Showing papers on "Kernel adaptive filter published in 1998"

A self-organizing state-space model

Abstract: A self-organizing filter and smoother for the general nonlinear non-Gaussian state-space model is proposed. An expanded state-space model is defined by augmenting the state vector with the unknown parameters of the original state-space model. The state of the augmented state-space model, and hence the state and the parameters of the original state-space model, are estimated simultaneously by either a non-Gaussian filter/smoother or a Monte Carlo filter/smoother. In contrast to maximum likelihood estimation of model parameters in ordinary state-space modeling, for which the recursive filter computation has to be done many times, model parameter estimation in the proposed self-organizing filter/smoother is achieved with only two passes of the recursive filter and smoother operations. Examples such as automatic tuning of dispersion and the shape parameters, adaptation to changes of the amplitude of a signal in seismic data, state estimation for a nonlinear state space model with unknown parameters. and seasonal adjustment with a nonlinear model with changing variance parameters are shown to exemplify the usefulness of the proposed method.

Oversampled filter banks

Abstract: Perfect reconstruction oversampled filter banks are equivalent to a particular class of frames in l/sup 2/(Z). These frames are the subject of this paper. First, the necessary and sufficient conditions of a filter bank for implementing a frame or a tight frame expansion are established, as well as a necessary and sufficient condition for perfect reconstruction using FIR filters after an FIR analysis. Complete parameterizations of oversampled filter banks satisfying these conditions are given. Further, we study the condition under which the frame dual to the frame associated with an FIR filter bank is also FIR and give a parameterization of a class of filter banks satisfying this property. Then, we focus on non-subsampled filter banks. Non-subsampled filter banks implement transforms similar to continuous-time transforms and allow for very flexible design. We investigate the relations of these filter banks to continuous-time filtering and illustrate the design flexibility by giving a procedure for designing maximally flat two-channel filter banks that yield highly regular wavelets with a given number of vanishing moments.

A game theoretic fault detection filter

Abstract: The fault detection process is approximated with a disturbance attenuation problem. The solution to this problem, for both linear time-varying and time-invariant systems, leads to a game theoretic filter which bounds the transmission of all exogenous signals except the fault to be detected. In the limit, when the disturbance attenuation bound is brought to zero, a complete transmission block is achieved by embedding the nuisance inputs into an unobservable, invariant subspace. Since this is the same invariant subspace structure seen in some types of detection filters, we can claim that the asymptotic game filter is itself a detection filter. One can also make use of this subspace structure to reduce the order of the limiting game theoretic filter by factoring this invariant subspace out of the state space. The resulting lower dimensional filter will then be sensitive only to the failure to be detected. A pair of examples given at the end of the paper demonstrate the effectiveness of the filter for time-invariant and time-varying problems in both full-order and reduced-order forms.

Theory and Methods

Abstract: A self-organizing filter and smoother for the general nonlinear non-Gaussian state-space model is proposed. An expanded state-space model is defined by augmenting the state vector with the unknown parameters of the original state-space model. The state of the augmented state-space model, and hence the state and the parameters of the original state-space model, are estimated simultaneously by either a non-Gaussian filter/smoother or a Monte Carlo filter/smoother. In contrast to maximum likelihood estimation of model parameters in ordinary state-space modeling, for which the recursive filter computation has to be done many times, model parameter estimation in the proposed self-organizing filter/smoother is achieved with only two passes of the recursive filter and smoother operations. Examples such as automatic tuning of dispersion and the shape parameters, adaptation to changes of the amplitude of a signal in seismic data, state estimation for a nonlinear state space model with unknown parameters, ...

A differential geometric approach to nonlinear filtering: the projection filter

Abstract: This paper presents a new and systematic method of approximating exact nonlinear filters with finite dimensional filters, using the differential geometric approach to statistics. The projection filter is defined rigorously in the case of exponential families. A convenient exponential family is proposed which allows one to simplify the projection filter equation and to define an a posteriori measure of the local error of the projection filter approximation. Finally, simulation results are discussed for the cubic sensor problem.

