Sparsity-driven reconstruction for FDOT with anatomical priors

In this paper we propose a method based on (2, 1)-mixed-norm penalization for incorporating a structural prior in FDOT image reconstruction. The effect of (2, 1)-mixed-norm penalization is twofold: first, a sparsifying effect which isolates few anatomical regions where the fluorescent probe has accumulated, and second, a regularization effect inside the selected anatomical regions. After formulating the reconstruction in a variational framework, we analyze the resulting optimization problem and derive a practical numerical method tailored to (2, 1)-mixed-norm regularization. The proposed method includes as particular cases other sparsity promoting regularization methods such as l(1)-norm penalization and total variation penalization. Results on synthetic and experimental data are presented.     

An equivalent current source model and laplacian weighted minimum norm current estimates of brain electrical activity

We have developed a method for estimating the three-dimensional distribution of equivalent current sources inside the brain from scalp potentials. Laplacian weighted minimum norm algorithm has been used in the present study to estimate the inverse solutions. A three-concentric-sphere inhomogeneous head model was used to represent the head volume conductor. A closed-form solution of the electrical potential over the scalp and inside the brain due to a point current source was developed for the three-concentric-sphere inhomogeneous head model. Computer simulation studies were conducted to validate the proposed equivalent current source imaging. Assuming source configurations as either multiple dipoles or point current sources/sinks, in computer simulations we used our method to reconstruct these sources, and compared with the equivalent dipole source imaging. Human experimental studies were also conducted and the equivalent current source imaging was performed on the visual evoked potential data. These results highlight the advantages of the equivalent current source imaging and suggest that it may become an alternative approach to imaging spatially distributed current sources-sinks in the brain and other organ systems.     

Expectation maximization reconstruction of positron emissiontomography images using anatomical magnetic resonance information

Using statistical methods the reconstruction of positron emission tomography (PET) images can be improved by high-resolution anatomical information obtained from magnetic resonance (MR) images. The authors implemented two approaches that utilize MR data for PET reconstruction. The anatomical MR information is modeled as a priori distribution of the PET image and combined with the distribution of the measured PET data to generate the a posteriori function from which the expectation maximization (EM)-type algorithm with a maximum a posteriori (MAP) estimator is derived. One algorithm (Markov-GEM) uses a Gibbs function to model interactions between neighboring pixels within the anatomical regions. The other (Gauss-EM) applies a Gauss function with the same mean for all pixels in a given anatomical region. A basic assumption of these methods is that the radioactivity is homogeneously distributed inside anatomical regions. Simulated and phantom data are investigated under the following aspects: count density, object size, missing anatomical information, and misregistration of the anatomical information. Compared with the maximum likelihood-expectation maximization (ML-EM) algorithm the results of both algorithms show a large reduction of noise with a better delineation of borders. Of the two algorithms tested, the Gauss-EM method is superior in noise reduction (up to 50%). Regarding incorrect a priori information the Gauss-EM algorithm is very sensitive, whereas the Markov-GEM algorithm proved to be stable with a small change of recovery coefficients between 0.5 and 3%     

On the active conductivity of a three-barrier resonant-tunneling structure and optimization of quantum cascade laser operation

Within the context of the model of effective masses and rectangular potentials, the theory of active electronic conductivity is proposed for a three-barrier resonant-tunneling structure in a dc electric field, as the active element of a quantum cascade laser. It is shown that the chosen geometrical parameters of the active regions in the first experimentally fabricated quantum cascade lasers are most optimal and the experimental and theoretical values of the radiation energies correlate with each other with an accuracy of up to a few percent.     

Modified beamformers for coherent source region suppression

Many tomographic source localization algorithms used in biomagnetic imaging assume, explicitly or sometimes implicitly, that the source activity at different brain locations are either independent or that the correlation structure between sources is known. Among these algorithms is a class of adaptive spatial filters known as beamformers, which have superior spatiotemporal resolution abilities. The performance of beamformers is robust to weakly coherent sources. However, these algorithms are extremely sensitive to the presence of strongly coherent sources. A frequent mode of failure in beamformers occurs with reconstruction of auditory evoked fields (AEFs), in which bilateral auditory cortices are highly coherent in their activation. Here, we present a novel beamformer that suppresses activation from regions with interfering coherent sources. First, a volume containing the interfering sources is defined. The lead field matrix for this volume is computed and reduced into a few significant columns using singular value decomposition (SVD). A vector beamformer is then constructed by rejecting the contribution of sources in the suppression region while allowing for source reconstruction at other specified regions. Performance of this algorithm was first validated with simulated data. Subsequent tests of this modified beamformer were performed on bilateral AEF data. An unmodified vector beamformer using whole head coverage misplaces the source medially. After defining a suppression region containing the temporal cortex on one side, the described method consistently results in clear focal activations at expected regions of the contralateral superior temporal plane.     

