Optimal Linear Filter Research Articles

Linear and non-linear approaches to solve the inverse problem: applications to positron annihilation experiments

We present linear and non-linear filters to solve the ill-posed inverse problem and we use them to extract relevant information from positron lifetime and 2D-angular correlation of the annihilation radiation of positrons in solids. A general optimal linear filter is first derived. Then a second linear approach, based on Bayes' theorem, is described. We show that these two linear approaches are indeed equivalent. Two non-linear methods are then discussed. The first is a Bayesian approach which makes use of the maximum entropy principle. The second is an iterative method derived from the general optimal linear filter. Applications of these filtering techniques to positron lifetime decay curves illustrate how lifetimes shorter than the instrumental resolution can be extracted. Finally, we apply the iterative non-linear filter to the problem of the ridge-like Fermi surface on the high temperature superconducting compound YBa 2Cu 3O 7−δ. For the first time a direct measurement of the ridge width through a Brillouin zone is obtained. It is compared with results of band structure calculations.

Smoothing for linear systems erxcited by point processes with state–dependent rates

Smoothing for a linear system driven by a marked point process with a rate that depends on the state of the system is considered. A linear combination of the states is observed in additive white Gaussian noise. A smoother that uses estimation and detection is simulated on a computer and its mean squared error (MSE) is compared with the theoretical MSE of the optimal linear smoother and filter. The falso alarm rate is shown to depend strongly on the region of support of the mark distribution. When false alarms are low, the estimation/detection scheme has lower MSE than the optimal linear smoother.

A fast algorithm for optimal linear interpolation

A fast algorithm for computing the optimal linear interpolation filter is developed. The algorithm is based on the Sherman-Morrison inversion formula for symmetric matrices. The relationship between the derived algorithm and the Levinson algorithm is illustrated. It is shown that the new algorithm, in comparison with the well-known algorithms, requires fewer multiplications and hence is of lower complexity. >

Experimental study of the signal-to-noise ratio of stochastic resonance systems.

Electric analog circuits are used to simulate stochastic resonance (SR) systems. It is found that the signal-to-noise ratio (SNR) obtained by the SR device can exceed the upper limit of the SNR obtained by the optimal linear filter. By applying two SR devices successively, the SNR obtained by the SR devices may be about eight times larger than that of the optimal linear filter.

Detectability of the gravitational wave signal from a close neutron star binary with mass transfer

view Abstract Citations (25) References (13) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Detectability of the Gravitational Wave Signal from a Close Neutron Star Binary with Mass Transfer Jaranowski, Piotr ; Krolak, Andrzej Abstract Two simple analytical model of a neutron star binary with mass transfer corresponding to different equations of state are developed. The members of the binary are assumed to move along Newtonian orbits, and the quadrupole formula is used to determine gravitational radiation. The detectability of the gravitational wave signal from such a system by laser interferometers with optimal linear filtering is calculated. Publication: The Astrophysical Journal Pub Date: August 1992 DOI: 10.1086/171610 Bibcode: 1992ApJ...394..586J Keywords: Binary Stars; Gravitational Waves; Neutron Stars; Stellar Mass Accretion; Computational Astrophysics; Laser Interferometry; Mass Transfer; Signal To Noise Ratios; Stellar Models; Astrophysics; STARS: BINARIES: CLOSE; RADIATION MECHANISMS: GRAVITATIONAL; STARS: NEUTRON; TECHNIQUES: INTERFEROMETRIC full text sources ADS |

On a Schur-algorithm based approach to spectral factorization: connection with the Riccati equation

This paper points out a connection between the Schur algorithm and the difference Riccati equation arising in linear optimal filtering. It is shown that a special version of the Schur algorithm leads to a Chandrasekhar-type algorithm.

Two methods for Toeplitz-plus-Hankel approximation to a data covariance matrix

Recently, fast algorithms have been developed for computing the optimal linear least squares prediction filters for nonstationary random processes (fields) whose covariances have (block) Toeplitz-Hankel form. If the covariance of the random process (field) must be estimated from the data, the following problem is presented: given a data covariance matrix, computer from the available data, find the Toeplitz-plus-Hankel matrix closest to this matrix in some sense. The authors give two procedures for computing the Toeplitz-plus-Hankel matrix that minimizes the Hilbert-Schmidt norm of the difference between the two matrices. The first approach projects the data covariance matrix onto the subspace of Toeplitz-plus-Hankel matrices, for which basis functions can be computed using a Gram-Schmidt orthonormalization. The second approach projects onto the subspace of symmetric Toeplitz plus skew-persymmetric Hankel matrices, resulting in a much simpler algorithm. The extension to block Toeplitz-plus-Hankel data covariance matrix approximation is also addressed. >

