Statistical independence in nonlinear model-based inversion for quantitative photoacoustic tomography

Modeling errors produced by differences between an actual electrical source in the heart and a model of the source have effects on least squares error (LSE) solutions for the model. These effects are analyzed using linear algebra theory and some modeling errors representative of those for actual heart measurements. It is found that increasing the number of dipoles in a multiple-dipole (MD) model increases the sensitivity of the solutions to small modeling error changes while increasing the number of terms in a multipole expansion (ME) model is likely to improve the accuracy of the solution for the dipolar terms. The results show that a MD model with more than two free-orientation dipoles will not provide accurate, useful, or reliable information for the representative modeling errors. Accurate solutions for the dipolar terms in a ME model are obtained for a model containing dipole, quadrupole, and octupole terms for these modeling errors. A new type of “average” LSE (AVL) solution for MD models with fixed-orientation dipoles is developed and compared with LSE and nonnegative LSE (NNL) solutions; the AVL solutions are found to be least sensitive to small modeling error changes but to provide misleading information for certain modeling errors. Finally, it is found that once a certain density of measurements is reached, the effects of modeling errors are nearly independent of the measurements used and, hence, no improvement in the solutions can be obtained by increasing the number of measurements.

Crosshole seismic tomography often is applied to image the velocity structure of an interwell medium. If the rocks are anisotropic, the tomographic technique must be adapted to the complex situation; otherwise, it leads to a false interpretation. We propose a nonlinear kinematic inversion method for crosshole seismic tomography in composite transversely isotropic media with known dipping symmetry axes. This method is based on a new version of the first-order traveltime perturbation equation. It directly uses the derivative of the phase velocity rather than the eigenvectors of the body-wave modes to overcome the singularity problem for application to the two quasi-shear waves. We applied an iterative nonlinear solver incorporating our kinematic ray-tracing scheme and directly compute the Jacobian matrix in an arbitrary reference medium. This reconstructs the five elastic moduli or Thomsen parameters from the first-arrival traveltimes of the three seismic body waves (qP, qSV, qSH) in strongly and weakly anisotropic media. We conducted three synthetic experiments that involve determining anisotropic parameters for a homogeneous rock, reconstructing a fault embedded in a strongly anisotropic background, and imaging a complicated four-layer model containing a small channel and a buried dipping interface. We compared results of our nonlinear inversion method with isotropic tomography and the traditional linear anisotropic inversion scheme, which showed the capability and superiority of the new scheme for crosshole tomographic imaging.

This paper presents a new method for amplitude versus offset(AVO) nonlinear inversion that solved by support vector machine(SVM).First the main principle of SVM is described,then the SVM model are established for AVO inversion.Finally,both real data and synthetic model are inverted based on SVM,the results show that the proposed method can resolve limitations associated with conventional inversion methods without sacrificing inversion effects;it can extract elastic parameters from synthetic seismogram directly;meanwhile the method is characterized by high inversion velocity and good stability.

Prestack amplitude versus offset (AVO) inversion is an essential tool to estimate elastic properties. Approximations of P-wave reflection coefficients based on the Zoeppritz equation are limited by the assumption of weak contrast and are inaccurate for far offset, and the existing nonlinear inversion method, like ant colony optimization (ACO), cannot converge to the global optimal solution within a limited time. Consequently, we propose a nonlinear AVO inversion method based on the exact Zoeppritz equation using hybrid quantum ant colony optimization (HQACO). The Zoeppritz equation is a forward modeling approach with high accuracy at far offset and is valid at the strong-contrast interface. HQACO, as a global optimization algorithm, not only has the potential of ACO to search global solutions but also exploits the power of quantum computing to speed up optimization procedures. The self-adaptive rotating strategy is proposed to improve the flexibility and efficiency of the conventional quantum rotating gate largely. Moreover, the quantum gate is introduced to enhance the global search ability. Numerical results show that the average evaluation number required for the global solution decreases largely and the solution converges to the global optimal solution closely using the proposed method. Synthetic applications verify that HQACO shows the most reliable exploring competence to find the global solution. The new inversion method is not only suitable for the strong-contrast interface with noise but also shows promising accuracy using the wide offset range.

Model error is one of the key factors restricting the accuracy of numerical weather prediction (NWP). Considering the continuous evolution of the atmosphere, the observed data (ignoring the measurement error) can be viewed as a series of solutions of an accurate model governing the actual atmosphere. Model error is represented as an unknown term in the accurate model, thus NWP can be considered as an inverse problem to uncover the unknown error term. The inverse problem models can absorb long periods of observed data to generate model error correction procedures. They thus resolve the deficiency and faultiness of the NWP schemes employing only the initial-time data. In this study we construct two inverse problem models to estimate and extrapolate the time-varying and spatial-varying model errors in both the historical and forecast periods by using recent observations and analogue phenomena of the atmosphere. Numerical experiment on Burgers' equation has illustrated the substantial forecast improvement using inverse problem algorithms. The proposed inverse problem methods of suppressing NWP errors will be useful in future high accuracy applications of NWP.

