Projection Filter Research Articles

フィルタ理論に基づくフレーム構造物の損傷同定解析

The structural damage identification analysis of structure models were performed by filtering algorithms as a frame work of inverse problem. In this study, three kinds of filtering algorithm based on the Wiener filter, the projection filter and the parametric projection filter were employed to detect the structural damage of a five-story frame model defined by the reduction of lateral stiffness. Natural frequencies corresponding to each eigen-mode measured by the experimental modal analysis are effectively used as the observation data characterized by the change of structural stiffness. The notable characteristics of each filtering algorithm in applying the structural damage identification analysis are made clear through several numerical calculations.

2101 メッシュレス有限要素法-フィルタ理論による弾性定数の分布同定解析(J02-1 逆問題解析手法の開発と最新応用(1),J02 逆問題解析手法の開発と最新応用)

One numerical solution approach to identification analysis of distribution of elastic constants is discussed. In our inverse analysis, the meshless finite element method is used to determine displacements of an elastic body and the filtering algorithms are utilized to identify elastic constants of sampling points. Applicability of our method is shown through comparison of distributions on two-dimensional elastic constant given by the Kalman filter and the parametric projection filter.

Optimal Sampling Operator for Signal Restoration in the Presence of Signal Space and Observation Space Noises

The partial projection filter (PTPF) for a given observation operator provides an optimal signal restoration in the presence of both the signal space and observation space noises. However, restoration error by the filter still depends on the observation operator which consists of measurement and sampling processes. In this paper, we determine a sampling operator which minimizes the restoration error by the PTPF. We see that under some assumptions about noise statistics, the restoration error by the PTPF is divided into two terms corresponding to the error arising from the signal space noise and that from the observation space noise. It has been found that although the restoration error due to the signal space noise is independent of the sampling operator, the restoration error arising from the observation space noise can arbitrarily be decreased by increasing the number of sample points in the proposed sampling operator. An illustrative example of optimal sampling in the trigonometric polynomial space is also given.

THEORETICAL ANALYSIS OF A TIME-FREQUENCY-PCNN AUDITORY CORTEX MODEL

A particular pulsed neural model of the auditory cortex, the Time-Frequency Pulse Coupled Neural Network (TF-PCNN), has shown to decompose its stimulus from the cochlea into characteristic pulse-coded time-frequency (TF) stop and pass regions. A derived sum of spectrograms representation with these zero- or one-valued TF weightings has already been applied for the denoising of speech in a previous work. This decomposition is now related to the concept of TF projection filters, which allows to reinterpret the model equations. The functionality imposed by the model equations can so be accessed and justified from a TF signal processing perspective, in addition to its biological motivation from experimentally observed neurophysiological behavior and simulations.

Quantum projection filter for a highly nonlinear model in cavity QED

Both in classical and quantum stochastic control theory a major role is played by the filtering equation, which recursively updates the information state of the system under observation. Unfortunately, the theory is plagued by infinite-dimensionality of the information state which severely limits its practical applicability, except in a few select cases (e.g. the linear Gaussian case.) One solution proposed in classical filtering theory is that of the projection filter. In this scheme, the filter is constrained to evolve in a finite-dimensional family of densities through orthogonal projection on the tangent space with respect to the Fisher metric. Here we apply this approach to the simple but highly nonlinear quantum model of optical phase bistability of a stongly coupled two-level atom in an optical cavity. We observe near-optimal performance of the quantum projection filter, demonstrating the utility of such an approach.

Artefact elimination in spatiotemporal cortical dipole layer imaging with parametric projection filter

We explore suitable spatiotemporal filters for inverse estimation of an equivalent cortical dipole layer (DL) distribution from the scalp electroencephalogram (EEG) for imaging of brain electric sources. We have previously developed the parametric projection filter (PPF)-based cortical dipole layer imaging technique, which allows estimating cortical dipole layer inverse solutions in the presence of noise covariance. We have expanded the PPF to the time-varying filter in order to handle the spatiotemporally varying nature of brain electrical activity. The present simulation results indicate that the estimation error is reduced substantially by taking the spatiotemporal properties of the noise into consideration, such as eye-blink artefacts, and the proposed time-variant PPF method provides enhanced performance in rejecting time-varying noise.

