accuracy is better than the dipole model. Index Terms--Cramer-Rao bounds, EEG, extended source modeling, likelihood ratio test.

We develop three parametric models for electroencephalography (EEG) to estimate current sources that are spatially distributed on a line. We assume a realistic head model and solve the EEG forward problem using the boundary element method (BEM). We present the models with increasing degrees of freedom, provide the forward solutions, and derive the maximum-likelihood estimates as well as Cramer-Rao bounds of the unknown source parameters. A series of experiments are conducted to evaluate the applicability of the proposed models. We use numerical examples to demonstrate the usefulness of our line-source models in estimating extended sources. We also apply our models to the real EEG data of N20 response that is known to have an extended source. We observe that the line-source models explain the N20 measurements better than the dipole model. Index Terms--Cramer-Rao bounds, EEG, extended source modeling.

We propose a number of electric source models that are spatially distributed on an unknown surface for biomagnetism. These can be useful to model, e.g., patches of electrical activity on the cortex. We use a realistic head (or another organ) model and discuss the special case of a spherical head model with radial sensors resulting in more efficient computations of the estimates for magnetoencephalography. We derive forward solutions, maximum likelihood (ML) estimates, and Cramer-Rao bound (CRB) expressions for the unknown source parameters. A model selection method is applied to decide on the most appropriate model. We also present numerical examples to compare the performances and computational costs of the different models and illustrate when it is possible to distinguish between surface and focal sources or line sources. Finally, we apply our methods to real biomagnetic data of phantom human torso and demonstrate the applicability of them. Index Terms--Biomagnetic measurements, magnetoencephalograph, source localization, spatially extended sources, surface-source models.

We study the effect of geometric head model perturbations on the electroencephalography (EEG) forward and inverse problems. Small magnitude perturbations of the shape of the head could represent uncertainties in the head model due to errors on images or techniques used to construct the model. They could also represent small scale details of the shape of the surfaces not described in a deterministic model, such as the sulci and fissures of the cortical layer. We perform a first-order perturbation analysis, using a meshless method for computing the sensitivity of the solution of the forward problem to the geometry of the head model. The effect on the forward problem solution is treated as noise in the EEG measurements and the Cramer-Rao bound is computed to quantify the effect on the inverse problem performance. Our results show that, for a dipolar source, the effect of the perturbations on the inverse problem performance is under the level of the uncertainties due to the spontaneous brain activity. Thus, the results suggest that an extremely detailed model of the head may be unnecessary when solving the EEG inverse problem. Index Terms--Cramer-Rao bound, EEG, inverse problem, perturbations analysis, stochastic modeling.

We present a formulation for the magnetoencephalography (MEG) forward problem with a layered head model. Traditionally the magnetic field is computed based on the electric potential on the interfaces between the layers. We propose to express the effect of the volumetric currents in terms of an equivalent surface current density on each interface, and obtain the magnetic field based on them. The boundary elements method is used to compute the equivalent current density and the magnetic field for a realistic head geometry. We present numerical results showing that the MEG forward problem is solved correctly with this formulation, and compare it with the performance of the traditional formulation. We conclude that the traditional formulation generally performs better, but still the new formulation is useful in certain situations. Index Terms--BEM, current density, forward problem, MEG.

We propose a number of source models that are spatially distributed on a line for magnetoencephalography (MEG) using both a spherical head with radial sensors for more efficient computation and a realistic head model for more accurate results. We develop these models with increasing degrees of freedom, derive forward solutions, maximum-likelihood (ML) estimates, and Cramer-Rao bound (CRB) expressions for the unknown source parameters. A model selection method is applied to select the most appropriate model. We also present numerical examples to compare the performances and computational costs of the different models, to determine the regions where better estimates are possible and when it is possible to distinguish between line and focal sources. We demonstrate the usefulness of the proposed line-source models over the previously available focal source model in certain distributed source cases. Finally, we apply our methods to real MEG data, the N20 response after electric stimulation of the median nerve known to be an extended source. Index Terms--Line-source models, magnetoencephalography, N20 responses, source localization.

