Inverse Source Reconstruction Research Articles

Forward and Inverse Source Reconstruction Problems for the Equations of Vibrations of a Rectangular Plate

Forward and Inverse Source Reconstruction Problems for the Equations of Vibrations of a Rectangular Plate

Forward and Inverse Source Reconstruction Problems for the Equations of Vibrations of a Rectangular Plate

For the equation of vibrations of a rectangular plate, the initial-boundary value and inverse problems of finding the right-hand side (the source of vibrations) are studied. Solutions of the problems are constructed explicitly as sums of series, and the corresponding uniqueness and existence theorems are proved. When substantiating the existence of a solution to the inverse problem of determining the factor on the right-hand side, which depends on spatial coordinates, the problem of small denominators of two natural variables arises, for which estimates of the separation from zero with the corresponding asymptotics are established. These estimates made it possible to prove the existence theorem for this problem in the class of regular solutions by imposing certain smoothness conditions on the given boundary functions.

Evaluating brain spectral and connectivity differences between silent mind-wandering and trance states.

Trance is an altered state of consciousness characterized by alterations in cognition. In general, trance states induce mental silence (i.e., cognitive thought reduction), and mental silence can induce trance states. Conversely, mind-wandering is the mind's propensity to stray its attention away from the task at hand and toward content irrelevant to the current moment, and its main component is inner speech. Building on the previous literature on mental silence and trance states and incorporating inverse source reconstruction advances, the study's objectives were to evaluate differences between trance and mind-wandering states using: (1) electroencephalography (EEG) power spectra at the electrode level, (2) power spectra at the area level (source reconstructed signal), and (3) EEG functional connectivity between these areas (i.e., how they interact). The relationship between subjective trance depths ratings and whole-brain connectivity during trance was also evaluated. Spectral analyses revealed increased delta and theta power in the frontal region and increased gamma in the centro-parietal region during mind-wandering, whereas trance showed increased beta and gamma power in the frontal region. Power spectra at the area level and pairwise comparisons of the connectivity between these areas demonstrated no significant difference between the two states. However, subjective trance depth ratings were inversely correlated with whole-brain connectivity in all frequency bands (i.e., deeper trance is associated with less large-scale connectivity). Trance allows one to enter mentally silent states and explore their neurophenomenological processes. Limitations and future directions are discussed.

The IAS-MEEG Package: A Flexible Inverse Source Reconstruction Platform for Reconstruction and Visualization of Brain Activity from M/EEG Data

We present a standalone Matlab software platform complete with visualization for the reconstruction of the neural activity in the brain from MEG or EEG data. The underlying inversion combines hierarchical Bayesian models and Krylov subspace iterative least squares solvers. The Bayesian framework of the underlying inversion algorithm allows to account for anatomical information and possible a priori belief about the focality of the reconstruction. The computational efficiency makes the software suitable for the reconstruction of lengthy time series on standard computing equipment. The algorithm requires minimal user provided input parameters, although the user can express the desired focality and accuracy of the solution. The code has been designed so as to favor the parallelization performed automatically by Matlab, according to the resources of the host computer. We demonstrate the flexibility of the platform by reconstructing activity patterns with supports of different sizes from MEG and EEG data. Moreover, we show that the software reconstructs well activity patches located either in the subcortical brain structures or on the cortex. The inverse solver and visualization modules can be used either individually or in combination. We also provide a version of the inverse solver that can be used within Brainstorm toolbox. All the software is available online by Github, including the Brainstorm plugin, with accompanying documentation and test data.

A Genetic Algorithm for Pointwise Source Reconstruction by the Method of Fundamental Solutions

Inverse source reconstruction problems offer great potential for applications of interest to engineering, such as the identification of polluting sources, and to medicine, such as electroencephalography, to cite at least two relevant examples. From a mathematical point of view, the identification of a concentrated source (intensity and location) corresponds to the identification of the centroid (location) and size (intensity) of a distributed source. On the other hand, from a numerical point of view, it is observed that the use of domain discretization methods is intrinsically associated with the introduction of numerical noise in reconstruction algorithms, which is strongly inadvisable since inverse problems are reckoned to be ill-posed. The objective of this work is to explore, in the context of a Poisson problem and taking into account a numerical point of view, a new reconstruction algorithm based on the method of fundamental solutions, where a source point adequately represents the pointwise source within the domain. The inverse problem is reformulated as an optimization problem solved through a genetic algorithm. Finally, numerical examples are performed to analyze the accuracy of the proposed algorithm for two and three dimensions.