Optimum linear filter of PPM receiver

AbstractThis paper considers the problem of an optimum linear filter on the receiving side of the PPM transmission system in which both the additive noise and the signal‐dependent noise exist. The optimum filter for the PPM transmission derived in this paper is the one in which the mean‐square value (MSE) of the timing error is minimized at the location of the pulse detection. In contrast to the optimum filter in the PAM transmission which maximizes the signal‐to‐noise ratio in the amplitude direction, the present optimum filter is of a different type which maximizes this ratio in the time‐axis direction.In this paper, the general equation which the optimum filter must satisfy is derived as an equation containing the previous research results. Subsequently, the timing error, optimum pulse detection level and the configurations of the filter on the receiving side and of the pulse location detector are presented. It is pointed out that, by the use of the optimum filter derived in this paper, baseband multiplexed transmission systems using pulses can be realized easily by combining the PAM and PPM systems. The method for multiplexing and the receiver configuration are shown.

A comparative analysis of several transformations for enhancement and segmentation of magnetic resonance image scene sequences

The performance of the eigenimage filter is compared with those of several other filters as applied to magnetic resonance image (MRI) scene sequences for image enhancement and segmentation. Comparisons are made with principal component analysis, matched, modified-matched, maximum contrast, target point, ratio, log-ratio, and angle image filters. Signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), segmentation of a desired feature (SDF), and correction for partial volume averaging effects (CPV) are used as performance measures. For comparison, analytical expressions for SNRs and CNRs of filtered images are derived, and CPV by a linear filter is studied. Properties of filters are illustrated through their applications to simulated and acquired MRI sequences of a phantom study and a clinical case; advantages and weaknesses are discussed. The conclusion is that the eigenimage filter is the optimal linear filter that achieves SDF and CPV simultaneously.

Microstatistics in signal decomposition and the optimal filtering problem

The author introduces and analyzes a large class of nonlinear filters which are based on signal decomposition and where the estimation in the decomposed space uses linear combinations of either the observation vector, the sorted observation vector, or, in general, a nonlinear transformation of the observation vector. Thus, nonlinear filter response characteristics are achieved, but with the machinery of linear systems theory available for their optimization and design. It is shown that linear filters are a subclass of microstatistic filters and that the optimal linear filter solution is suboptimal in the decomposed signal space. The filtering problem reduces to a set of filters operating on the decomposed signals; the output is a weighted sum of the decomposed filtered signals. The optimal interconnection structure between decomposed signals has complexity O(M-1), where M is the cardinality of the decomposition. The formulation is given for a radix-1 decomposition and generalized for a radix-q decomposition. Computer simulations illustrate the performance. >

Optimal mean-square N-observation digital morphological filters : II. Optimal gray-scale filters

The second part of this two-part study interprets digital gray-scale morphological operations as numerical functionals on integer-valued vectors. The result is a gray-scale morphological statistical estimation theory based on N observation random variables and a consequent theory of mean-square optimization. Whereas in the binary setting the search for optimal structuring elements is clearly restricted by the requirement of binary N-vector structuring elements, gray-scale structuring elements are N-vectors of integers (not confined to the range of the images). Thus, it is necessary to find a set of structuring elements from which both singleand multiple-erosion filters can be optimized, the latter being characterized within the framework of the gray-scale Matheron representation. Consequently, a significant part of the paper is concerned with the derivation of the fundamental set, this set being a minimal family of structuring elements from which it is always possible to select the erosions comprising an optimal filter. As in the case of binary optimization, we treat constrained optimality; however, here we apply it to construction of optimal linear filters. Finally, we demonstrate that erosion optimization is equivalent to dilation optimization.

A coupled rainfall-runoff and runoff-routing model for adaptive real-time flood forecasting

This paper describes an adaptive hydrologic modelling technique for real-time flood forecasting. The modelling approach is based on a linear stochastic time-varying representation of the rainfall-runoff process and on the Muskingum routing method formulated as an optimal linear filtering problem. The most general stochastic rainfall-runoff model used for linear forecasting is known as the transfer function noise model. An on-line identification procedure based on an extension of the recursive Instrumental Variable estimator is discussed. The routing procedure, based on the Muskingum method, is written in a state-space representation. This allows real-time updating of the state and the system parameters by means of Kalman filtering. The described method is used to forecast extreme flood events for the River Ourthe (drainage basin: approx 3626 km2), one of the main tributaries of the River Meuse, Belgium. The method is compared with stationary modelling procedures and its superiority based on objective forecasting criteria is demonstrated.