The adjoint filter operator in large-eddy simulation of turbulent flow

Adjoint and self-adjoint filter operators are introduced, such that large-eddy simulation (LES) with a spatially variable filter width satisfies important physical properties: Conservation of momentum and dissipation of kinetic energy. The combination of an arbitrary nonuniform explicit filter with the Smagorinsky model leads to a new model of the turbulent stress tensor, which includes backscatter, while the total subgrid dissipation is still positive (analytically). Nonuniform filter theory is further developed, in order to provide a more solid foundation of practical LES. The paper distinguishes between three sets of equations: The Navier–Stokes equations (which are physical conservation laws), the filtered equations and the modeled large-eddy equations. It is shown that general filtering of the Navier–Stokes equations destroys their local and global conservation properties. However, it is proven that the adjoint of a normalized filter is conservative. As a result, the filtering equations are globally conservative, for special nonuniform (e.g., self-adjoint) filters. Implications for six subgrid-models that require explicit filter operations are considered, such as dynamic, similarity, filtering multiscale, and relaxation models. Incorporation of the adjoint filter analytically ensures several models to conserve momentum and dissipate kinetic energy. Examples of adjoint and self-adjoint filters are also provided, including a “three-points” self-adjoint filter and an adjoint filter that is applicable on unstructured grids. In addition, it is shown that positive nonuniform (self-adjoint) filters satisfy mathematical smoothing properties. The focus is on kernel filters, but projection filters are also discussed, and nonuniform self-adjoint Laplace filters are defined. The (orthogonal) projection operator is proven to be a nonuniform kernel filter.

Spatio-temporal cortical source imaging of brain electrical activity by means of time-varying parametric projection filter.

In the present study, we explore suitable spatio-temporal filters for inverse estimation of an equivalent dipole-layer distribution from the scalp electroencephalogram (EEG) for imaging of brain electric sources. We propose a time-varying parametric projection filter (tPPF) for the spatio-temporal EEG analysis. The performance of this tPPF algorithm was evaluated by computer simulation studies. An inhomogeneous three-concentric-spheres model was used in the present simulation study to represent the head volume conductor. An equivalent dipole layer was used to represent equivalently brain electric sources and estimated from the scalp potentials. The tPPF filter was tested to remove time-varying noise such as instantaneous artifacts caused by eyes-blink. The present simulation results indicate that the proposed time-variant tPPF method provides enhanced performance in rejecting time-varying noise, as compared with the time-invariant parametric projection filter.

Cortical Potential Imaging of Brain Electrical Activity by Means of Parametric Projection Filter

The objective of this study was to explore suitable spatial filters for inverse estimation of cortical potentials from the scalp electroencephalogram. The effect of incorporating noise covariance into inverse procedures was examined by computer simulations and tested in human experiment. The parametric projection filter, which allows inverse estimation with the presence of information on the noise, was applied to an inhomogeneous three-concentric-sphere model under various noise conditions in order to estimate the cortical potentials from the scalp potentials. The method for determining the optimum regularization parameter, which can be applied for parametric inverse techniques, is also discussed. Human visual evoked potential experiment was carried out to examine the performance of the proposed restoration method. The parametric projection filter gave more localized inverse solution of cortical potential distribution than the truncated SVD and Tikhonov regularization. The present simulation results suggest that incorporation of information on the noise covariance allows better estimation of cortical potentials, than inverse solutions without knowledge about the noise covariance, when the correlation between the signal and noise is low.

Design of kinematic DGNSS filters with consistent error covariance information

Consistent and realistic error covariance information is important for position estimation, error analysis, fault detection, and integer ambiguity resolution for the applications of global navigation satellite systems. In designing a position domain carrier-smoothed-code filter where incremental carrier-phases are used for time-propagation, formulation of consistent error covariance information is not easy due to correlation of successive propagation noises. To provide consistent and correct error covariance information, two recursive filter algorithms are proposed based on carrier-smoothed-code techniques: the stepwise optimal position projection filter, and the stepwise unbiased position projection filter. A Monte Carlo simulation result shows that the proposed filter algorithms actually generate consistent error covariance information and the neglecting of carrier-phase noise induces optimistic error covariance information. It is also shown that the stepwise unbiased position projection filter is attractive since its performance is good and its computational burden is moderate.