Sparsity-enhanced equivalent source method for acoustic source reconstruction via the Generalized Minimax-Concave penalty

The Equivalent Source Method (ESM) is a powerful technique for acoustic source reconstruction, which has been widely used in noise control and machinery fault detection. Because the inverse acoustic source reconstruction problem is typically ill-conditioned, regularization techniques are often adopted in ESM to achieve meaningful solutions. Based on the sparse distribution assumption of acoustic sources, sparse regularization can be utilized in ESM to promote the spatial resolution of reconstructed results. Existing sparse ESMs often adopt convex l1 norm or nonconvex lp norm as the regularization terms. However, l1 norm-regularized ESM suffers from an insufficient sparsity-inducing problem, which decreases the spatial resolution and reconstruction accuracy. Meanwhile, reconstructed results of lp norm-regularized ESM are often unstable due to multiple local minimas. In this paper, a sparsity-enhanced ESM is proposed, which introduces a nonconvex Generalized Minimax-Concave (GMC) penalty into ESM as the regularization term. The GMC penalty can enhance the sparsity of solutions and simultaneously maintain the convexity of the overall objective function in acoustic source reconstruction. Consequently, the GMC penalty-regularized ESM can improve the spatial resolution and reconstruction accuracy of the reconstructed results. To solve the acoustic source reconstruction problem rapidly, a computation framework based on Alternating Direction Method of Multipliers (ADMM) is derived. Simulation studies indicate that the proposed method can improve the acoustic source reconstruction accuracy in a wide frequency band, compared with existing l1 and lp norm-regularized ESMs. Two experimental cases further verify that the proposed sparsity-enhanced ESM can effectively reconstruct the acoustic sources with high spatial resolution and reconstruction accuracy at higher frequencies.

Brain-wide functional diffuse optical tomography of resting state networks

Objective. Diffuse optical tomography (DOT) has the potential in reconstructing resting state networks (RSNs) in human brains with high spatio-temporal resolutions and multiple contrasts. While several RSNs have been reported and successfully reconstructed using DOT, its full potential in recovering a collective set of distributed brain-wide networks with the number of RSNs close to those reported using functional magnetic resonance imaging (fMRI) has not been demonstrated. Approach. The present study developed a novel brain-wide DOT (BW-DOT) framework that integrates a cap-based whole-head optode placement system with multiple computational approaches, i.e. finite-element modeling, inverse source reconstruction, data-driven pattern recognition, and statistical correlation tomography, to reconstruct RSNs in dual contrasts of oxygenated (HbO) and deoxygenated hemoglobins (HbR). Main results. Our results from the proposed framework revealed a comprehensive set of RSNs and their subnetworks, which collectively cover almost the entire neocortical surface of the human brain, both at the group level and individual participants. The spatial patterns of these DOT RSNs suggest statistically significant similarities to fMRI RSN templates. Our results also reported the networks involving the medial prefrontal cortex and precuneus that had been missed in previous DOT studies. Furthermore, RSNs obtained from HbO and HbR suggest similarity in terms of both the number of RSN types reconstructed and their corresponding spatial patterns, while HbR RSNs show statistically more similarity to fMRI RSN templates and HbO RSNs indicate more bilateral patterns over two hemispheres. In addition, the BW-DOT framework allowed consistent reconstructions of RSNs across individuals and across recording sessions, indicating its high robustness and reproducibility, respectively. Significance. Our present results suggest the feasibility of using the BW-DOT, as a neuroimaging tool, in simultaneously mapping multiple RSNs and its potential values in studying RSNs, particularly in patient populations under diverse conditions and needs, due to its advantages in accessibility over fMRI.

Study on Reciprocal Models for Magneto-Acousto-Electrical Tomography With Coil Detection

Magneto-Acousto-Electric Tomography with coil detection, known as Magneto-Acousto-Electric Tomography with Magnetic Induction (MAET-MI), is a non-contact resistivity-based imaging method that employs a coil to detect the induced current generated by the ultrasound in biological tissue, which lie under a static magnetic field. To reconstruct an image of the tissue's conductivity, we propose a reciprocal model to describe the relationship between the inducted voltage of a coil and its conductivity. Previous work on the reciprocal theorem demonstrates that reconstructing conductivity using this method is effective. The forward and inverse problem are usually not verified both numerically and experimentally. In this paper, different approaches are adopted to calculate the forward and the inverse problems for verification of the reciprocal model. This verifies that the reconstruction method based on electrode detection can be applied to MAET-MI. This means that the inverse problem of MAET-MI can be transformed into an inverse source reconstruction of a wave equation based on the coil detection. In the forward problem, the moment method is employed to calculate the Radon transform and generate the ultrasonic signals. For the inverse problem, the filtered back projection method is chosen to reconstruct the ultrasound sources, which are related to the curl of the current density in the reciprocal process. Based on the curl of the current density in the reciprocal process, four sets of correlation coefficients of the original and reconstructed images' model are all greater than 90%. The uniform error criterion is obtained via multiple reconstructions and comparison of multiple models. The reciprocal model exhibits a good uniformity and stability when describing the actual physical process. It also provides additional effective ideas for solving the inverse problem quickly to reconstruct the ultrasonic sources, which is corresponding to the actual distribution of the conductivity.