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.     

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.     

Wavefront-based models for inverse electrocardiography

We introduce two wavefront-based methods for the inverse problem of electrocardiography, which we term wavefront-based curve reconstruction (WBCR) and wavefront-based potential reconstruction (WBPR). In the WBCR approach, the epicardial activation wavefront is modeled as a curve evolving on the heart surface, with the evolution governed by factors derived phenomenologically from prior measured data. The body surface potential/wavefront relationship is modeled via an intermediate mapping of wavefront to epicardial potentials, again derived phenomenologically. In the WBPR approach, we iteratively construct an estimate of epicardial potentials from an estimated wavefront curve according to a simplified model and use it as an initial solution in a Tikhonov regularization scheme. Initial simulation results using measured canine epicardial data show considerable improvement in reconstructing activation wavefronts and epicardial potentials with respect to standard Tikhonov solutions. In particular the WBCR method accurately finds the anisotropic propagation early after epicardial pacing, and the WBPR method finds the wavefront (regions of sharp gradient of the potential) both accurately and with minimal smoothing.     

A state-space modeling approach for localization of focal current sources from MEG

State-space modeling is a promising approach for current source reconstruction from magnetoencephalography (MEG) because it constrains the spatiotemporal behavior of inverse solutions in a flexible manner. However, state-space model-based source localization research remains underdeveloped; extraction of spatially focal current sources and handling of the high dimensionality of the distributed source model remain problematic. In this study, we propose a novel state-space model-based method that resolves these problems, extending our previous source localization method to include a temporal constraint by state-space modeling. To enable focal current reconstruction, we account for spatially inhomogeneous temporal dynamics by introducing dynamics model parameters that differ for each cortical position. The model parameters and the intensity of the current sources are jointly estimated according to a bayesian framework. We circumvent the high dimensionality of the problem by assuming prior distributions of the model parameters to reduce the sensitivity to unmodeled components, and by adopting variational bayesian inference to reduce the computational cost. Through simulation experiments and application to real MEG data, we have confirmed that our proposed method successfully reconstructs focal current activities, which evolve with their temporal dynamics.     

Robust bilayer video segmentation by adaptive propagation of global shape and local appearance

Segmenting semantic objects of interest from video has long been an active research topic, with a wide range of potential applications. In this paper, we present a bilayer video segmentation method robust to abrupt motion and change in appearance for both the foreground and background. Specifically, based on a few manually segmented keyframes, the proposed method propagates the global shape of the foreground as priors to adjacent frames by applying branch-and-mincut [1], which jointly estimates what is optimal among a set of shapes along with its pose and the corresponding segmentation in the current image. Based on this preliminary segmentation we determine two types of local regions likely to have erroneous results, and apply a probabilistic framework where shape and appearance cues are adaptively emphasized for local refinement. With each successive frame segmentation, the set of shapes applied as priors are incrementally updated. Experimental results support the robustness of the proposed method for obstacles such as background clutter, motion, and appearance changes, from only a small number of user segmented keyframes.     

Inversion of simulated evoked potentials to charge distribution inside the human brain using an algebraic reconstruction technique

An analytic method is presented to estimate the evolution of electrical charge distribution inside the human brain related to the evoked potentials observed on the head surface. A three-layer concentric spherical human head model is adopted to express the relation between the observed potentials on the head surface and the spatial charge distribution inside the brain. An integral equation associated with the three-layer concentric head model Green's function is employed. Assuming the electric potentials are measured on the head surface, the charge distributions inside the human brain are computed by solving an inverse problem. The Green's function integral equation is inverted by using an algebraic reconstruction technique widely employed in X-ray tomography imaging. The accuracy of the proposed technique is examined by employing computer simulations and by checking the self-consistency of the algorithm.     

