Differential characterization of neural sources with the bimodal truncated SVD pseudo-inverse for EEG and MEG measurements

Emission Ghost Imaging: reconstruction with data augmentation

Ghost Imaging enables 2D reconstruction of an object even though particles transmitted or emitted by the object of interest are detected with a single pixel detector without spatial resolution. This is possible because for the particular implementation of ghost imaging presented here, the incident beam is spatially modulated with a non-configurable attenuating mask whose orientation is varied (e.g. via transverse displacement or rotation) in the course of the ghost imaging experiment. Each orientation yields a distinct spatial pattern in the attenuated beam. In many cases, ghost imaging reconstructions can be dramatically improved by factoring the measurement matrix which consists of measured attenuated incident radiation for each of many orientations of the mask at each pixel to be reconstructed as the product of an orthonormal matrix Q and an upper triangular matrix R provided that the number of orientations of the mask (N ) is greater than or equal to the number of pixels (P ) reconstructed. For the N < P case, we present a data augmentation method that enables QR factorization of the measurement matrix. To suppress noise in the reconstruction, we determine the Moore-Penrose pseudoinverse of the measurement matrix with a truncated singular value decomposition approach. Since the resulting reconstruction is still noisy, we denoise it with the Adaptive Weights Smoothing method. In simulation experiments, our method outperforms a modification of an existing alternative orthogonalization method where rows of the measurement matrix are orthogonalized by the Gram-Schmidt method. We apply our ghost imaging methods to experimental X-ray fluorescence data acquired at Brookhaven National Laboratory.

EEG-based source localization with enhanced virtual aperture using second order statistics

For the past few decades source localization, based on EEG modality, has been a very active area of research. EEG signal provides temporal resolution in millisecond range that can capture rapidly changing patterns of brain activity but it has a low spatial resolution as compared to techniques like fMRI, PET, CT scan, etc. So, one of the motives of this research is to improve the spatial resolution of the EEG signal. Many successful attempts have been made to localise the active neural sources using EEG signals with the introduction of techniques like MNE, LORETA, sLORETA, FOCUSS, etc. But these techniques require a large number of electrodes for correct localization of a few sources. This paper aims at providing a new method for the localization of EEG sources with a fewer electrode. This is achieved by exploiting the second-order statistics to enhance the aperture and solve the EEG localization problem. The comparison of the proposed method with the state-of-the-art methods is done by observing the localization error with variation in SNR, number of snapshots (time samples), number of active sources, and number of electrodes. The results show that the proposed method can detect a greater number of sources with fewer electrodes and with higher accuracy as compared to methods available in the literature. Real -time EEG signal during an arithmetic task is considered and the proposed algorithm clearly shows a sparse activity in the frontal region.

Neural silences can be localized rapidly using noninvasive scalp EEG

A rapid and cost-effective noninvasive tool to detect and characterize neural silences can be of important benefit in diagnosing and treating many disorders. We propose an algorithm, SilenceMap, for uncovering the absence of electrophysiological signals, or neural silences, using noninvasive scalp electroencephalography (EEG) signals. By accounting for the contributions of different sources to the power of the recorded signals, and using a hemispheric baseline approach and a convex spectral clustering framework, SilenceMap permits rapid detection and localization of regions of silence in the brain using a relatively small amount of EEG data. SilenceMap substantially outperformed existing source localization algorithms in estimating the center-of-mass of the silence for three pediatric cortical resection patients, using fewer than 3 minutes of EEG recordings (13, 2, and 11mm vs. 25, 62, and 53 mm), as well for 100 different simulated regions of silence based on a real human head model (12 ± 0.7 mm vs. 54 ± 2.2 mm). SilenceMap paves the way towards accessible early diagnosis and continuous monitoring of altered physiological properties of human cortical function.