Identifiability analysis of Prandtl–Ishilinskii hysteresis model with saturation

Independent components analysis (ICA) maximizes the statistical independence of the representational components of a training image ensemble, but it cannot distinguish between the different factors, or modes, inherent to image formation, including scene structure, illumination, and imaging. We introduce a nonlinear, multifactor model that generalizes ICA. Our multilinear ICA (MICA) model of image ensembles learns the statistically independent components of multiple factors. Whereas ICA employs linear (matrix) algebra, MICA exploits multilinear (tensor) algebra. We furthermore introduce a multilinear projection algorithm which projects an unlabeled test image into the N constituent mode spaces to simultaneously infer its mode labels. In the context of facial image ensembles, where the mode labels are person, viewpoint, illumination, expression, etc., we demonstrate that the statistical regularities learned by MICA capture information that, in conjunction with our multilinear projection algorithm, improves automatic face recognition.

Reticle systems are considered to be the classical approach for estimating the position of a target in a considered field of view and are widely used in IR seekers. Due to the simplicity and low cost, since only a few detectors are used, reticle seekers are still in use and are subject of further research. However, the major disadvantage of the reticle trackers has been proven to be sensitivity on the IR countermeasures. To resolve this problem modification of optical trackers is analyzed here for a wide class of reticles that are producing frequency or amplitude modulated signals either by nutation or by spinning. When Independent Component Analysis (ICA) algorithms are applied on the outputs of appropriately modified trackers the reticle type dependent transmission functions, also called the source signals in the context of the ICA theory, can be recovered on the basis of the output signals only. Position of each optical source is obtained by applying appropriate demodulation method on the recovered source signals. The three conditions necessary for the ICA theory to work (statistical independence and non-Gaussianity of the source signals and nonsingularity of the mixing matrix) are shown to be fulfilled in principle for any kind of the reticle geometry. In relation to some IR counter-countermeasures algorithms which are based on heuristic and sometimes unrealistic assumptions (target performs no maneuvering) the approach exposed here has been proven to be theoretically consistent without any special constraints imposed on the optical sources.

Decomposition of working memory-related scalp ERPs: Crossvalidation of fMRI-constrained source analysis and ICA

A method of structural damage identification using harmonic excitation force is presented. It considers the effects of both measurement and modelling errors in the baseline finite element model. Damage that accompanies changes in structural parameters can be estimated for a damaged structure from the change between measured vibration responses and ones calculated from the analytical model of the intact structure. In practice, modelling errors exist in the analytical model due to material and geometric uncertainties and a reduction in the degrees of freedom as well as measurement errors, making identification difficult. To surmount these problems, bootstrap hypothesis testing, which enables statistical judgment without information about these errors, was introduced. The method was validated by numerical simulation using a three-dimensional frame structure and real vibration data for a three-storey steel frame structure. Copyright © 2005 John Wiley & Sons, Ltd.

The common mode error (CME) and optimal noise model are the two most important factors affecting the accuracy of time series in regional Global Navigation Satellite System (GNSS) networks. Removing the CME and selecting the optimal noise model can effectively improve the accuracy of GNSS coordinate time series. The CME, a major source of error, is related to the spatiotemporal distribution; hence, its detrimental effects on time series can be effectively reduced through spatial filtering. Independent component analysis (ICA) is used to filter the time series recorded by 79 GPS stations in Antarctica from 2010 to 2018. After removing stations exhibiting strong local effects using their spatial responses, the filtering results of residual time series derived from principal component analysis (PCA) and ICA are compared and analyzed. The Akaike information criterion (AIC) is then used to determine the optimal noise model of the GPS time series before and after ICA/PCA filtering. The results show that ICA is superior to PCA regarding both the filter results and the consistency of the optimal noise model. In terms of the filtering results, ICA can extract multisource error signals. After ICA filtering, the root mean square (RMS) values of the residual time series are reduced by 14.45%, 8.97%, and 13.27% in the east (E), north (N), and vertical (U) components, respectively, and the associated speed uncertainties are reduced by 13.50%, 8.06% and 11.82%, respectively. Furthermore, different GNSS time series in Antarctica have different optimal noise models with different noise characteristics in different components. The main noise models are the white noise plus flicker noise (WN+FN) and white noise plus power law noise (WN+PN) models. Additionally, the spectrum index of most PN is close to that of FN. Finally, there are more stations with consistent optimal noise models after ICA filtering than there are after PCA filtering.

This paper presents an efficient three-dimensional nonlinear electromagnetic inversion method in a multilayered medium for geophysical exploration. The stabilized biconjugate-gradient fast Fourier transform algorithm is used for forward modeling, whereas the distorted Born iterative method is used in the inversion. The conjugate-gradient method is applied at each inversion iteration to minimize the cost function. The usage of an iterative solver based on the FFT algorithm and the developed recursive matrix method combined with an interpolation technique to evaluate the layered medium Green's functions rapidly, make this method highly efficient, with the requirement of very low time and memory, O (N log N ) and O (N) respectively. Numerical experiments about the 3D forward modeling with application in Borehole to Surface Electromagnetic Method will be presented in this paper; in addition, we will show the examples about 3D inversion applied in geophysical exploration. All these results will demonstrate the high efficiency and accuracy of the proposed method.