Adaptive weighted myriad filter algorithms for robust signal processing in /spl alpha/-stable noise environments

Abstract: Stochastic gradient-based adaptive algorithms are developed for the optimization of weighted myriad filters (WMyFs). WMyFs form a class of nonlinear filters, motivated by the properties of /spl alpha/-stable distributions, that have been proposed for robust non-Gaussian signal processing in impulsive noise environments. The weighted myriad for an N-long data window is described by a set of nonnegative weights {w/sub i/}/sub i=l//sup N/ and the so-called linearity parameter K>0. In the limit, as K/spl rarr//spl infin/, the filter reduces to the familiar weighted mean filter (which is a constrained linear FIR filter). Necessary conditions are obtained for optimality of the filter weights under the mean absolute error criterion. An implicit formulation of the filter output is used to find an expression for the gradient of the cost function. Using instantaneous gradient estimates, an adaptive steepest-descent algorithm is then derived to optimize the weights. This algorithm involves a very simple update term that is computationally comparable to the update in the classical LMS algorithm. The robust performance of this adaptive algorithm is demonstrated through a computer simulation example involving lowpass filtering of a one-dimensional chirp-type signal in impulsive noise.

Skewed approach to filtering

Abstract: The dynamics of many physical system are nonlinear and non- symmetric. The motion of a missile, for example, is strongly determined by aerodynamic drag whose magnitude is a function of the square of speed. Conversely, nonlinearity can arise from the coordinate system used, such as spherical coordinates for position. If a filter is applied these types of system, the distribution of its state estimate will be non-symmetric. The most widely used filtering algorithm, the Kalman filter, only utilizes mean and covariance and odes not maintain or exploit the symmetry properties of the distribution. Although the Kalman filter has been successfully applied in many highly nonlinear and non- symmetric system, this has been achieved at the cost of neglecting a potentially rich source of information. In this paper we explore methods for maintaining and utilizing information over and above that provided by means and covariances. Specifically, we extend the Kalman filter paradigm to include the skew and examine the utility of maintaining this information. We develop a tractable, convenient algorithm which can be used to predict the first three moments of a distribution. This is achieved by extending the sigma point selection scheme of the unscented transformation to capture the mean, covariance and skew. The utility of maintaining the skew and using nonlinear update rules is assessed by examining the performance of the new filter against a conventional Kalman filter in a realistic tracking scenario.

A pipelined LMS adaptive FIR filter architecture without adaptation delay

Abstract: Past methods for mapping the least-mean-square (LMS) adaptive finite-impulse-response (FIR) filter onto parallel and pipelined architectures either introduce delays in the coefficient updates or have excessive hardware requirements. We describe a hardware-efficient pipelined architecture for the LMS adaptive FIR filter that produces the same output and error signals as would be produced by the standard LMS adaptive filter architecture without adaptation delays. Unlike existing architectures for delayless LMS adaptation, the new architecture's throughput is independent of the filter length.

On adaptive filtering in oversampled subbands

Abstract: For a number of applications like acoustic echo cancellation, adaptive filters are required to identify very long impulse responses. To reduce the computational cost in implementations, adaptive filtering in subband is known to be beneficial. Based on a review of popular fullband adaptive filtering algorithms and various subband approaches, this thesis investigates the implementation, design, and limitations of oversampled subband adaptive filter systems based on modulated complex and real valued filter banks. The main aim is to achieve a computationally efficient implementation for adaptive filter systems, for which fast methods of performing both the subband decomposition and the subband processing are researched. Therefore, a highly efficient polyphase implementation of a complex valued modulated generalized DFT (GDFT) filter bank with a judicious selection of properties for non-integer oversampling ratios is introduced. By modification, a real valued single sideband modulated filter bank is derived. Non-integer oversampling ratios are particularly important when addressing the efficiency of the subband processing. Analysis is presented to decide in which cases it is more advantageous to perform real or complex valued subband processing. Additionally, methods to adaptively adjust the filter lengths in subband adaptive filter (SAF) systems are discussed. Convergence limits for SAFs and the accuracy of the achievable equivalent fullband model based on aliasing and other distortions introduced by the employed filter banks are explicitly derived. Both an approximation of the minimum mean square error and the model accuracy can be directly linked to criteria in the design of the prototype filter for the filter bank. Together with an iterative least-squares design algorithm, it is therefore possible to construct filter banks for SAF applications with pre-defined performance limits. Simulation results are presented which demonstrate the validity and properties of the discussed SAF methods and their advantage over fullband and critically sampled SAF systems.

Method and apparatus for adaptively reducing the level of noise in an acquired signal

Abstract: An adaptive filtering method and apparatus for reducing the level of an undesired noise component in an acquired physiological signal having a desired signal component. The acquired physiological signal is applied to one input of the adaptive filter, and a synthetic reference signal that is modeled so as to exhibit a correlation with the desired signal component is applied to another input of the adaptive filter. Thereafter, in a feedback manner, the adaptive filter iteratively adjusts the modeled synthetic reference signal so as to progressively generate a more accurate approximation of the desired signal component in the adaptive filter, which approximation becomes a reconstruction of the acquired physiological signal wherein the level of the undesired noise component is reduced.

