The need for correct realistic geometry in the inverse EEG problem

For accurate electroencephalogram-based localization of mesial temporal and frontal sources correct modeling of skull shape and thickness is required. In a simulation study in which results for matched sets of computed tomography and magnetic resonance (MR) images are compared, it is found that errors arising from skull models based on smooth and inflated segmented MR images of the cortex are of the order of 1 cm. These errors are comparable to those found when overestimating or underestimating skull conductivity by a factor of two.     

Noise sensitivity of sparse signal representations: reconstruction error bounds for the inverse problem

Certain sparse signal reconstruction problems have been shown to have unique solutions when the signal is known to have an exact sparse representation. This result is extended to provide bounds on the reconstruction error when the signal has been corrupted by noise or is not exactly sparse for some other reason. Uniqueness is found to be extremely unstable for a number of common dictionaries.     

Use of the ventricular propagated excitation model in the magnetocardiographic inverse problem for reconstruction of electrophysiological properties

A novel magnetocardiographic inverse method for reconstructing the action potential amplitude (APA) and the activation time (AT) on the ventricular myocardium is proposed. This method is based on the propagated excitation model, in which the excitation is propagated through the ventricle with nonuniform height of action potential. Assumption of stepwise waveform on the transmembrane potential was introduced in the model. Spatial gradient of transmembrane potential, which is defined by APA and AT distributed in the ventricular wall, is used for the computation of a current source distribution. Based on this source model, the distributions of APA and AT are inversely reconstructed from the QRS interval of magnetocardiogram (MCG) utilizing a maximum a posteriori approach. The proposed reconstruction method was tested through computer simulations. Stability of the methods with respect to measurement noise was demonstrated. When reference APA was provided as a uniform distribution, root-mean-square errors of estimated APA were below 10 mV for MCG signal-to-noise ratios greater than, or equal to, 20 dB. Low-amplitude regions located at several sites in reference APA distributions were correctly reproduced in reconstructed APA distributions. The goal of our study is to develop a method for detecting myocardial ischemia through the depression of reconstructed APA distributions.     

Region-based super-resolution for compression

Every user of multimedia technology expects good image and video visual quality independently of the particular characteristics of the receiver or the communication networks employed. Unfortunately, due to factors like processing power limitations and channel capabilities, images or video sequences are often downsampled and/or transmitted or stored at low bitrates, resulting in a degradation of their final visual quality. In this paper, we propose a region-based framework for intentionally introducing downsampling of the high resolution (HR) image sequences before compression and then utilizing super resolution (SR) techniques for generating an HR video sequence at the decoder. Segmentation is performed at the encoder on groups of images to classify their blocks into three different types according to their motion and texture. The obtained segmentation is used to define the downsampling process at the encoder and it is encoded and provided to the decoder as side information in order to guide the SR process. All the components of the proposed framework are analyzed in detail. A particular implementation of it is described and tested experimentally. The experimental results validate the usefulness of the proposed method.     

Resolving the hemodynamic inverse problem

The "hemodynamic inverse problem" is the determination of arterial system properties from pressures and flows measured at the entrance of an arterial system. Conventionally, investigators fit reduced arterial system models to data, and the resulting model parameters represent putative arterial properties. However, no unique solution to the inverse problem exists-an infinite number of arterial system topologies result in the same input impedance (Zin) and, therefore, the same pressure and flow. Nevertheless, there are exceptions to this theoretical limitation; total peripheral resistance (Rtot), total arterial compliance (Ctot), and characteristic impedance (ZO) can be uniquely determined from input pressure and flow. Zin is determined completely by Ctot and Rtot at low frequencies, Zo at high frequencies, and arterial topology and reflection effects at intermediate frequencies. We present a novel method to determine the relative contribution of Zo, Ctot, Rtot and arterial topology/reflection to Zin without assuming a particular reduced model. This method is tested with a large-scale distributed model of the arterial system, and is applied to illustrative cases of measured pressure and flow. This work, thus, lays the theoretical foundation for determining the arterial properties responsible for increased pulse pressure with age and various arterial system pathologies.     

Travelling wave expansion: a model fitting approach to the inverse problem of elasticity reconstruction

In this paper, a novel approach to the problem of elasticity reconstruction is introduced. In this approach, the solution of the wave equation is expanded as a sum of waves travelling in different directions sharing a common wave number. In particular, the solutions for the scalar and vector potentials which are related to the dilatational and shear components of the displacement respectively are expanded as sums of travelling waves. This solution is then used as a model and fitted to the measured displacements. The value of the shear wave number which yields the best fit is then used to find the elasticity at each spatial point. The main advantage of this method over direct inversion methods is that, instead of taking the derivatives of noisy measurement data, the derivatives are taken on the analytical model. This improves the results of the inversion. The dilatational and shear components of the displacement can also be computed as a byproduct of the method, without taking any derivatives. Experimental results show the effectiveness of this technique in magnetic resonance elastography. Comparisons are made with other state-of-the-art techniques.     