Composite inductive posts in waveguide-a multifilament analysis

A multifilament moment solution for the analysis of composite dielectric posts in rectangular waveguide is presented. This method permits the analysis of inductive posts composed of disparate regions, each with its own homogeneous complex permittivity. The solution uses the fields generated by sets of fixed-amplitude current filaments to simulate both the field scattered by the posts and the field inside every homogeneous region comprising the posts. Point matching the electric and magnetic fields on the boundaries between regions of different permittivity yields the as-yet-unknown amplitudes for the current filaments. These currents can in turn be used to calculate field-related parameters of interest such as the scattering matrix and the equivalent circuit parameters. Inductive posts of any shape, composition, size, location, and number can be handled by this method accurately and with very good numerical efficiency. The results obtained are in good agreement with the few cases for which data are available. They also behave well in the limiting cases studied. The solution is further applied to other situations for which no experimental or calculated results are known     

Time-dependent scalar Beltrami-Hertz potentials in free space

We have solved the Beltrami-Maxwell equations for free space in terms of time-dependent scalar functions, the so-called scalar Beltrami-Hertz potentials. The two Beltrami fields have been represented in terms of scalar Beltrami-Hertz potentials. While the method is formulated for general sources, it is at its most powerful when the impressed source current densities are unidirectional: each Beltrami field, a complex-valued vector, can then be derived from a single scalar Beltrami-Hertz potential. We have calculated the corresponding scalar Green function explicity and given closed-form solutions for dipolar sources. Finally, the connection between the Beltrami-Maxwell formalism and conventional electromagnetic theory has been re-affirmed.     

Use of Finite Difference Approximations to Partial Differential Equations for Problems Having Boundaries at Infinity (Correspondence)

A computationally simple technique is presented for solving finite difference equations arising from potential problems, part of whose boundary is at infinity. The procedure makes use of an arbitrary "fictitious" boundary drawn close to the regions of physical interest. An initial guess is made of the potential on this boundary as well as at all interior points. Well-known iterative techniques are used to correct the values of the interior potentials. Meanwhile the potentials on the boundary are corrected iteratively by recalculating them from the sources or charges in the entire region, which in turn are calculated from the current iteration of the interior potential. The technique is valid even if parts of the physical structure, such as an air-dielectric interface in microstrip, extend toward infinity. The fictitious boundary need not include all of the structure, providing the rate of falloff of the sources outside the boundary is known.     

Uniqueness of the generators of brain evoked potential maps

This study considers the uniqueness of neuronal generators of human brain evoked potentials measured on the scalp using the physical and mathematical properties of the volume conductor model. The results are applicable to a realistic, nonhomogeneous head shape where the potential map is known on a continuous set of points on the scalp. It is shown that sources which occupy “zero volume” in space such as point dipoles or sources distributed on an open surface or a line are uniquely defined by the potential maps. Finite volume nonoverlapping sources are also uniquely defined by their potential map. However, there are infinitely many different but overlapping sources which can create the same map. Several examples of such sources are provided. It is shown that there is a unique, minimum volume source which can be defined in this case. Results suggest that if a reconstruction of the sources starts from a continuous scalp map (obtained by interpolation of the data between electrode sites), one can obtain unique results concerning the source parameters that are not available in a search for a source whose potential map fits only at a discrete set of points     

Improved performance of bayesian solutions for inverse electrocardiography using multiple information sources

The usual goal in inverse electrocardiography (ECG) is to reconstruct cardiac electrical sources from body surface potentials and a mathematical model that relates the sources to the measurements. Due to attenuation and smoothing that occurs in the thorax, the inverse ECG problem is ill-posed and imposition of a priori constraints is needed to combat this ill-posedness. When the problem is posed in terms of reconstructing heart surface potentials, solutions have not yet achieved clinical utility; limitations include the limited availability of good a priori information about the solution and the lack of a "good" error metric. We describe an approach that combines body surface measurements and standard forward models with two additional information sources: statistical prior information about epicardial potential distributions and sparse simultaneous measurements of epicardial potentials made with multielectrode coronary venous catheters. We employ a Bayesian methodology which offers a general way to incorporate these information sources and additionally provides statistical performance analysis tools. In a simulation study, we first compare solutions using one or more of these information sources. Then, we study the effects of varying the number of sparse epicardial potential measurements on reconstruction accuracy. To evaluate accuracy, we used the Bayesian error covariance as well as traditional error metrics such as relative error. Our results show that including even sparsely sampled information from coronary venous catheters can substantially improve the reconstruction of epicardial potential distributions and that a Bayesian framework provides a feasible approach to using this information. Moreover, computing the Bayesian error standard deviations offers a means to indicate confidence in the results even in the absence of validation data.     