Application of a wavelet adaptive filter to minimise distortion of the ST-segment

Abstract: A wavelet adaptive filter (WAF) for the removal of baseline wandering in ECG signals is described. The WAF consists of two parts. The first part is a wavelet transform that decomposes the ECG signal into seven frequency bands using Vaidyanathan-Hoang wavelets. The second part is an adaptive filter that uses the signal of the seventh lowest-frequency band among the wavelet transformed signals as primary input and a constant as reference input. To evaluate the performance of the WAF, two baseline wandering elimination filters are used, a commercial standard filter with a cutoff frequency of 0.5 Hz and a general adaptive filter. The MIT/BIH database and the European ST-T database are used for the evaluation. The WAF performs better in the average power of eliminated noise than the standard filter and adaptive filter. Furthermore, it shows a lower ST-segment distortion than the standard filter and the adaptive filter.

Selection of task-dependent diffusion filters for the post-processing of SPECT images.

Abstract: Iterative reconstruction from single photon emission computed tomography (SPECT) data requires regularization to avoid noise amplification and edge artefacts in the reconstructed image. This is often accomplished by stopping the iteration process at a relatively low number of iterations or by post-filtering the reconstructed image. The aim of this paper is to develop a method to automatically select an optimal combination of stopping iteration number and filters for a particular imaging situation. To this end different error measures between the distribution of a phantom and a corresponding filtered SPECT image are minimized for different iteration numbers. As a study example, simulated data representing a brain study are used. For post-reconstruction filtering, the performance of 3D linear diffusion (Gaussian filtering) and edge preserving 3D nonlinear diffusion (Catte scheme) is investigated. For reconstruction methods which model the image formation process accurately, error measures between the phantom and the filtered reconstruction are significantly reduced by performing a high number of iterations followed by optimal filtering compared with stopping the iterative process early. Furthermore, this error reduction can be obtained over a wide range of iteration numbers. Only a negligibly small additional reduction of the errors is obtained by including spatial variance in the filter kernel. Compared with Gaussian filtering, Catte diffusion can further reduce the error in some cases. For the examples considered, using accurate image formation models during iterative reconstruction is far more important than the choice of the filter.

Word-length optimization for high-level synthesis of digital signal processing systems

Abstract: Word-length optimization software is developed not only to reduce the hardware cost but also to minimize the optimization time. It inserts quantizers to a data flow graph representation, partitions the resultant graph, determines the minimum required word-length for each partitioned signal, conducts scheduling and binding using the minimum word-length information, and finally optimizes the word-lengths of functional units. Fixed-point simulation results are used as for the performance measure, thus this method can be applied to nonlinear and time-varying algorithms. Although this approach requires iterative fixed-point simulations, the search space is reduced significantly by grouping signals using the high-level synthesis, or hardware sharing, results. A fourth-order IIR filter, a fifth-order elliptic filter, and a 12th-order adaptive LMS filter are implemented using this software. The hardware cost of functional units is reduced by 25% in the IIR filter and 7% in the elliptic filter compared to the previous results.

Adaptive non-uniformity compensation algorithm

Abstract: An adaptive method for removing fixed pattern noise from focal plane array (FPA) imagery A set of correction terms (26) is applied to the focused image from the FPA, and a filter (24C) is applied to the corrected, focused image The set of correction terms is also applied to a blurred version of the FPA image, and the filter is applied to the corrected, blurred image Fixed pattern noise errors are then calculated using the filtered imagery, and employed to update the correction terms The updated correction terms are then used for processing the next image In one embodiment, the filter is an anti-median filter In another embodiment, the filter is an anti-mean filter

Adaptive reduced-rank residual correlation algorithms for DS-CDMA interference suppression

Abstract: A class of adaptive algorithms for DS-CDMA interference suppression is presented based on the multistage Wiener filter introduced by Goldstein and Reed (see IEEE Trans. Inform. Theory, vol. 44, no.7, 1998). Unlike the principal-components method for reduced-rank filtering this method performs well when the subspace spanned by the filter is less than the dimension of the signal subspace. We present block and recursive algorithms for estimating the filter parameters, which do not require matrix inversion or an eigen-decomposition The algorithm performance in the context of a heavily loaded DS-CDMA system is characterized via computer simulation.