EEG and MEG: forward solutions for inverse methods

A solution of the forward problem is an important component of any method for computing the spatio-temporal activity of the neural sources of magnetoencephalography (MEG) and electroencephalography (EEG) data. The forward problem involves computing the scalp potentials or external magnetic field at a finite set of sensor locations for a putative source configuration. We present a unified treatment of analytical and numerical solutions of the forward problem in a form suitable for use in inverse methods. This formulation is achieved through factorization of the lead field into the product of the moment of the elemental current dipole source with a "kernel matrix" that depends on the head geometry and source and sensor locations, and a "sensor matrix" that models sensor orientation and gradiometer effects in MEG and differential measurements in EEG. Using this formulation and a recently developed approximation formula for EEG, based on the "Berg parameters," we present novel reformulations of the basic EEG and MEG kernels that dispel the myth that EEG is inherently more complicated to calculate than MEG. We also present novel investigations of different boundary element methods (BEM's) and present evidence that improvements over currently published BEM methods can be realized using alternative error-weighting methods. Explicit expressions for the matrix kernels for MEG and EEG for spherical and realistic head geometries are included.     

高分辨电子显微学的求逆问题

本文评述了高分辨电子显微镜学中一种求逆问题的方法。此方法的实质是把衍射晶体学融合到高分辨电子显微学中。文章阐述了显微像衬度随晶体厚度的变化,从而说明当晶体厚度小于临界值时,可以合理地把建立在运动学衍射理论基础上的衍射分析方法等引用到高分辨电子显微学中,使测得晶体结构和缺陷的分辨率远高于电子显微镜的点分辨本领。文章简要地介绍了方法的原理和过程,及其在测定晶体结构和缺陷上的应用。     

New cascaded control system for current-source rectifiers

A control method for current-source rectifiers (CSRs), which realizes substantially sinusoidal line currents, unity displacement power factor, and a dc-link current control with excellent dynamic properties is presented. CSRs are usually operated by pulsewidth-modulation (PWM) or space-vector-modulation techniques. However, due to the mains LC filter resonant circuits when using these modulation methods the system stability has to be investigated, resulting in restrictions on the minimum PWM frequency and the minimum size of the LC filter. Furthermore most known dc-link current control loops use dc-link inductors of considerable size. This limits the dynamic performance and, therefore, reduces the attainable efficiency of CSRs. To overcome these problems, a new cascaded dc-link current control system for CSRs is presented. Its inner capacitor voltage controller is based on a time-discrete modulation method, which realizes a fundamentally stable control of the mains LC filter resonant circuits, avoiding the mentioned restrictions. The system controlled by the superimposed dc-link current controller is linearized by a new approach, allowing excellent dynamic performance and, therefore, a comparatively small dc-link inductor to be used. The paper includes guidelines on how to design the mains filter components and the dc-link inductor. The feasibility of the presented cascaded controller is confirmed by measurements taken on a 60-kVA model current-source converter and different loads.     

A meshless method for solving the EEG forward problem

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.     

Soft-switched current-source inverter for single-phase utilityinterfaces

A novel soft-switched current-source inverter for single-phase utility interfaces is presented. To provide the soft-switching capability under the pulsewidth modulation for a single-phase line-commutated thyristor inverter, an auxiliary resonant switch to bypass the current on the DC side is connected across the DC input of a thyristor inverter     

Single-trial EEG source reconstruction for brain-computer interface.

A new way to improve the classification rate of an EEG-based brain-computer interface (BCI) could be to reconstruct the brain sources of EEG and to apply BCI methods to these derived sources instead of raw measured electrode potentials. EEG source reconstruction methods are based on electrophysiological information that could improve the discrimination between BCI tasks. In this paper, we present an EEG source reconstruction method for BCI. The results are compared with results from raw electrode potentials to enable direct evaluation of the method. Features are based on frequency power change and Bereitschaft potential. The features are ranked with mutual information before being fed to a proximal support vector machine. The dataset IV of the BCI competition II and data from four subjects serve as test data. Results show that the EEG inverse solution improves the classification rate and can lead to results comparable to the best currently known methods.     