Domain-specific image analysis for cervical neoplasia detection based on conditional random fields

This paper presents a domain-specific automated image analysis framework for the detection of pre-cancerous and cancerous lesions of the uterine cervix. Our proposed framework departs from previous methods in that we include domain-specific diagnostic features in a probabilistic manner using conditional random fields. Likewise, we provide a novel window-based performance assessment scheme for 2D image analysis which addresses the intrinsic problem of image misalignment. Image regions corresponding to different tissue types are indentified for the extraction of domain-specific anatomical features. The unique optical properties of each tissue type and the diagnostic relationships between neighboring regions are incorporated in the proposed conditional random field model. The validity of our method is examined using clinical data from 48 patients, and its diagnostic potential is demonstrated by a performance comparison with expert colposcopy annotations, using histopathology as the ground truth. The proposed automated diagnostic approach can support or potentially replace conventional colposcopy, allow tissue specimen sampling to be performed in a more objective manner, and lower the number of cervical cancer cases in developing countries by providing a cost effective screening solution in low-resource settings.     

Relating the Sodium Current and Conductance to the Shape of Transmembrane and Extracellular Potentials by Simulation: Effects of Propagation Boundaries

The purpose of this paper is to describe how the transmembrane and extracellular potential waveforms, and their derivatives, are related to each other and to the sodium current and conductance in propagating cardiac action potentials. The results show that the shape of the transmembrane potential and the kinetics of the sodium current and conductance are highly determined by boundary effects at sites where impulse conduction begins and where it ends at a collision or an anatomical end. These propagation nonuniformities produced a relationship between Vmax and the internal membrane variables gNa and INa that is just the opposite of the classical relation between Vmax and the magnitude of the sodium current. For example, in these cases, both peak INa and the area under the gNa curve decreased when Vmax increased. In addition, Vmax, was shown to coincide in time with the maximum rate of increase of gNa and INa. The maximum negative slope of the extracellular waveform coincided in time with Vmax of the transmembrane potential for all shapes of the waveforms. Therefore, either the maximum negative slope of the extracellular waveform or Vmax of the action potential provides a time marker for the same underlying depolarizing event, i.e., the maximum rate of increase of the depolarizing current and its conductance.     

Numerical tests of a method for simulating electrical potentials onthe cortical surface

A mathematical imaging method for simulating cortical surface potentials was introduced at recent neurosciences meetings [1a], [1b], [2] and was applied to elucidate the neural origins of evoked responses in normal volunteers and certain patient populations. This method consists of the solution of an inward harmonic continuation problem and its effect is to simulate data that has not been attenuated and smeared by the skull. This cortical imaging technique (CIT) is validated by applying it to artificially derived data. Pairs of dipolar sources with different depths and separations are introduced into a spherical conducting medium simulating the head. Scalp potential maps are constructed by interpolating the simulated data between 28 "scalp" electrode positions. Noise is added to the data to approximate the variability in measured potentials that would be observed in practice. CIT is used in each case to construct potential maps on layers concentric to and within the layer representing the scalp. In several instances when the dipole pair is deep and closely spaced, the sources cannot be separated by the scalp topographical maps but are easily separated by the "cortical" topographical maps. CIT is also applied to scalp-recorded potentials evoked by bilateral median nerve stimulation and pattern-reversal visual stimulation.     

An Optimal Excitation Method in Multi-Applicator Systems for Forming a Hot Zone Inside the Human Body

A method is proposed for determining the excitation amplitude and phase of each applicator in electromagnetic multi-applicator systems for forming a narrow high temperature zone inside the human body. The principal advantage of this method for determining the optimal amplitudes and phases is its simplicity and reasonableness. The general principle is explained by using the example of an elliptical body region, heated by several line current sources placed outside the body. Numerical examples are presented for the case where a human abdominal region composed of muscular and spinal layers surrounded by a cooling water layer is excited by several line sources at 40.68 MHz.