Mean-Square Performance of a Family of Affine Projection Algorithms

Affine projection algorithms are useful adaptive filters whose main purpose is to speed the convergence of LMS-type filters. Most analytical results on affine projection algorithms assume special regression models or Gaussian regression data. The available analysis also treat different affine projection filters separately. This paper provides a unified treatment of the mean-square error, tracking, and transient performances of a family of affine projection algorithms. The treatment relies on energy conservation arguments and does not restrict the regressors to specific models or to a Gaussian distribution. Simulation results illustrate the analysis and the derived performance expressions.

The possibility of increasing the spatial resolution in diffusion optical tomography

This paper discusses the possibility of increasing the resolution of diffusion optical tomography, using the method of average photon trajectories. It is shown that this method makes it possible to use fast reconstruction algorithms based on both iterative algebraic procedures and integral transformations with filtering of projections. The latter case not only suppresses the discretization noise but also substantially compensates the diffusion smearing of the reconstructed images.

Correlation spectroscopy with diffractive grating synthetic spectra and orthogonal subspace projection filters

We evaluate the feasibility of implementing correlation spec- troscopy for remote sensing with a passive IR sensor that incorporates a diffractive grating on which a synthetic spectrum is imbedded. The spec- tral diffraction reflectances of diffractive gratings are measured and com- pared to the theoretical design spectra and to the library absorbance spectra. Five gratings are evaluated: sulfur hexafluoride (SF6), ((dimethoxyphosphinothioyl)thio)butanedioic acid, diethyl ester (malathion), diisopropyl-methylphosphonate (DIMP), methylphosphono- fluoridic acid,(1-methylethyl) ester (Sarin or GB), and O-ethyl-S-(2- diisopropylamino)ethyl methylphosphonothioate (VX). While the gratings were designed from liquid phase infrared spectra, the measurements and models provide a satisfactory proof of principle for the exploitation of synthetic spectra in correlation spectroscopy. The predicted noise equivalent concentration pathlength (NECL) for detecting GB and VX in a desert environment is computed for distances up to 5 km. The device was found to have high sensitivity in terms of NECL. The selectivity of the grating is found to be poor, but can be improved dramatically with the use of orthogonal subspace projection (OSP) filters that reduce the false alarm (improve selectivity) from misidentifying a GB as VX (and vice versa) at the ''cost'' of a slight increase of the NECL (reduce sensitivity). © 2003 Society of Photo-Optical Instrumentation Engineers. (DOI: 10.1117/1.1531638) Subject terms: correlation spectroscopy; infrared spectroscopy; orthogonal sub- space projection (OSP); vapor detection; false alarm; diffractive optics; synthetic spectra.

337 連成系の逆解析に用いるためのパラメトリック射影フィルタの特性について

This paper is concerned with the inverse analysis of the fluid coupled system by coupled free vibration analysis, in combination with filtering algorithm. The structural damage analysis is generally formulated as an inverse problem. The formulated inverse problem must be analyzed under the consideration of stochastic properties on the response of structural system. The filtering algorithms have been known as one of the inverse analysis method. In this study, algorithm based on parametric projection filter is employed as new analytical algorithm on the inverse analysis. The coupled natural frequencies used as the observations and stochastic properties of system responses adopted the data obtained by experimental modal analysis. From identification results, adaptability and characteristics of the algorithm based on parametric projection filter are made clear through the inverse analysis of the fluid-structure interaction coupled system.