Application of Inverse Source Reconstruction to Conformal Antennas Synthesis

The inverse source problem for a 2-D geometry is considered in the circular geometry. The mathematical relationship between the radiated pattern and the source current is investigated by the appropriate singular value decomposition for different 2-D planar and curved shapes. The spectral analysis allows discussing the number of degrees of freedom of each geometry and reveals a peculiar common passband behavior of the radiation operator. For some geometries, this can significantly affect the inverse source reconstruction problem by reducing the class of sources that can be stably reconstructed, and therefore, it can impact the achievable resolution. In addition, when the source is made of an arc of circumference, the number of degrees of freedom is reduced. The numerical results show how this affects the class of patterns that can be radiated and, consequently, be of interest in conformal sources antenna synthesis problems.

Multimodal, noninvasive seizure network mapping software: A novel tool for preoperative epilepsy evaluation

BackgroundDespite rigorous preoperative evaluation, epilepsy surgery achieves seizure freedom in only two-thirds of cases. Current preoperative evaluation does not include a detailed network analysis despite the association of network-level changes with epilepsy. ObjectiveWe sought to create a software algorithm to map individualized epilepsy networks by combining noninvasive electroencephalography (EEG) source localization and nonconcurrent resting state functional magnetic resonance imaging (rsfMRI). MethodsScalp EEG and rsfMRI data were acquired for three sample cases: one healthy control case, one case of right temporal lobe epilepsy, and one case of bitemporal seizure onset. Data from rsfMRI were preprocessed, and a time-series function was extracted. Connection coefficients were used to threshold out spurious connections and model global functional networks in a 3D map. Epileptic discharges were localized using a forward model of cortical mesh dipoles followed by an empirical Bayesian approach of inverse source reconstruction and co-registered with rsfMRI. Co-activating brain regions were mapped. ResultsThree illustrative sample cases are presented. In the healthy control case, the software showed symmetrical global connectivity. In the right temporal lobe epilepsy case, asymmetry was found in the global connectivity metrics with a paucity of connectivity ipsilateral to the epileptogenic cortex. The superior longitudinal fasciculus, uncinate fasciculus, and commissural fibers connecting disparate and discontinuous cortical regions involved in the epilepsy network were visualized. In the case with bitemporal lobe epilepsy, global connectivity was symmetric. It showed a network of correlating cortical activity local to epileptogenic tissue in both temporal lobes. The network involved white matter tracks in a similar pattern to those seen in the right temporal case. ConclusionsThis modeling algorithm allows better definition of the global brain network and potentially demonstrates differences in connectivity between an epileptic and a non-epileptic brain. This finding may be useful for mapping cortico-cortical connections representing the putative epilepsy networks. With this methodology, we localized the epileptogenic brain and showed network asymmetry and long-distance cortical co-activation. This software tool is the first to use a multimodal, nonconcurrent, and noninvasive approach to model and visualize the epilepsy network.

In-duct identification of a rotating sound source with high spatial resolution

To understand and reduce the flow noise generation from in-duct fluid machines, it is necessary to identify the acoustic source characteristics precisely. In this work, a source identification technique, which can identify the strengths and positions of the major sound radiators in the source plane, is studied for an in-duct rotating source. A linear acoustic theory including the effects of evanescent modes and source rotation is formulated based on the modal summation method, which is the underlying theory for the inverse source reconstruction. A validation experiment is conducted on a duct system excited by a loudspeaker in static and rotating conditions, with two different speeds, in the absence of flow. Due to the source rotation, the measured pressure spectra reveal the Doppler effect, and the amount of frequency shift corresponds to the multiplication of the circumferential mode order and the rotation speed. Amplitudes of participating modes are estimated at the shifted frequencies in the stationary reference frame, and the modal amplitude set including the effect of source rotation is collected to investigate the source behavior in the rotating reference frame. By using the estimated modal amplitudes, the near-field pressure is re-calculated and compared with the measured pressure. The obtained maximum relative error is about −25 and −10dB for rotation speeds at 300 and 600rev/min, respectively. The spatial distribution of acoustic source parameters is restored from the estimated modal amplitude set. The result clearly shows that the position and magnitude of the main sound source can be identified with high spatial resolution in the rotating reference frame.