Noise canceling method and apparatus for the same

Abstract: A noise canceler of the present invention is of the type including an adaptive filter for generating a pseudo noise signal, subtracting the pseudo noise signal from a received signal to thereby output an error signal, and sequentially correcting the filter coefficient of the filter in accordance with the error signal. A second adaptive filter produces a second pseudo noise signal and a second error signal. A first and a second power mean circuit each calculates the signal power of the respective signal. A divider performs division with the resulting two kinds of signal power, so that a signal-to-noise power ratio is estimated. A comparator compares the estimated signal-to-noise power ratio and a delayed version of the same and outputs greater one of them as an extended signal-to-noise power ratio. A step size output circuit corrects, based on the extended signal-to-noise power ratio and reference noise signal power output from a power mean circuit, a step size used to adaptively vary the filter coefficient of the first adaptive filter.

MRL-filters: a general class of nonlinear systems and their optimal design for image processing

Abstract: A class of morphological/rank/linear (MRL)-filters is presented as a general nonlinear tool for image processing. They consist of a linear combination between a morphological/rank filter and a linear filter. A gradient steepest descent method is proposed to optimally design these filters, using the averaged least mean squares (LMS) algorithm. The filter design is viewed as a learning process, and convergence issues are theoretically and experimentally investigated. A systematic approach is proposed to overcome the problem of nondifferentiability of the nonlinear filter component and to improve the numerical robustness of the training algorithm, which results in simple training equations. Image processing applications in system identification and image restoration are also presented, illustrating the simplicity of training MRL-filters and their effectiveness for image/signal processing.

Threshold Calibration in CLARIT Adaptive Filtering.

Abstract: In this paper, we describe the system and methods used for the CLARITECH entries in the TREC–7 Filtering Track. Our main aim was to study algorithms, designs, and parameters for Adaptive Filtering, as this comes closest to actual applications. For efficiency's sake, however, we adapted a system largely geared towards retrieval and introduced a few critical new components. The first of these components, the delivery ratio mechanism, is used to obtain a profile threshold when no feedback has been received. A second method, which we call beta–gamma regulation, is used for threshold updating. It takes into account the number of judged documents processed by the system as well as an expected bias in optimal threshold calculation. Several parameters were determined empirically: apart from the parameters pertaining to the new components, we also experimented with different choices for the reference corpus, and different "chunk" sizes for processing news stories. Gradually increasing chunk sizes over "time" appears to help profile learning. Finally, we examined the effect of terminating underperforming queries over the AP90 corpus and found that the utility metric over AP88–AP89 was a good predictor. All of the above innovations contributed to the success of the CLARITECH system in the adaptive filtering track.

Adaptive filtering for use with data compression and signal reconstruction

Abstract: A data compression system (200) employs an encoder (210) optimized to decorrelate and make independent from the original signal (202), the quantization noise produced during signal compression by a quantizer (214). Because the quantization noise produced during signal compression is made independent from and orthogonal (i.e., uncorrelated) to the original signal (202), filtering is achievable by filter (223) which is an adaptive oriented uncorrelated Weiner (AOW). The filter (223) adaptively selects a filter mask from a plurality of available filter masks. Mask selection is based, in part, upon either filter orientation or generation of a minimum variance output. Image component processing is performed on a local (e.g., pixel-by-pixel or 2-by-2) basis as opposed to a global basis (e.g., across the entire image).

Method and apparatus for filtering digital television signals

Abstract: A system for filtering digital television signals is provided. The system comprises a generator for providing a first data sequence to a private data packetizer, and a transmitter for transmitting the packetized first data sequence in a data channel of a digital television signal. The system further includes a receiver for receiving the digital television signal and recovering the first data sequence. The receiver includes a channel estimator for providing an estimate of channel characteristics, such as estimated channel impulse estimate and estimated noise variance. The receiver further includes an adaptive equalizer filter having an input for receiving the digital television signal and an input for receiving adaptive filter coefficients. The receiver further includes a coefficient processor for calculating adaptive filter coefficients based on the channel estimate, and providing the adaptive filter coefficients to the adaptive equalizer filter. The digital television signal is thus filtered to remove undesired channel effects.