The inverse problem in electroencephalography using the bidomain model of electrical activity

BACKGROUND

Acquiring information about the distribution of electrical sources in the brain from electroencephalography (EEG) data remains a significant challenge. An accurate solution would provide an understanding of the inner mechanisms of the electrical activity in the brain and information about damaged tissue.

NEW METHOD

In this paper, we present a methodology for reconstructing brain electrical activity from EEG data by using the bidomain formulation. The bidomain model considers continuous active neural tissue coupled with a nonlinear cell model. Using this technique, we aim to find the brain sources that give rise to the scalp potential recorded by EEG measurements taking into account a non-static reconstruction.

COMPARISON WITH EXISTING METHODS

We simulate electrical sources in the brain volume and compare the reconstruction to the minimum norm estimates (MNEs) and low resolution electrical tomography (LORETA) results. Then, with the EEG dataset from the EEG Motor Movement/Imagery Database of the Physiobank, we identify the reaction to visual stimuli by calculating the time between stimulus presentation and the spike in electrical activity. Finally, we compare the activation in the brain with the registered activation using the LinkRbrain platform.

RESULTS/CONCLUSION

Our methodology shows an improved reconstruction of the electrical activity and source localization in comparison with MNE and LORETA. For the Motor Movement/Imagery Database, the reconstruction is consistent with the expected position and time delay generated by the stimuli. Thus, this methodology is a suitable option for continuously reconstructing brain potentials.

Independent Component Analysis of Gait-Related Movement Artifact Recorded using EEG Electrodes during Treadmill Walking

There has been a recent surge in the use of electroencephalography (EEG) as a tool for mobile brain imaging due to its portability and fine time resolution. When EEG is combined with independent component analysis (ICA) and source localization techniques, it can model electrocortical activity as arising from temporally independent signals located in spatially distinct cortical areas. However, for mobile tasks, it is not clear how movement artifacts influence ICA and source localization. We devised a novel method to collect pure movement artifact data (devoid of any electrophysiological signals) with a 256-channel EEG system. We first blocked true electrocortical activity using a silicone swim cap. Over the silicone layer, we placed a simulated scalp with electrical properties similar to real human scalp. We collected EEG movement artifact signals from ten healthy, young subjects wearing this setup as they walked on a treadmill at speeds from 0.4-1.6 m/s. We performed ICA and dipole fitting on the EEG movement artifact data to quantify how accurately these methods would identify the artifact signals as non-neural. ICA and dipole fitting accurately localized 99% of the independent components in non-neural locations or lacked dipolar characteristics. The remaining 1% of sources had locations within the brain volume and low residual variances, but had topographical maps, power spectra, time courses, and event related spectral perturbations typical of non-neural sources. Caution should be exercised when interpreting ICA for data that includes semi-periodic artifacts including artifact arising from human walking. Alternative methods are needed for the identification and separation of movement artifact in mobile EEG signals, especially methods that can be performed in real time. Separating true brain signals from motion artifact could clear the way for EEG brain computer interfaces for assistance during mobile activities, such as walking.

Algorithmic procedures for Bayesian MEG/EEG source reconstruction in SPM

The MEG/EEG inverse problem is ill-posed, giving different source reconstructions depending on the initial assumption sets. Parametric Empirical Bayes allows one to implement most popular MEG/EEG inversion schemes (Minimum Norm, LORETA, etc.) within the same generic Bayesian framework. It also provides a cost-function in terms of the variational Free energy-an approximation to the marginal likelihood or evidence of the solution. In this manuscript, we revisit the algorithm for MEG/EEG source reconstruction with a view to providing a didactic and practical guide. The aim is to promote and help standardise the development and consolidation of other schemes within the same framework. We describe the implementation in the Statistical Parametric Mapping (SPM) software package, carefully explaining each of its stages with the help of a simple simulated data example. We focus on the Multiple Sparse Priors (MSP) model, which we compare with the well-known Minimum Norm and LORETA models, using the negative variational Free energy for model comparison. The manuscript is accompanied by Matlab scripts to allow the reader to test and explore the underlying algorithm.