Performances of electroencephalography (EEG) and magnetoencephalography (MEG) source estimation methods depend on the validity of the assumed model. In many cases, the model structure is related to physical information. We discuss a number of statistical selection methods to distinguish between two possible models using least-squares estimation and assuming a spherical head model. The first model has a single moving source whereas the second has two stationary sources; these may result in similar EEG/MEG measurements. The need to decide between such models occurs for example in Jacksonian seizures (e.g., epilepsy) or in intralobular activities, where a model with either two stationary dipole sources or a single moving dipole source may be possible. We also show that all of the selection methods discussed choose the correct model with probability one when the number of trials goes to infinity. Finally we present numerical examples and compare the performances of the methods by varying parameters such as the signal-to-noise ratio, source depth, and separation of sources, and also apply the methods to real MEG data for epilepsy. Index Terms--Electroencephalography, epilepsy, magnetoencephalography, model selection.

We present a numerical method to solve the quasistatic Maxwell equations and compute the electroencephalography (EEG) forward problem solution. More generally, we develop a computationally efficient method to obtain the electric potential distribution generated by a source of electric activity inside a three-dimensional body of arbitrary shape and layers of different electric conductivities. The method needs only a set of nodes on the surface and inside the head, but not a mesh connecting the nodes. This represents an advantage over traditional methods like boundary elements or finite elements since the generation of the mesh is typically computationally intensive. The performance of the proposed method is compared with the boundary element method (BEM) by numerically solving some EEG forward problems examples. For a large number of nodes and the same precision, our method has lower computational load than BEM due to a faster convergence rate and to the sparsity of the linear system to be solved. Index Terms--EEG, EEG forward problem, layered media, meshless method, moving least squares approximation, numerical solution, volume conductor.

Techniques based on electroencephalography (EEG) measure the electric potentials on the scalp and process them to infer the location, distribution, and intensity of underlying neural activity. Accuracy in estimating these parameters is highly sensitive to uncertainty in the conductivities of the head tissues. Furthermore, dissimilarities among individuals are ignored when standarized values are used. In this paper, we apply the maximum-likelihood and maximum a posteriori (MAP) techniques to simultaneously estimate the layer conductivity ratios and source signal using EEG data. We use the classical 4-sphere model to approximate the head geometry, and assume a known dipole source position. The accuracy of our estimates is evaluated by comparing their standard deviations with the Cramer-Rao bound (CRB). The applicability of these techniques is illustrated with numerical examples on simulated EEG data. Our results show that the estimates have low bias and attain the CRB for sufficiently large number of experiments. We also present numerical examples evaluating the sensitivity to imprecise assumptions on the source position and skull thickness. Finally, we propose extensions to the case of unknown source position and present examples for real data. Index Terms--Brain conductivities, Cramer-Rao bound, electroencephalography, maximum-likelihood estimation, parameter estimation, sensor array processing.

A clamped-mode resonant converter (CMRC) is proposed to be used as a transmitter which broadcasts correction signals in a differential Global Positioning System (DGPS). The digital information of the DGPS modulates the carrier with different modulation methods minimum shift keying (MSK) (recommended for the marine radiobeacon band), stepped binary phase shift keying (S-BPSK) and BPSK. The first two methods allow keeping the converter's operation in soft switching mode. Extensive trials under impedance mismatch and modulation conditions confirm that the soft switching mode is preserved.

An innovative frequency-domain approach to multi-input, multi-output (MIMO) linear filter design for sample-data systems is described and discussed.

A mean-square error lower bound for the discrete-time nonlinear filtering problem was obtained based on the Van Trees version of the Cramer-Rao inequality. The case of singular conditional distribution of the one-step-ahead state vector given the present state was examined. The bound was analyzed for three examples: the recursive estimation of slowly changing parameters of an autoregressive process, tracking a slowly varying frequency of a single cisoid in noise, and tracking parameters of a sinusoidal frequency with sinusoidal phase modulation.