Image restoration by the family of signal adaptive parametric projection filters

AbstractMany of the image restoration techniques can roughly be classified into two types: those that are formulated as an optimization problem with regard to the restored image and those that are formulated as an optimization problem with regard to the restoration operator. The former has the advantage that the local information on the image can easily be expressed in the optimization reference. A problem is that the closeness of the image needs to be evaluated indirectly in the observation image space instead of the original image space. On the other hand, in the latter the closeness of the image can be evaluated in the original image space. However, because the optimization reference used to obtain the appropriate restoration operator does not include the information on the individual images, it is difficult to express the local information on the image, in contrast to the former type. Based on such a background, the objective of this paper is to propose a restoration method that can evaluate the closeness of images in the original image space while the local information on the images can be used systematically, based on improvement of the optimization reference of the parametric projection filter family belonging to the latter. The effectiveness of the proposed method is verified by numerical examples. © 2002 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 86(3): 77–86, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.1142

Image restoration by the family of M‐N‐norm parametric projection filters

AbstractIn image restoration, if knowledge about the unknown original image could be used, reflecting that knowledge in the restoration process would enable effective restoration. However, in statistical image restoration that employs the family of projection filters or the family of parametric projection filters, the knowledge cannot be information other than information that limits the range in which the original image belongs to a linear subspace and limits the spatial measures to decisions based on the variance structure of the image population. We propose a family of signal‐adaptive parametric projection filters that introduces knowledge about the image that should solve this problem in the form of Pareto optimization. In this paper, we construct a family of filters that can reflect knowledge about the image in the spatial measures as a new approach. We also present an example illustrating the construction of the measures and prove the effectiveness of these filters through numerical examples. © 2002 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 85(11): 9–17, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.10008

Optimizing of recurrence plots for noise reduction.

We propose a way to automatically detect the best neighborhood size for a local projective noise reduction filter, where a typical problem is the proper identification of the noise level. Here we make use of concepts from the recurrence quantification analysis in order to adaptively tune the filter along the incoming time series. We define an index, to be computed via recurrence plots, whose minimum gives a clear indication of the best size of the neighborhood in the embedding space. Comparison of the local projective noise reduction filter using this optimization scheme with the state of the art is also provided.

Equivalent dipole source imaging of brain electric activity by means of parametric projection filter.

In the present study, spatial filters for inverse estimation of an equivalent dipole layer from the scalp-recorded potentials have been explored for their suitability in achieving high-resolution electroencephalogram (EEG) imaging. The performance of the parametric projection filter (PPF), which we propose to use for high-resolution EEG imaging, has been evaluated by computer simulations in the presence of a priori information on noise. An inhomogeneous three-concentric-sphere head model was used in the present simulation study to represent the head volume conductor. An equivalent dipole layer was used to model brain electric sources and estimated from the scalp potentials. Various noise conditions were simulated and the parametric projection filter was compared with standard regularization procedures such as the truncated singular value decomposition (TSVD) and the Tikhonov regularization (TKNV). The present simulation results suggest that the proposed method performs better than that of commonly used inverse regularization techniques, such as the general inverse using the TSVD and the TKNV, when the correlation between the original source distribution and the noise distribution is low, and performs similarly when the correlation is high. A method for determining the optimum regularization parameter, which can be applied to parametric inverse techniques, has also been developed.

AM-FM Interference Excision in Spread Spectrum Communications via Projection Filtering

Recently, Amin et al. introduced a projection filtering method for excising constant amplitude FM jammers from DSSS communications, with minimal distortion to the PN sequence. In this paper, we show that this approach can be applied to AM-FM jammers as well, with a simple modification. Theoretical performance measures (correlator SNR) of the AM-FM projection method are derived, and demonstrate that near ideal performance is achieved for unbiased estimates of the jammer parameters. Results showing the effects of estimation errors in the AM and FM of the jammer on SNR are also provided. In general, FM errors cause greater performance degradation than the same level of error in estimating the AM.

フィルタリングアルゴリズムを用いた大型浮遊式海洋建築物模型の損傷同定解析

This paper is concerned with the identification analysis of structural damage detection on the unit-linked floating structure model based on fluid-coupled free vibration equation and filtering algorithm. The problem of structural damage detection is formulated as an inverse problem in structural engineering. The formulated inverse problem must be analyzed under the consideration of stochastic properties on the responses of system because the observations of the system are usually measured in the presence of noise. The filtering algorithm has been well known as the solution method that is able to consider stochastic properties. In this paper two kinds of filtering algorithm, namely the extended Kalman filtering algorithm and new filtering algorithm based on the projection filter, are employed in the identification analysis. The coupled natural frequencies used as the observations and stochastic properties of system responses adopted the data obtained by experimental modal analysis.