Localization of synchronous cortical neural sources

Neural synchronization is a key mechanism to a wide variety of brain functions, such as cognition, perception, or memory. High temporal resolution achieved by EEG recordings allows the study of the dynamical properties of synchronous patterns of activity at a very fine temporal scale but with very low spatial resolution. Spatial resolution can be improved by retrieving the neural sources of EEG signal, thus solving the so-called inverse problem. Although many methods have been proposed to solve the inverse problem and localize brain activity, few of them target the synchronous brain regions. In this paper, we propose a novel algorithm aimed at localizing specifically synchronous brain regions and reconstructing the time course of their activity. Using multivariate wavelet ridge analysis, we extract signals capturing the synchronous events buried in the EEG and then solve the inverse problem on these signals. Using simulated data, we compare results of source reconstruction accuracy achieved by our method to a standard source reconstruction approach. We show that the proposed method performs better across a wide range of noise levels and source configurations. In addition, we applied our method on real dataset and identified successfully cortical areas involved in the functional network underlying visual face perception. We conclude that the proposed approach allows an accurate localization of synchronous brain regions and a robust estimation of their activity.

Review on solving the inverse problem in EEG source analysis

In this primer, we give a review of the inverse problem for EEG source localization. This is intended for the researchers new in the field to get insight in the state-of-the-art techniques used to find approximate solutions of the brain sources giving rise to a scalp potential recording. Furthermore, a review of the performance results of the different techniques is provided to compare these different inverse solutions. The authors also include the results of a Monte-Carlo analysis which they performed to compare four non parametric algorithms and hence contribute to what is presently recorded in the literature. An extensive list of references to the work of other researchers is also provided. This paper starts off with a mathematical description of the inverse problem and proceeds to discuss the two main categories of methods which were developed to solve the EEG inverse problem, mainly the non parametric and parametric methods. The main difference between the two is to whether a fixed number of dipoles is assumed a priori or not. Various techniques falling within these categories are described including minimum norm estimates and their generalizations, LORETA, sLORETA, VARETA, S-MAP, ST-MAP, Backus-Gilbert, LAURA, Shrinking LORETA FOCUSS (SLF), SSLOFO and ALF for non parametric methods and beamforming techniques, BESA, subspace techniques such as MUSIC and methods derived from it, FINES, simulated annealing and computational intelligence algorithms for parametric methods. From a review of the performance of these techniques as documented in the literature, one could conclude that in most cases the LORETA solution gives satisfactory results. In situations involving clusters of dipoles, higher resolution algorithms such as MUSIC or FINES are however preferred. Imposing reliable biophysical and psychological constraints, as done by LAURA has given superior results. The Monte-Carlo analysis performed, comparing WMN, LORETA, sLORETA and SLF, for different noise levels and different simulated source depths has shown that for single source localization, regularized sLORETA gives the best solution in terms of both localization error and ghost sources. Furthermore the computationally intensive solution given by SLF was not found to give any additional benefits under such simulated conditions.

Towards magnetic detection electrical impedance tomography: data acquisition and image reconstruction of current density in phantoms andin vivo

The objective of magnetic detection electrical impedance tomography (MD-EIT) is to reconstruct in vivo images of conductivity from magnetic field measurements taken around the body. MD-EIT is performed by applying an alternating current, at one of a range of frequencies, to a conducting object through a pair of electrodes fixed to the surface of the object. Magnetic field measurements recorded by search coils at a number of positions around the object are used to determine the current distribution that is generating the magnetic field. From this distribution, a conductivity map of a cross-section of the object can be reconstructed. This paper describes the development of an MD-EIT data acquisition system and discusses the related image reconstruction issues. The ill-conditioned nature of the inverse problem is examined and a number of image reconstruction methods are compared. The technical feasibility of MD-EIT data collection and image reconstruction is demonstrated with example images of current density from both phantom and human data.