In this work, the authors analyse the estimation of the generalised autoregressive conditional heteroscedastic (GARCH) process conditional variance based on three non‐linear filtering approaches: extended Kalman filter (EKF), unscented Kalman filter and cubature Kalman filter. The authors present a state model for a GARCH process and derive an EKF including second‐order non‐linear terms for simultaneous estimation of state and parameters. Using synthetic data, the authors evaluate the consistency and the correlation of the innovations for the three filters, by means of numerical simulations. The authors also study the performance of smoothed versions of the non‐linear Kalman filters using real clutter data in comparison with a conventional quasi‐maximum likelihood estimation method for the GARCH process coefficients. The authors show that with all methods the process coefficients estimates are of the same order and the resulting conditional variances are commensurable. However, the non‐linear Kalman filters greatly reduce the computational load. These kind of filters could be used for the radar detector based on a GARCH clutter model that uses an adaptive threshold that demands the conditional variance at each decision instant. [ABSTRACT FROM AUTHOR]

This paper presents a seven-port modulator capable of switching the polarization state of the transmitting signal. Similar to the six-port modulator, the proposed device modulates the carrier signal through the reflection coefficients generated by four variable loads. The additional seventh port allows feeding two antennas or a dual-port antenna. The loads control both the complex envelope and the polarization of the transmitted carrier signal. The mathematical model of the device, developed in this paper, is applied to analyze its performance and different modes of operation. For validation, a prototype is manufactured for a center frequency of 1575.42 MHz. It is used to generate M-quadratic-amplitude modulation at different polarizations. The signals recorded at the output of the prototype show good agreement with the values predicted by the model. [ABSTRACT FROM AUTHOR]

In this paper, a design procedure for clamped-mode resonant converters working with variable load is proposed and analyzed. The operation of these converters with general parallel or series loads is reviewed first. The operation of the transistors as zero-voltage switches is identified and characterized as mode A. Mode A is preferred to simplify the implementation of the power switches and to increment the converter efficiency. As a case study, the design of an RF power amplifier is presented. The amplifier is connected to a variable load with reactive characteristics, through a low-pass filter of three elements. The validity of the proposed design approach is verified with an experimental setup. Index Terms--Power amplifier, resonant power conversion.

This letter proposes a polarimetric synthetic aperture radar image classification method based on the expectation–maximization algorithm. It is an unsupervised algorithm that determines the number of classes in the scene following a top–down strategy using a covariance-based hypothesis test. A \mathcal Gp^{0} mixture model is used to describe multilook complex polarimetric data, and the proposed algorithm is tested in simulated and real data sets obtaining good results. The classification performance is evaluated by means of the overall accuracy and the kappa indices obtained from the Monte Carlo analysis. Finally, the results are compared with those obtained by other classic and recently developed classification algorithms. [ABSTRACT FROM PUBLISHER]

The localization of intracranial electrodes is a fundamental step in the analysis of invasive electroencephalography (EEG) recordings in research and clinical practice. The conclusions reached from the analysis of these recordings rely on the accuracy of electrode localization in relationship to brain anatomy. However, currently available techniques for localizing electrodes from magnetic resonance (MR) and/or computerized tomography (CT) images are time consuming and/or limited to particular electrode types or shapes. Here we present iElectrodes, an open-source toolbox that provides robust and accurate semi-automatic localization of both subdural grids and depth electrodes. Using pre- and post-implantation images, the method takes 2-3 min to localize the coordinates in each electrode array and automatically number the electrodes. The proposed pre-processing pipeline allows one to work in a normalized space and to automatically obtain anatomical labels of the localized electrodes without neuroimaging experts. We validated the method with data from 22 patients implanted with a total of 1,242 electrodes. We show that localization distances were within 0.56 mm of those achieved by experienced manual evaluators. iElectrodes provided additional advantages in terms of robustness (even with severe perioperative cerebral distortions), speed (less than half the operator time compared to expert manual localization), simplicity, utility across multiple electrode types (surface and depth electrodes) and all brain regions. [ABSTRACT FROM AUTHOR]