An explicit solution of the linear filtering problem for certain classes of nonrational spectral densities

We present an explicit solution of the problem of optimal linear filtering: the recovery of the “useful signal”ξ(s) at the instantt+τ, (τ>0,τ<0, orτ=0) from known values of the received signalρ(s)=ξ(s)+η(s) in the “past,” i.e., at the instantt−s, s≥0. In doing so we assume the random processesξ(s) and /gr(s) are stationary and jointly stationary, while the stationary process of “noise” η(s) with zero mean is assumed to be mutually correlated and jointly stationary with the processξ(s) under the assumption that there exists a common spectral densityfɛη(λ) for these processes.

Accuracy bounds for the solution of the linear optimal filtering problem in the presence of colored noise in the observations

Accuracy bounds for the solution of the linear optimal filtering problem in the presence of colored noise in the observations

Nonlinear techniques for interference suppression in spread-spectrum systems

The binary nature of direct-sequence signals is exploited to obtain nonlinear filters that outperform the linear filters hitherto used for this purpose. The case of a Gaussian interferer with known autoregressive parameters is considered. Using simulations, it is shown that an approximate conditional mean (ACM) filter of the Masreliez type performs significantly better than the optimum linear (Kalman-Bucy) filter. For the case of interferers with unknown parameters, the nature of the nonlinearity in the ACM filter is used to obtain an adaptive filtering algorithm that is identical to the linear transversal filter except that the previous prediction errors are transformed nonlinearly before being incorporated into the linear prediction. Two versions of this filter are considered: one in which the filter coefficients are updated using the Widrow LMS algorithm, and another in which the coefficients are updated using an approximate gradient algorithm. Simulations indicate that the nonlinear filter with LMS updates performs substantially better than the linear filter for both narrowband Gaussian and single-tone interferers, whereas the gradient algorithm gives slightly better performance for Gaussian interferers but is rather ineffective in suppressing a sinusoidal interferer. >

Optimal linear phase digital filter design by one-phase linear programming

An improved linear programming algorithm for the design of optimal linear-phase FIR filters with extra time-domain or frequency-domain constraints is presented. After stating the problem as involving the minimization of a linear function of filter parameters with linear constraints, a method is given for choosing an initial basic feasible solution of the dual problem that does not require the introduction of artificial variables. This significantly reduces the number of iterations of the revised simplex algorithm needed to reach the optimal solution.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Bayesian Filtering for Discrete-Time Systems with Random Structure

Nonlinear filtering problem for discrete-time systems with random structure is treated by the systematic use of Bayes approach. The main result lies in difference equations for the posterior distribution of the system state and structure index which can serve as a basis for any optimal or suboptimal filter construction. The optimal filtering equations have such a structure that even in the linear Gaussian case optimal finite-dimensional filters do not exist. An approximate filtering problem is considered.

Application of multivariate geostatistics to macroprobe mappings in steels.

X-ray mappings on very large samples are used for the studies of segregations in steel. This has some consequences in terms of electron beam defocusing, calibration and time of acquisition.To minimize this time, it is possible to increase the signal to noise ratio by using optimal linear filters. Traditionally these filtes are used in a univariate case, but as well study many elements simultaneously, the calculation of cross-correlations between elements allows a generalization of these filters to the multivariate case. The model is described with the assumption of a locally stationary phenomenon.It can give the principal components of the spatial structure (i.e., synthetic images at different scales). This facilitates the next step which is to characterize the segregations by classical image analysis of the X-ray mappings. Application to an industrial program of reduction of segregation is presented.

Innovation approach to reduced-order estimation of complementary states.

A reduced-order filler algorithm is developed for estimation of the complementary states of a linear system driven by white noise. The estimator gives an unbiased estimate of the states, and the error in the estimate is orthogonal to the subspace of the observations of those states that are common to the observations and the estimated states, The filter performance is suboptimal relative to the full-order optimal linear filter, but benefits are reaped from computational savings in the filtering and associated Riccati equations. The algorithms are developed using a concept of the ‘reduced-order innovation process’. The design uses only a priori information for z, the states to be estimated. The estimator is shown to be unique. The requirements of the stability of the filter are also presented, and its determination can precede its implementation. The basic limitation of this approach is that one is constrained by the minimum order of the filter, because of the assumption in (2.11) that the states to be est...

An extension of the split Levinson algorithm and its relatives to the joint process estimation problem

It is shown that the split Levinson algorithm, the split Schur algorithm, and the split lattice algorithm to compute the reflection coefficients of the optimal linear prediction filter for a discrete-time stationary stochastic process can be extended to the more general case of the joint process estimation problem. The new algorithms are essentially based on well-defined recurrence relations for symmetric prediction filters and symmetric estimation filters. They are more economical than the standard methods in terms of storage space and number of arithmetic operations. >