Experimental results for 2D magnetic resonance electrical impedance tomography (MR-EIT) using magnetic flux density in one direction

Magnetic resonance electrical impedance tomography (MR-EIT) is an emerging imaging technique that reconstructs conductivity images using magnetic flux density measurements acquired employing MRI together with conventional EIT measurements. In this study, experimental MR-EIT images from phantoms with conducting and insulator objects are presented. The technique is implemented using the 0.15 T Middle East Technical University MRI system. The dc current method used in magnetic resonance current density imaging is adopted. A reconstruction algorithm based on the sensitivity matrix relation between conductivity and only one component of magnetic flux distribution is used. Therefore, the requirement for object rotation is eliminated. Once the relative conductivity distribution is found, it is scaled using the peripheral voltage measurements to obtain the absolute conductivity distribution. Images of several insulator and conductor objects in saline filled phantoms are reconstructed. The L2 norm of relative error in conductivity values is found to be 13%, 17% and 14% for three different conductivity distributions.

ECG data compression using truncated singular value decomposition

The method of truncated singular value decomposition (SVD) is proposed for electrocardiogram (ECG) data compression. The signal decomposition capability of SVD is exploited to extract the significant feature components of the ECG by decomposing the ECG into a set of basic patterns with associated scaling factors. The signal informations are mostly concentrated within a certain number of singular values with related singular vectors due to the strong interbeat correlation among ECG cycles. Therefore, only the relevant parts of the singular triplets need to be retained as the compressed data for retrieving the original signals. The insignificant overhead can be truncated to eliminate the redundancy of ECG data compression. The Massachusetts Institute of Technology-Beth Israel Hospital arrhythmia database was applied to evaluate the compression performance and recoverability in the retrieved ECG signals. The approximate achievement was presented with an average data rate of 143.2 b/s with a relatively low reconstructed error. These results showed that truncated SVD method can provide an efficient coding with high-compression ratios. The computational efficiency of the SVD method in comparing with other techniques demonstrated the method as an effective technique for ECG data storage or signals transmission. Index Terms-Data compression, electrocardiogram, feature extraction, quasi-periodic signal, singular value decomposition.

Source potential mapping: a new modality to image neural electric activities

A new neural electric imaging modality-source potential mapping (SPM)-is presented here, which images the neural sources by the potential produced by the sources in a homogeneous infinite conducting medium. Compared with the extant cortical surface potential mapping (CPM). SPM is a more direct reflection of the sources and is a simpler physical model, thus assuring easy understanding. The simulations show that SPM has a slightly higher spatial resolution than CPM and the calculation of SPM is more economical than that of CPM.

Electrical conductivity imaging via contactless measurements

A new imaging modality is introduced to image electrical conductivity of biological tissues via contactless measurements. This modality uses magnetic excitation to induce currents inside the body and measures the magnetic fields of the induced currents. In this study, the mathematical basis of the methodology is analyzed and numerical models are developed to simulate the imaging system. The induced currents are expressed using the A-phi formulation of the electric field where A is the magnetic vector potential and phi is the scalar potential function. It is assumed that A describes the primary magnetic vector potential that exists in the absence of the body. This assumption considerably simplifies the solution of the secondary magnetic fields caused by induced currents. In order to solve phi for objects of arbitrary conductivity distribution a three-dimensional (3-D) finite-element method (FEM) formulation is employed. A specific 7 x 7-coil system is assumed nearby the upper surface of a 10 x 10 x 5-cm conductive body. A sensitivity matrix, which relates the perturbation in measurements to the conductivity perturbations, is calculated. Singular-value decomposition of the sensitivity matrix shows various characteristics of the imaging system. Images are reconstructed using 500 voxels in the image domain, with truncated pseudoinverse. The noise level is assumed to produce a representative signal-to-noise ratio (SNR) of 80 dB. It is observed that it is possible to identify voxel perturbations (of volume 1 cm3) at 2 cm depth. However, resolution gradually decreases for deeper conductivity perturbations.