Singular value decomposition-based reconstruction algorithm forseismic traveltime tomography

A reconstruction method is given for seismic transmission traveltime tomography. The method is implemented via the combinations of singular value decomposition, appropriate weighting matrices, and variable regularization parameter. The problem is scaled through the weighting matrices so that the singular spectrum is normalized. Matching the normalized singular values, a regularization parameter varies within the interval [0, 1], and linearly increases with singular value index from a small, initial value rather than a fixed one to eliminate the impacts of smaller singular values' components. The experimental results show that the proposed method is superior to the ordinary singular value decomposition (SVD) methods such as truncated SVD and Tikhonov (1977) regularization.     

Adaptive identification of nonminimum phase ARMA models usinghigher order cumulants alone

An adaptive identification algorithm for causal nonminimum phase ARMA models in additive colored Gaussian noise is proposed. The algorithm utilizes higher order cumulants of the observed signal alone. It estimates the AR and MA parameters successively in each iteration without computing the residual time series. The steepest descent method is used for parameter updating     

Semiblind identification of nonminimum-phase ARMA models via orderrecursion with higher order cumulants

This paper develops a novel identification methodology for nonminimum-phase autoregressive moving average (ARMA) models of which the models' orders are not given. It is based on the third-order statistics of the given noisy output observations and assumed input random sequences. The semiblind identification approach is thereby named. By the order-recursive technique, the model orders and parameters can be determined simultaneously by minimizing well-defined cost functions. At each updated order, the AR and MA parameters are estimated without computing the residual time series (RTS), with the result of decreasing the computational complexity and memory consumption. Effects of the AR estimation error on the MA parameters estimation are also reduced. Theoretical statements and simulations results, together with practical application to the train vibration signals' modeling, illustrate that the method provides accurate estimates of unknown linear models, despite the output measurements being corrupted by arbitrary Gaussian noises of unknown pdf     

Characterization and estimation of two-dimensional ARMA models

A class of finite-order two-dimensional autoregressive moving average (ARMA) is introduced that can represent any process with rational spectral density. In this model the driving noise is correlated and need not be Gaussian. Currently known classes of ARMA models or AR models are shown to be subsets of the above class. The three definitions of Markov property are discussed, and the class of ARMA models are precisely stated which have the noncausal and semicausal Markov property without imposing any specific boundary conditions. Next two approaches are considered to estimate the parameters of a model to fit a given image. The first method uses only the empirical correlations and involves the solution of linear equations. The second method is the likelihood approach. Since the exact likelihood function is difficult to compute, we resort to approximations suggested by the toroidal models. Numerical experiments compare the quality of the two estimation schemes. Finally the problem of synthesizing a texture obeying an ARMA model is considered.     

ARMA models, prewhitening, and minimum cross entropy

The problem of spectral estimation on the basis of observations from a finite stretch of a stationary time series is considered, in connection with knowledge of a prior estimate of the spectral density. A reasonable posterior spectral density estimate would be the density that is closest to the prior according to some measure of divergence, while at the same time being compatible with the data. The cross entropy has often been proposed to serve as such a measure of divergence. A correction of the original minimum-cross-entropy spectral analysis (MCESA) method of J.E. Shore (see IEEE Trans. Acoust. Speech Signal Process, vol.29, p.230-7, 1981) to traditional prewhitening techniques and to autoregressive moving average (ARMA) models is pointed out and a fast approximate solution of the minimum cross entropy problem is proposed. The solution is in a standard multiplicative form, that is, the posterior is equal to the prior multiplied by a correction factor     

ARMA model order selection for 2D-FD-LS algorithm based on groupingmeasure

A new approach to model order selection for the two-dimensional frequency domain least square (2D-FD-LS) algorithm is proposed. The approach is based on a proposed grouping measure. Analysis and simulation results demonstrate the applicability of the new approach     

An analog architecture on parameter estimation of ARMA models

An analog architecture that is suitable for parameter estimation of autoregressive moving average (ARMA) models is proposed. The convergence theorem that connects this architecture with ARMA parameter estimation is presented. Simulation results indicate that its convergence takes only a few microseconds. Hence, this architecture can lead to online implementations     