A novel Bayesian technique for the joint estimation of real and integer parameters in a linear measurement model is presented. The integer parameters take values on a finite set, and the real ones are assumed to be a Gaussian random vector. The posterior distribution of these parameters is sequentially determined as new measurements are incorporated. This is a mixed distribution with a Gaussian continuous part and a discrete one. Estimators for the integer and real parameters are derived from this posterior distribution. A Maximum A Posteriori (MAP) estimator modified with the addition of a confidence threshold is used for the integer part and a Minimum Mean Squared Error (MMSE) is used for the real parameters. Two different cases are addressed: i) both real and integer parameters are time invariant and ii) the integer parameters are time invariant but the real ones are time varying. Our technique is applied to the GNSS carrier phase ambiguity resolution problem, that is key for high precision positioning applications. The good performance of the proposed technique is illustrated through simulations in different scenarios where different kind of measurements as well as different satellite visibility conditions are considered. Comparisons with state-of-the-art ambiguity solving algorithms confirm performance improvement. The new method is shown to be useful not only in the estimation stage but also for validating the estimates ensuring a predefined success rate through proper threshold selection. [ABSTRACT FROM AUTHOR]

We consider the problem of estimating a signal which has been corrupted with structured noise. When the signal of interest accepts a sparse representation, only a small number of measurements are required to retain all the information. The measurements are mapped to a lower dimensional space through a projection matrix. We propose a method to optimize the design of this matrix where the objective is not only to reduce the amount of data to be processed but also to reject the undesired signal components. As a result, we reduce the computation time and the error on the estimation of the unknown parameters of the sparse model, with respect to the uncompressed data. The proposed method has tunable parameters that can affect its performance. Optimal tuning would require a comprehensive study of parameter variations and options. To avoid this learning burden, we also introduce a variant of the algorithm that is free from tuning, without significant loss of performance. Using synthetic data, we analyze the performance of the proposed algorithms and their robustness against errors in the model parameters. Additionally, we illustrate the performance of the method through a radar application using real clutter data with a still target and with a synthetic moving target. [ABSTRACT FROM PUBLISHER]

Research describing a static current dipole source is presented. In particular data from magneto-encephalography and electro-encephalography is used to study a realistic head model for cerebral activity.

In this letter, we present a new variable impedance termination consisting of two polarized diodes. To generate a complex-valued impedance, two controlled current sources polarize the diodes, which are interconnected with a Wilkinson power divider through transmission lines of different electric lengths. Because of the reduced number of diodes, this structure presents low power consumption and simple control. We validated the proposed design by implementing a prototype at the operating frequency of 1575.42 MHz. Mapping the measured results in the Smith chart, the impedance can produce reflection coefficients with full-phase coverage within the circle of magnitude 0.35 over a frequency range of 1.5–1.6 GHz. [ABSTRACT FROM PUBLISHER]

We propose a model for radar clutter that combines an autoregressive (AR) process with a two-dimensional generalized autoregressive conditional heteroscedastic (GARCH-2D) process. Based on this model, we derive an adaptive detection test, called AR-GARCH-2D detector, for a target with known Doppler frequency and unknown complex amplitude. Using real radar data, we evaluate its performance for different model orders, and we use a model selection criteria to choose the best fit to the data. The resulting detector is not the constant false alarm rate (CFAR) with respect to the process coefficients, but we show that in practical situations it is very robust. Finally, we compare the AR-GARCH-2D detector performance with the performance of the generalized likelihood ratio test (GLRT), the adaptive linear-quadratic (ALQ), and the autoregressive generalized likelihood ratio (ARGLR) detectors by processing the real radar data. We show that the proposed detector offers a higher probability of detection than the other tests, for a given probability of false alarm. [ABSTRACT FROM PUBLISHER]

In this paper we address the problem of sparse signal reconstruction. We propose a new algorithm that determines the signal support applying statistical thresholding to accept the active components of the model. This adaptive decision test is integrated into the sparse Bayesian learning method, improving its accuracy and reducing convergence time. Moreover, we extend the formulation to accept multiple measurement sequences of signal contaminated by structured noise in addition to white noise. We also develop analytical expressions to evaluate the algorithm estimation error as a function of the problem sparsity and indeterminacy. By simulations, we compare the performance of the proposed algorithm with respect to other existing methods. We show a practical application processing real data of a polarimetric radar to separate the target signal from the clutter. [ABSTRACT FROM AUTHOR]