Adaptive equalization using a minimum- jitter criterion

Abstract: An adaptive equalizer is implemented using digital feedback control and using jitter as the adjustment criteria. An adjustable transfer function is implemented to equalize an input signal to enhance the frequency response of the associated system. Jitter is determined for the filtered signal, and the frequency response of the transfer function is varied accordingly by applying a digital adjustment signal to the transfer function structure (for example, a lead-lag filter). The adaptive equalizer can thereby adapt to various transmission medium lengths and signal degradation levels.

Comparison of reduced-rank signal processing techniques

Abstract: This paper compares several reduced-rank signal processing algorithms for adaptive sensor array processing. The comparisons presented here use Monte Carlo analysis to evaluate the algorithmic performance as a function of both rank and sample support when the covariance matrix is unknown and estimated from collected sensor data. The adaptive techniques considered are the principal components algorithm, the cross-spectral metric and the multistage Wiener filter. It is shown that the new multistage Wiener filtering technique provides more robust performance as a function of both rank and sample support.

Direct reconstruction of cone-beam data acquired with a vertex path containing a circle

Abstract: Cone-beam data acquired with a vertex path satisfying the data sufficiency condition of Tuy can be reconstructed using exact filtered backprojection algorithms. These algorithms are based on the application to each cone-beam projection of a two-dimensional (2-D) filter that is nonstationary, and therefore more complex than the one-dimensional (1-D) ramp filter used in the approximate algorithm of Feldkamp, Davis, and Kress (1984) (FDK). We determine in this paper the general conditions under which the 2-D nonstationary filter reduces to a 2-D stationary filter, and also give the explicit expression of the corresponding convolution kernel. Using this result and the redundancy of the cone-beam data, a composite algorithm is derived for the class of vertex paths that consist of one circle and some complementary subpath designed to guarantee data sufficiency. In this algorithm the projections corresponding to vertex points along the circle are filtered using a 2-D stationary filter, whereas the other projections are handled with a 2-D nonstationary filter. The composite algorithm generalizes the method proposed by Kudo and Saito (1990), in which the circle data are processed with a 1-D ramp filter as in the FDK algorithm. The advantage of the 2-D filter introduced in this paper is to guarantee that the filtered cone-beam projections do not contain singularities in smooth regions of the object. Tests of the composite algorithm on simulated data are presented.

On existence of FIR principal component filter banks

Abstract: In this paper we have two interesting results. One is of theoretical interest and the other practical. The theoretical result is that the optimum FIR orthonormal filter bank of a fixed finite degree that maximizes the coding gain does not always contain an optimum compaction filter. In other words, in general, there does not exist a principal component filter bank (PCFB) of a given nonzero degree. This is sharply in contrast to the cases of transform coders and ideal subband coders where the existence of PCFB's are assured by their very construction. The practical result of the paper is that constraining the filter corresponding to the largest subband variance to be a compaction filter does not result in a significant loss of performance for practical input signals. Since there exist very efficient methods to design FIR compaction filters and since the best completion of the filter bank given the first filter is trivially done by a KLT, we see that this is an extremely efficient method despite the fact that it is suboptimum.

Phase-only LMS and perturbation adaptive algorithms

Abstract: The author defines a phase-only gradient-based adaptive algorithm analogous to the least mean square (LMS) algorithm. Two phase-only perturbation algorithms are then defined. It is shown that the gradient for the perturbation algorithms can be obtained by cross-correlating binary perturbation sequences, that are applied to the adaptive phases, with the resulting instantaneous output power or voltage. It is also shown that a single set of phase-only adaptive weights can be used to simultaneously null interference in multiple output beams. Simulation results are presented for all of the new algorithms. The phase-only perturbation techniques eliminate the need for element level receivers and support low cost retrofitting of adaptive nulling on phased arrays by using conventional beamsteering circuits to apply the adaptive weights.

Multichannel parametric adaptive matched filter receiver

Abstract: Apparatus and method for improving the detection of signals obscured by either correlated Gaussian or non-Gaussian noise plus additive white Gaussian noise using Estimates from multi-channel data of model parameters that describe the noise disturbance correlation are obtained from data that contain signal-free data vectors, referred to as “secondary” or “reference” cell data. These parameters form the coefficients of a multi-channel whitening filter. A data vector to be tested for the presence of a signal passes through the multi-channel whitening filter. The filter's output is then processed to form a test statistic. The test statistic is compared to a threshold value to decide whether a signal is “present” or “absent”. Embodiments of the apparatus and method include estimating the signal amplitude both implicitly and explicitly and calculating test statistics for signal detection in both Gaussian and non-Gaussian noise.