An application of time-dependent ARMA models to reliability-decay processes

This paper describes a somewhat different approach to the analysis of failure data of systems that operate under varying operational and/or environmental conditions. Surprisingly enough, it was found during the course of investigations that if the failure times of a system follow either Rayleigh, Weibull or exponential distributions and if the reliability-decay process of the system is represented by an AR(1) model with a specific time-dependent coefficient in each case, then the conditional mean of the AR(1) process, given that the initial value is equal to 1, is the same as the maximum likelihood estimate of the reliability function obtained by the classical method. Advantages of such a representation are discussed in a later section. Properties of time-dependent ARMA(1, 1) processes are discussed and asymptotic results are obtained in the last section.     

Recursive scheme for ARMA coefficient and order estimation withnoisy input-output data

A novel estimation scheme for determining ARMA orders and coefficients is presented. The system is assumed to be excited by a non-Gaussian random sequence. Third-order cumulants of the input-output data are introduced to eliminate additive Gaussian noise of unknown variances at the measurement site. The proposed algorithm is performed order-recursively until the estimated coefficients converge where the defined norm of error squares (NES) nearly stays at a constant value. The system orders thereby need not be known a priori. Theoretical analyses together with experimental results indicate that the system orders can be accurately determined with the same procedures while the corresponding system coefficients are being estimated     

Singular value analysis of deformable systems

Singular value analysis, balancing, and approximation of a class of deformable systems are investigated. The deformable systems considered herein include several important cases of flexible aerospace vehicles and are characterized by countably infinitely many poles and zeros on the imaginary axis. The analysis relies completely on the so-called asymptotic singular value decompositon of the Hankel operator associated with the impulse response of the system. A parametric study of a six-dimensional single-input single-output case is performed.This research was supported by AFOSR Grant 80-0013 and by the Joint Services Electronics Program through AFOSR/AFSC under Contract No. F44620-71-C-0067.     

ARMA-cepstrum Recursion Algorithm for the Estimation of the MA Parameters of 2-D ARMA Models

This paper considers the problem of estimating the moving average (MA) parameters of a two-dimensional autoregressive moving average (2-D ARMA) model. To solve this problem, a new algorithm that is based on a recursion relating the ARMA parameters and cepstral coefficients of a 2-D ARMA process is proposed. On the basis of this recursion, a recursive equation is derived to estimate the MA parameters from the cepstral coefficients and the autoregressive (AR) parameters of a 2-D ARMA process. The cepstral coefficients are computed benefiting from the 2-D FFT technique. Estimation of the AR parameters is performed by the 2-D modified Yule–Walker (MYW) equation approach. The development presented here includes the formulation for real-valued homogeneous quarter-plane (QP) 2-D ARMA random fields, where data are propagated using only the past values. The proposed algorithm is computationally efficient especially for the higher-order 2-D ARMA models, and has the advantage that it does not require any matrix inversion for the calculation of the MA parameters. The performance of the new algorithm is illustrated by some numerical examples, and is compared with another existing 2-D MA parameter estimation procedure, according to three performance criteria. As a result of these comparisons, it is observed that the MA parameters and the 2-D ARMA power spectra estimated by using the proposed algorithm are converged to the original ones     

Singular higher order complete vector bases for finite methods

This paper presents new singular curl- and divergence-conforming vector bases that incorporate the edge conditions. Singular bases complete to arbitrarily high order are described in a unified and consistent manner for curved triangular and quadrilateral elements. The higher order basis functions are obtained as the product of lowest order functions and Silvester-Lagrange interpolatory polynomials with specially arranged arrays of interpolation points. The completeness properties are discussed and these bases are proved to be fully compatible with the standard, high-order regular vector bases used in adjacent elements. The curl (divergence) conforming singular bases guarantee tangential (normal) continuity along the edges of the elements allowing for the discontinuity of normal (tangential) components, adequate modeling of the curl (divergence), and removal of spurious modes (solutions). These singular high-order bases should provide more accurate and efficient numerical solutions of both surface integral and differential problems. Sample numerical results confirm the faster convergence of these bases on wedge problems.     