In this work we present the design and implementation of a GNSS receiver that can work with the civil signals of the L1 and L2 bands of GPS and GLONASS, and the E1 Open Service signal of Galileo. The developed prototype has two RF front-ends, one for the L1 band and another for the L2 band. The signals from each band are amplified and then down-converted to an intermediate frequency. The two local oscillator tones used for the mixing, and the clock signals for the next digitalization and processing stages are generated by a frequency synthesizer board, from a common reference. The digitalization and posterior processing of the signals can be carried out using generic devices, like an acquisition board and an FPGA, according to the Software Defined Radio (SDR) concept. In this way a programmable receiver is obtained. These kinds of receivers are versatile since they can be used for testing acquisition, tracking, and navigation algorithms for research and develop purposes. Commercial receivers do not have that capability, because their digital processing stages cannot be modified by the user. Moreover, a multi-band and multi-constellation receiver allows to greatly increase the performance in relation to mass market GNSS receivers which relay on only one navigation system and one carrier frequency. Measurements realized to the implemented prototype that validate the proposed design are presented. [ABSTRACT FROM PUBLISHER]

Carrier phase estimation in real-time Global Navigation Satellite System (GNSS) receivers is usually performed by tracking loops due to their very low computational complexity. We show that a careful design of these loops allows them to operate properly in high-dynamics environments, that is, accelerations up to 40 g or more. Their phase and frequency discriminators and loop filter are derived considering the digital nature of the loop inputs. Based on these ideas, we propose a new loop structure named Unambiguous Frequency-Aided Phase-Locked Loop (UFA-PLL). In terms of tracking capacity and noise resistance UFA-PLL has the same advantages of frequently used coupled-loop schemes, but it is simpler to design and to implement. Moreover, it can keep phase lock in situations where other loops cannot. The loop design is completed selecting the correlation time and loop bandwidth that minimize the pull-out probability, without relying on typical rules of thumb. Optimal and efficient ways to smooth the phase estimates are also presented. Hence, high-quality phase measurements&$8212;usually exploited in offline and quasistatic applications—become practical for real-time and high-dynamics receivers. Experiments with fixed-point implementations of the proposed loops and actual radio signals are also shown. [ABSTRACT FROM AUTHOR]

We propose to design a small-size antenna array having high direction-of-arrival (DOA) estimation performance, inspired by the Ormia ochracea's coupled ears. The female Ormia is able to locate male crickets' call accurately, for reproduction purposes, despite the small distance between its ears compared with the incoming wavelength. This phenomenon has been explained by the mechanical coupling between the Ormia's ears, modeled by a pair of differential equations. In this paper, we first solve the differential equations governing the Ormia ochracea's ear response, and convert the response to the prespecified radio frequencies. Using the converted response, we then implement the biologically inspired coupling as a multi-input multi-output filter on a uniform linear antenna array output. We derive the maximum likelihood estimates of source DOAs, and compute the corresponding Cramér–Rao bound on the DOA estimation error as a performance measure. We also consider a circular array configuration and compute the mean-square angular error bound on the three-dimensional localization accuracy. Moreover, we propose an algorithm to optimally choose the biologically inspired coupling for maximum localization performance. We use Monte Carlo numerical examples to demonstrate the advantages of the coupling effect. [ABSTRACT FROM PUBLISHER]