A genetic algorithm for the inverse problem in synthesis of fibergratings

A new method for synthesis of fiber gratings with advanced characteristics is proposed. By combining the Runge-Kutta method for calculating the reflection spectrum of a fiber grating and a genetic algorithm, we obtain a promising method for the synthesis. Compared to other methods, the proposed method facilitates the task of weighting the different requirements to the filter spectrum. In addition, the method is general, and would thus be useful for other inverse problems     

The potential for Laplacian maps to solve the inverse problem ofelectrocardiography

Presents a method to solve the inverse problem of electrocardiography using the Laplacian of the body surface potentials. The method presented is studied first using trade-off curves from a concentric spheres model representing a heart-torso system. Then a more conventional study is undertaken where a limited number of current dipoles are placed within the inner sphere and noise is added to the resulting potentials and Laplacians on the surface of the outer sphere. The results indicate that measurements of the outer surface Laplacian can more accurately reconstruct epicardial potentials than measurements of the outer surface potentials. The reconstructions are more accurate in that extrema are placed very close to their correct positions and multiple extrema and high potential gradients are recovered. Identical conclusions are observed in the presence of noise and even when the Laplacians are subject to greater noise than the potentials     

The electromagnetic inverse scattering problem for layered dispersionless dielectrics

The problem of exactly reconstructing the one-dimensional refractive index profile of a dispersionless dielectric from reflection data is considered. The available data consist of reflection coefficient measurements at many wavenumbers due to a normally incident electromagnetic plane wave upon a dielectric half-space or equivalently the impulse response measurement of the half-space. A closed-form analytical technique is described and applied to several solutions. These solutions are compared with results from a numerical method that uses leapfrogging in space and time and other analytical methods. Finally, the robustness of this technique with respect to imprecise and bandlimited data is examined and compared with a previous result.     

Selective minimum-norm solution of the biomagnetic inverse problem

A new multidipole estimation method which gives a sparse solution of the biomagnetic inverse problem is proposed. This solution is extracted from the basic feasible solutions of linearly independent data equations. These feasible solutions are obtained by selecting exactly as many dipole-moments as the number of magnetic sensors. By changing the selection, the authors search for the minimum-norm vector of selected moments. As a result, a practically sparse solution is obtained; computer-simulated solutions for L_p-norm (p=2, 1, 0.5, 0.2) have a small number of significant moments around the real source-dipoles. In particular, the solution for L₁-norm is equivalent to the minimum-L₁-norm solution of the original inverse problem. This solution can be uniquely computed by using linear programming     

A common formalism for the integral formulations of the forward EEG problem

The forward electroencephalography (EEG) problem involves finding a potential V from the Poisson equation inverted Delta x (sigma inverted Delta V) f, in which f represents electrical sources in the brain, and sigma the conductivity of the head tissues. In the piecewise constant conductivity head model, this can be accomplished by the boundary element method (BEM) using a suitable integral formulation. Most previous work uses the same integral formulation, corresponding to a double-layer potential. In this paper we present a conceptual framework based on a well-known theorem (Theorem 1) that characterizes harmonic functions defined on the complement of a bounded smooth surface. This theorem says that such harmonic functions are completely defined by their values and those of their normal derivatives on this surface. It allows us to cast the previous BEM approaches in a unified setting and to develop two new approaches corresponding to different ways of exploiting the same theorem. Specifically, we first present a dual approach which involves a single-layer potential. Then, we propose a symmetric formulation, which combines single- and double-layer potentials, and which is new to the field of EEG, although it has been applied to other problems in electromagnetism. The three methods have been evaluated numerically using a spherical geometry with known analytical solution, and the symmetric formulation achieves a significantly higher accuracy than the alternative methods. Additionally, we present results with realistically shaped meshes. Beside providing a better understanding of the foundations of BEM methods, our approach appears to lead also to more efficient algorithms.     

A critical analysis of linear inverse solutions to theneuroelectromagnetic inverse problem

This paper explores the possibilities of using linear inverse solutions to reconstruct arbitrary current distributions within the human brain. The authors formally prove that due to the underdetermined character of the problem, the only class of measurable current distributions that can be totally retrieved are those of minimal norm. The reconstruction of smooth or averaged versions of the currents is also explored. A solution that explicitly attempts to reconstruct averages of the current is proposed and compared with the minimum norm and the minimum Laplacian solution. In contrast to the majority of previous analysis carried out in the field, in the comparisons, the authors avoid the use of measures designed for the case of dipolar sources. To allow for the evaluation of distributed solutions in the case of arbitrary current distributions the authors use the concept of resolution kernels. Two summarizing measures, source identifiability and source visibility, are proposed and applied to the comparison. From this study can be concluded: (1) linear inverse solutions are unable to produce adequate estimates of arbitrary current distributions at many brain sites and (2) averages or smooth solutions are better than the minimum norm solution estimating the position of single point sources. However, they systematically underestimate their amplitude or strength especially for the deeper brain areas. Based on these result, it appears unlikely that a three-dimensional (3-D) tomography of the brain electromagnetic activity can be based on linear reconstruction methods without the use of a significant amount of a priori information