Bayesian inversion and sequential Monte Carlo sampling techniques applied to nearfield acoustic sensor arrays

This paper demonstrates that inverse source reconstruction can be performed using a methodology of particle filters that relies primarily on the Bayesian approach of parameter estimation. The proposed approach is applied in the context of nearfield acoustic holography based on the equivalent source method (ESM). A state-space model is formulated in light of the ESM. The parameters to estimate are amplitudes and locations of the equivalent sources. The parameters constitute the state vector which follows a first-order Markov process with the transition matrix being the identity for every frequency-domain data frame. The implementation of recursive Bayesian filters involves a sequential Monte Carlo sampling procedure that treats the estimates as point masses with a discrete probability mass function (PMF) which evolves with iteration. It is evident from the results that the inclusion of the appropriate prior distribution is crucial in the parameter estimation.

Bayesian approach of nearfield acoustic reconstruction with particle filters

This paper demonstrates that inverse source reconstruction can be performed using a methodology of particle filters that relies primarily on the Bayesian approach of parameter estimation. In particular, the proposed approach is applied in the context of nearfield acoustic holography based on the equivalent source method (ESM). A state-space model is formulated in light of the ESM. The parameters to estimate are amplitudes and locations of the equivalent sources. The parameters constitute the state vector which follows a first-order Markov process with the transition matrix being the identity for every frequency-domain data frame. Filtered estimates of the state vector obtained are assigned weights adaptively. The implementation of recursive Bayesian filters involves a sequential Monte Carlo sampling procedure that treats the estimates as point masses with a discrete probability mass function (PMF) which evolves with iteration. The weight update equation governs the evolution of this PMF and depends primarily on the likelihood function and the prior distribution. It is evident from the simulation results that the inclusion of the appropriate prior distribution is crucial in the parameter estimation.

Source Reconstruction by Far-Field Data for Imaging of Defects in Frequency Selective Radomes

In this letter, an inverse source reconstruction method with great potential in radome diagnostics is presented. Defects, e.g., seams in large radomes, and lattice dislocations in frequency selective surface (FSS) radomes, are inevitable, and their electrical effects demand analysis. Here, defects in a frequency selective radome are analyzed with a method based on an integral formulation. Several far-field measurement series, illuminating different parts of the radome wall at 9.35 GHz, are employed to determine the equivalent surface currents and image the disturbances on the radome surface.

Comparative studies of l_p-regularization-based reconstruction algorithms for bioluminescence tomography

Inverse source reconstruction is the most challenging aspect of bioluminescence tomography (BLT) because of its ill-posedness. Although many efforts have been devoted to this problem, so far, there is no generally accepted method. Due to the ill-posedness property of the BLT inverse problem, the regularization method plays an important role in the inverse reconstruction. In this paper, six reconstruction algorithms based on lp regularization are surveyed. The effects of the permissible source region, measurement noise, optical properties, tissue specificity and source locations on the performance of the reconstruction algorithms are investigated using a series of single source experiments. In order to further inspect the performance of the reconstruction algorithms, we present the double sources and the in vivo mouse experiments to study their resolution ability and potential for a practical heterogeneous mouse experiment. It is hoped to provide useful guidance on algorithm development and application in the related fields.

Harmony: EEG/MEG linear inverse source reconstruction in the anatomical basis of spherical harmonics.

EEG/MEG source localization based on a “distributed solution” is severely underdetermined, because the number of sources is much larger than the number of measurements. In particular, this makes the solution strongly affected by sensor noise. A new way to constrain the problem is presented. By using the anatomical basis of spherical harmonics (or spherical splines) instead of single dipoles the dimensionality of the inverse solution is greatly reduced without sacrificing the quality of the data fit. The smoothness of the resulting solution reduces the surface bias and scatter of the sources (incoherency) compared to the popular minimum-norm algorithms where single-dipole basis is used (MNE, depth-weighted MNE, dSPM, sLORETA, LORETA, IBF) and allows to efficiently reduce the effect of sensor noise. This approach, termed Harmony, performed well when applied to experimental data (two exemplars of early evoked potentials) and showed better localization precision and solution coherence than the other tested algorithms when applied to realistically simulated data.