We compute lower bounds on the mean-square error of multiple change-point estimation. In this context, the parameters are discrete and the Cramér-Rao bound is not applicable. Consequently, we focus on computing the Barankin bound (BB), the greatest lower bound on the covariance of any unbiased estimator, which is still valid for discrete parameters. In particular, we compute the multi-parameter version of the Hammersley– Chapman–Robbins, which is a Barankin-type lower bound. We first give the structure of the so-called Barankin information matrix (BIM) and derive a simplified form of the BB. We show that the particular case of two change points is fundamental to finding the inverse of this matrix. Several closed-form expressions of the elements of BIM are given for changes in the parameters of Gaussian and Poisson distributions. The computation of the BB requires finding the supremum of a finite set of positive definite matrices with respect to the Loewner partial ordering. Although each matrix in this set of candidates is a lower bound on the covariance matrix of the estimator, the existence of a unique supremum w.r.t. to this set, i.e., the tightest bound, might not be guaranteed. To overcome this problem, we compute a suitable minimal-upper bound to this set given by the matrix associated with the Loewner-John Ellipsoid of the set of hyper-ellipsoids associated to the set of candidate lower-bound matrices. Finally, we present some numerical examples to compare the proposed approximated BB with the performance achieved by the maximum likelihood estimator. [ABSTRACT FROM PUBLISHER]

Electroencephalography (EEG) is an important tool for studying the brain functions and is becoming popular in clinical practice. In this paper, we develop four parametric EEG models to estimate current sources that are spatially distributed on a surface. Our models approximate the source shape and extent explicitly and can be applied to localize extended sources which are often encountered, e.g., in epilepsy diagnosis. We assume a realistic head model and solve the EEG forward problem using the boundary element method. We present the source models with increasing degrees of freedom, provide the forward solutions, and derive the maximum-likelihood estimates as well as Cramér-Rao bounds of the unknown source parameters. In order to evaluate the applicability of the proposed models, we first compare their estimation performances with the dipole model's using several known source distributions. We then discuss the conditions under which we can distinguish between the proposed extended sources and the focal dipole using the generalized likelihood ratio test. We also apply our models to the electric measurements obtained from a phantom body in which an extended electric source is imbedded. We observe that the proposed model can capture the source extent information satisfactorily and the localization accuracy is better than the dipole model. [ABSTRACT FROM AUTHOR]

We develop three parametric models for electroencephalography (EEG) to estimate current sources that are spatially distributed on a line. We assume a realistic head model and solve the EEG forward problem using the boundary element method (BEM). We present the models with increasing degrees of freedom, provide the forward solutions, and derive the maximum-likelihood estimates as well as Cramér-Rao bounds of the unknown source parameters. A series of experiments are conducted to evaluate the applicability of the proposed models. We use numerical examples to demonstrate the usefulness of our line-source models in estimating extended sources. We also apply our models to the real EEG data of N20 response that is known to have an extended source. We observe that the line-source models explain the N20 measurements better than the dipole model. [ABSTRACT FROM AUTHOR]

We propose a number of source models that are spatially distributed on a line for magnetoencephalography (MEG) using both a spherical head with radial sensors for more efficient computation and a realistic head model for more accurate results. We develop these models. with increasing degrees of freedom, derive forward solutions, maximum-likelihood (ML) estimates, and Cramér-Rao bound (CRB) expressions for the unknown source parameters. A model selection method is applied to select the most appropriate model. We also present numerical examples to compare the performances and computational costs of the different models, to determine the regions where better estimates are possible and when it is possible to distinguish between line and focal sources. We demonstrate the usefulness of the proposed line-source models over the previously available focal source model in certain distributed source cases. Finally, we apply our methods to real MEG data, the N20 response after electric stimulation of the median nerve known to be an extended source. [ABSTRACT FROM AUTHOR]

We present a numerical method to solve the quasistatic Maxwell equations and compute the electroencephalography (EEG) forward problem solution. More generally, we develop a computationatly efficient method to obtain the electric potential distribution generated by a source of electric activity inside a three- dimensional body of arbitrary shape and layers of different electric. conductivities. The method needs only a set of nodes on the surface and inside the head, but not a mesh connecting the nodes. This represents an advantage over traditional methods like boundary elements or finite elements since the generation of the mesh is typically computationally intensive. The performance of the proposed method is compared with the boundary element method (BEM) by numerically solving some EEG forward problems examples. For a large number of nodes and the same precision, out method has bier computational load than BEM due to a faster convergence rate and to the sparsity of the linear system to be solved. [ABSTRACT FROM AUTHOR]