Quality Management (QM) is one of the key supply chain processes. Previous studies have shown that QM provides a major contribution to the supply chain performance. One area that is essential in the managing of quality is Statistical Process Control (SPC). Control chart is one of the quality tools used in SPC for achieving process stability, controlling process and improving process by the reduction of process variations. Numerous techniques have been used to identify the presence of unnatural control chart patterns (CCPs); however, these approaches mostly focus on recognizing basic CCPs from a single type of unnatural assignable cause. In the situation where a mixture of CCPs exist, where more than one type of unnatural variation exist at the same time within the manufacturing process, this mixture of CCPs might be incorrectly classified. The Independent Component Analysis (ICA) technique has been applied recently to separate independent components from a mixture of two basic CCPs. This technique tries to maximize the statistical independence of the mixing components and uses kurtosis or a fourth-cumulant as a measure of non-Gaussianity, which implies statistical independence. Therefore, the CCP mixture separation performance and accuracy of using ICA greatly depend on kurtosis values and distributions of the basic CCPs. This paper will investigate the impact of the kurtosis values and distributions of basic CCPs on the effectiveness of the ICA-based approach in terms of being able to separate basic CCPs from a mixture, when using neural network as the pattern classifier.

Corticomuscular coupling analysis, i.e., examining the relations between simultaneously recorded brain (e.g., electroencephalography--EEG) and muscle (e.g., electro-myography-EMG) signals, is a useful tool for understanding aspects of human motor control. Traditionally, the most popular method to assess corticomuscular coupling has been the pairwise magnitude-squared coherence (MSC) between EEG and concomitant EMG recordings. In this paper, we propose assessing corticomuscular coupling by combining partial least squares (PLS) and independent component analysis (ICA), which addresses many of the limitations of MSC, such as difficulty in robustly assessing group inference and relying on the biologically implausible assumption of pairwise interaction between brain and muscle recordings. In the proposed framework, response relevance and statistical independence are jointly incorporated into a multiobjective optimization function to meaningfully combine the goals of PLS and ICA under the same mathematical umbrella. Simulations, performed under realistic assumptions, illustrated the utility of such an approach. The method was extended to address intersubject variability to robustly discover common corticomuscular coupling patterns across subjects. We then applied the proposed framework to concurrent EEG and EMG data collected in a Parkinson's disease (PD) study. The results from applying the proposed technique revealed temporal components in the EEG and EMG that were significantly correlated with one another. In addition to the expected motor areas, the corresponding spatial activation patterns demonstrated enhanced occipital connectivity in PD subjects, consistent with previous studies suggesting that PD subjects rely excessively on visual information to counteract the deficiency in being able to generate internal commands from their affected basal ganglia.

The local field potential (LFP), the low-frequency part of the extracellular potential, reflects transmembrane currents in the vicinity of the recording electrode. Thought mainly to stem from currents caused by synaptic input, it provides information about neural activity complementary to that of spikes, the output of neurons. However, the many neural sources contributing to the LFP, and likewise the derived current source density (CSD), can often make it challenging to interpret. Efforts to improve its interpretability have included the application of statistical decomposition tools like principal component analysis (PCA) and independent component analysis (ICA) to disentangle the contributions from different neural sources. However, their underlying assumptions of, respectively, orthogonality and statistical independence are not always valid for the various processes or pathways generating LFP. Here, we expand upon and validate a decomposition algorithm named Laminar Population Analysis (LPA), which is based on physiological rather than statistical assumptions. LPA utilizes the multiunit activity (MUA) and LFP jointly to uncover the contributions of different populations to the LFP. To perform the validation of LPA, we used data simulated with the large-scale, biophysically detailed model of mouse V1 developed by the Allen Institute. We find that LPA can identify laminar positions within V1 and the temporal profiles of laminar population firing rates from the MUA. We also find that LPA can estimate the salient current sinks and sources generated by feedforward input from the lateral geniculate nucleus (LGN), recurrent activity in V1, and feedback input from the lateromedial (LM) area of visual cortex. LPA identifies and distinguishes these contributions with a greater accuracy than the alternative statistical decomposition methods, PCA and ICA. The contributions from different cortical layers within V1 could however not be robustly separated and identified with LPA. This is likely due to substantial synchrony in population firing rates across layers, which may be reduced with other stimulus protocols in the future. Lastly, we also demonstrate the application of LPA on experimentally recorded MUA and LFP from 24 animals in the publicly available Visual Coding dataset. Our results suggest that LPA can be used both as a method to estimate positions of laminar populations and to uncover salient features in LFP/CSD contributions from different populations.