Recent advances in bioluminescence tomography: methodology and system as well as application

Optical molecular imaging has been rapidly developed to noninvasively visualize in vivo physiological and pathological processes involved in normal and suffering organisms at the cellular and molecular levels, in which advanced optical imaging technology and modern molecular biology are being combined to provide a state-of-the-art tool for preclinical biomedical research. Among optical molecular imaging modalities, bioluminescence tomography (BLT) has experienced considerable growth and attracted much attention in recent years for its excellent performance, unique advantages, and high cost-effectiveness. This article focuses on the genesis and development of BLT, especially for its computational methodology, imaging system, and biomedical application. An overview of the advantages and challenges of the conventional planar bioluminescence imaging technique is first described in comparison with currently available molecular imaging modalities. The imaging algorithms for inverse source reconstruction are classified and summarized according to different a priori knowledge, followed by a simple depiction of the uniqueness theorems of BLT solution. Diverse imaging systems for obtaining three-dimensional quantitative information of internal bioluminescent sources are then reviewed. The latest application examples of BLT in tumor study and drug discovery are introduced and compared with other mature imaging technologies. Finally, the paper is concluded and an attractive prospect for BLT ispredicted.

A critical assessment of connectivity measures for EEG data: A simulation study

Information flow between brain areas is difficult to estimate from EEG measurements due to the presence of noise as well as due to volume conduction. We here test the ability of popular measures of effective connectivity to detect an underlying neuronal interaction from simulated EEG data, as well as the ability of commonly used inverse source reconstruction techniques to improve the connectivity estimation. We find that volume conduction severely limits the neurophysiological interpretability of sensor-space connectivity analyses. Moreover, it may generally lead to conflicting results depending on the connectivity measure and statistical testing approach used. In particular, we note that the application of Granger-causal (GC) measures combined with standard significance testing leads to the detection of spurious connectivity regardless of whether the analysis is performed on sensor-space data or on sources estimated using three different established inverse methods. This empirical result follows from the definition of GC. The phase-slope index (PSI) does not suffer from this theoretical limitation and therefore performs well on our simulated data. We develop a theoretical framework to characterize artifacts of volume conduction, which may still be present even in reconstructed source time series as zero-lag correlations, and to distinguish their time-delayed brain interaction. Based on this theory we derive a procedure which suppresses the influence of volume conduction, but preserves effects related to time-lagged brain interaction in connectivity estimates. This is achieved by using time-reversed data as surrogates for statistical testing. We demonstrate that this robustification makes Granger-causal connectivity measures applicable to EEG data, achieving similar results as PSI. Integrating the insights of our study, we provide a guidance for measuring brain interaction from EEG data. Software for generating benchmark data is made available.

Recent advances in bioluminescence tomography: methodology and system as well as application

Optical molecular imaging has been rapidly developed to noninvasively visualize in vivo physiological and pathological processes involved in normal and suffering organisms at the cellular and molecular levels, in which advanced optical imaging technology and modern molecular biology are being combined to provide a state-of-the-art tool for preclinical biomedical research. Among optical molecular imaging modalities, bioluminescence tomography (BLT) has experienced considerable growth and attracted much attention in recent years for its excellent performance, unique advantages, and high cost-effectiveness. This article focuses on the genesis and development of BLT, especially for its computational methodology, imaging system, and biomedical application. An overview of the advantages and challenges of the conventional planar bioluminescence imaging technique is first described in comparison with currently available molecular imaging modalities. The imaging algorithms for inverse source reconstruction are classified and summarized according to different a priori knowledge, followed by a simple depiction of the uniqueness theorems of BLT solution. Diverse imaging systems for obtaining three-dimensional quantitative information of internal bioluminescent sources are then reviewed. The latest application examples of BLT in tumor study and drug discovery are introduced and compared with other mature imaging technologies. Finally, the paper is concluded and an attractive prospect for BLT is predicted.

Bioluminescence tomography based on the phase approximation model

A reconstruction method of bioluminescence sources is proposed based on a phase approximation model. Compared with the diffuse approximation, this phase approximation model more correctly predicts bioluminescence photon propagation in biological tissues, so that bioluminescence tomography can accurately locate and quantify the distribution of bioluminescence sources. The compressive sensing (CS) technique is applied to regularize the inverse source reconstruction to enhance numerical stability and efficiency. The numerical simulation and phantom experiments demonstrate the feasibility of the proposed approach.