Combining pattern recognition techniques with Akaike's informationcriteria for identifying ARMA models

ARMA models are identified by combining pattern recognition techniques with Akaike's (1974, 1979) information criteria. First, pattern vectors of ARMA models are obtained by the extended sample autocorrelation functions method proposed by Tsay and Tiao (1984). Second, decision functions of various training samples are specified by the perceptron algorithm used in learning machines. Third, Akaike's AIC and BIC criteria are introduced. The practical utility of the proposed approach is illustrated by both simulated and practical data     

Parameter estimation for noncausal ARMA models of non-Gaussiansignals via cumulant matching

We consider the problem of estimating the parameters of a stable (stationary), scalar ARMA(p,q) signal model driven by an i.i.d. non-Gaussian sequence. The driving noise sequence is not observed. The signal is allowed to be nonminimum phase and/or noncausal (i.e., poles may lie both inside as well as outside the unit circle). We address the problem of parameter identifiability given the higher order cumulants of the signal on a finite set of lags. The sufficient set of lags required to achieve parameter identifiability is the smallest to date. The sufficient conditions for parameter identifiability are also the least restrictive to date. We also propose a frequency-domain approach for time-domain, nonlinear optimization of a quadratic cumulant matching criterion. Illustrative computer simulation results are presented     

ADAPTIVE ALGORITHM FOR CONSISTENTMA PARAMETER ESTIMATION VIATHIRD ORDER CUMULANT

This paper addresses the problem of adaptive,consistent parameter estimation for a MA model from the 3rd order cumulant of the system output. The proposed adaptive algorithm is derived by using the new linear equation system (J. K. Tugnait, 1990), which is proved to have unique solution,and hence guarantees the consistence of the MA parameters. Simulation results are provided to show the performance of the new algorithm.     

Diffusion augmented complex adaptive IIR algorithm for training widely linear ARMA models

In this paper, our aim is to propose a fully distributed adaptive algorithm for learning the parameters of a widely linear autoregressive moving average model by measurements collected by a network. To this end, we consider a connected network where every node uses the augmented complex adaptive infinite impulse response (ACA-IIR) filter as the learning rule. We firstly formulate the learning problem as an optimization problem and resort to stochastic gradient optimization argument to solve it and derive the proposed algorithm, which will be referred to as diffusion ACAIIR (DACA-IIR) algorithm. We also introduce a reduced-complexity version of the DACA-IIR algorithm. We use both synthetic and real-world signals in our simulations where the results show that the proposed cooperative algorithm outperforms the noncooperative solution.     

Maximum likelihood estimation of the parameters of nonminimum phaseand noncausal ARMA models

The well-known prediction-error-based maximum likelihood (PEML) method can only handle minimum phase ARMA models. This paper presents a new method known as the back-filtering-based maximum likelihood (BFML) method, which can handle nonminimum phase and noncausal ARMA models. The BFML method is identical to the PEML method in the case of a minimum phase ARMA model, and it turns out that the BFML method incorporates a noncausal ARMA filter with poles outside the unit circle for estimation of the parameters of a causal, nonminimum phase ARMA model     

Mixture models with higher order moments

The authors present a novel method for mixed pixel classification where the classification of groups of mixed pixels is achieved by taking into consideration the higher order moments of the distributions of the pure and the mixed classes. The equations expressing the relationship between the higher order moments are used to augment the set of equations that express the relationship between the means only. The authors show that weighting these equations does not make the set of equations available less reliable. As a consequence, the number of equations can be increased and thus more classes than available bands can be identified. The method is exhaustively tested using simulated data and is also applied to real Landsat TM data for which ground data are available     

Singular value decomposition for approximate block matching inimage coding

The minimum Euclidean distance matching of a 2-D image block can be reorganised, via singular value decomposition, into a set of computations with the block's singular vectors. The first two or three pairs of singular vectors are usually sufficient to achieve a good approximation, calculated with fewer operations than Euclidean matching. Full search motion estimation can be speeded up by at least a factor of 2, with minimal loss of accuracy