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Showing papers on "Kernel adaptive filter published in 2010"


Book
01 Mar 2010
TL;DR: Kernel Adaptive Filtering is the first book to present a comprehensive, unifying introduction to online learning algorithms in reproducing kernel Hilbert spaces and addresses the principal bottleneck of kernel adaptive filterstheir growing structure.
Abstract: Online learning from a signal processing perspective There is increased interest in kernel learning algorithms in neural networks and a growing need for nonlinear adaptive algorithms in advanced signal processing, communications, and controls. Kernel Adaptive Filtering is the first book to present a comprehensive, unifying introduction to online learning algorithms in reproducing kernel Hilbert spaces. Based on research being conducted in the Computational Neuro-Engineering Laboratory at the University of Florida and in the Cognitive Systems Laboratory at McMaster University, Ontario, Canada, this unique resource elevates the adaptive filtering theory to a new level, presenting a new design methodology of nonlinear adaptive filters. Covers the kernel least mean squares algorithm, kernel affine projection algorithms, the kernel recursive least squares algorithm, the theory of Gaussian process regression, and the extended kernel recursive least squares algorithm Presents a powerful model-selection method called maximum marginal likelihood Addresses the principal bottleneck of kernel adaptive filterstheir growing structure Features twelve computer-oriented experiments to reinforce the concepts, with MATLAB codes downloadable from the authors' Web site Concludes each chapter with a summary of the state of the art and potential future directions for original research Kernel Adaptive Filtering is ideal for engineers, computer scientists, and graduate students interested in nonlinear adaptive systems for online applications (applications where the data stream arrives one sample at a time and incremental optimal solutions are desirable). It is also a useful guide for those who look for nonlinear adaptive filtering methodologies to solve practical problems.

551 citations


MonographDOI
12 Feb 2010

334 citations


Journal ArticleDOI
TL;DR: A robust filter in a batch-mode regression form to process the observations and predictions together, making it very effective in suppressing multiple outliers, and results revealed that this filter compares favorably with the H¿-filter in the presence of outliers.
Abstract: A new robust Kalman filter is proposed that detects and bounds the influence of outliers in a discrete linear system, including those generated by thick-tailed noise distributions such as impulsive noise. Besides outliers induced in the process and observation noises, we consider in this paper a new type called structural outliers. For a filter to be able to counter the effect of these outliers, observation redundancy in the system is necessary. We have therefore developed a robust filter in a batch-mode regression form to process the observations and predictions together, making it very effective in suppressing multiple outliers. A key step in this filter is a new prewhitening method that incorporates a robust multivariate estimator of location and covariance. The other main step is the use of a generalized maximum likelihood-type (GM) estimator based on Schweppe's proposal and the Huber function, which has a high statistical efficiency at the Gaussian distribution and a positive breakdown point in regression. The latter is defined as the largest fraction of contamination for which the estimator yields a finite maximum bias under contamination. This GM-estimator enables our filter to bound the influence of residual and position, where the former measures the effects of observation and innovation outliers and the latter assesses that of structural outliers. The estimator is solved via the iteratively reweighted least squares (IRLS) algorithm, in which the residuals are standardized utilizing robust weights and scale estimates. Finally, the state estimation error covariance matrix of the proposed GM-Kalman filter is derived from its influence function. Simulation results revealed that our filter compares favorably with the H?-filter in the presence of outliers.

295 citations


Proceedings ArticleDOI
26 Jul 2010
TL;DR: A new formulation of the PHD filter which distinguishes between persistent and newborn objects is presented, and numerical simulations indicate a significant improvement in the estimation accuracy of the proposed SMC-PHD filter.
Abstract: The paper makes two contributions. First, a new formulation of the PHD filter which distinguishes between persistent and newborn objects is presented. This formulation results in an efficient sequential Monte Carlo (SMC) implementation of the PHD filter, where the placement of newborn object particles is determined by the measurements. The second contribution is a novel method for the state and error estimation from an SMC implementation of the PHD filter. Instead of clustering the particles in an ad-hoc manner after the update step (which is the current approach), we perform state estimation and, if required, particle clustering, within the update step in an exact and principled manner. Numerical simulations indicate a significant improvement in the estimation accuracy of the proposed SMC-PHD filter.

170 citations


Journal ArticleDOI
TL;DR: Results show that ASWM provides better performance in terms of PSNR and MAE than many other median filter variants for random-valued impulse noise and can preserve more image details in a high noise environment.
Abstract: A new Adaptive Switching Median (ASWM) filter for removing impulse noise from corrupted images is presented. The originality of ASWM is that no a priori Threshold is needed as in the case of a classical Switching Median filter. Instead, Threshold is computed locally from image pixels intensity values in a sliding window. Results show that ASWM provides better performance in terms of PSNR and MAE than many other median filter variants for random-valued impulse noise. In addition it can preserve more image details in a high noise environment.

152 citations


Journal ArticleDOI
01 Oct 2010-Tellus A
TL;DR: In this paper, two data assimilation methods based on sequential Monte Carlo sampling are studied and compared: the ensemble Kalman filter and the particle filter, each of which has its own advantages and drawbacks.
Abstract: In this paper, two data assimilation methods based on sequential Monte Carlo sampling are studied and compared: the ensemble Kalman filter and the particle filter. Each of these techniques has its own advantages and drawbacks. In this work, we try to get the best of each method by combining them. The proposed algorithm, called the weighted ensemble Kalman filter, consists to rely on the Ensemble Kalman Filter updates of samples in order to define a proposal distribution for the particle filter that depends on the history of measurement. The corresponding particle filter reveals to be efficient with a small number of samples and does not rely anymore on the Gaussian approximations of the ensemble Kalman filter. The efficiency of the new algorithm is demonstrated both in terms of accuracy and computational load. This latter aspect is of the utmost importance in meteorology or in oceanography since in these domains, data assimilation processes involve a huge number of state variables driven by highly non-linear dynamical models. Numerical experiments have been performed on different dynamical scenarios. The performances of the proposed technique have been compared to the ensemble Kalman filter procedure, which has demonstrated to provide meaningful results in geophysical sciences.

118 citations


Journal ArticleDOI
TL;DR: A new method for computing ensemble increments in observation space is proposed that does not suffer from the pathological behavior of the deterministic filter while avoiding much of the sampling error of the stochastic filter.
Abstract: A deterministic square root ensemble Kalman filter and a stochastic perturbed observation ensemble Kalman filter are used for data assimilation in both linear and nonlinear single variable dynamical systems. For the linear system, the deterministic filter is simply a method for computing the Kalman filter and is optimal while the stochastic filter has suboptimal performance due to sampling error. For the nonlinear system, the deterministic filter has increasing error as ensemble size increases because all ensemble members but one become tightly clustered. In this case, the stochastic filter performs better for sufficiently large ensembles. A new method for computing ensemble increments in observation space is proposed that does not suffer from the pathological behavior of the deterministic filter while avoiding much of the sampling error of the stochastic filter. This filter uses the order statistics of the prior observation space ensemble to create an approximate continuous prior probability dis...

113 citations


Journal ArticleDOI
TL;DR: In this article, an auxiliary particle filter (APF) is proposed to enhance the efficiency of the probability hypothesis density (PHD) filter, which is the equivalent of the bootstrap particle filter.
Abstract: Optimal Bayesian multi-target filtering is, in general, computationally impractical owing to the high dimensionality of the multi-target state. The probability hypothesis density (PHD) filter propagates the first moment of the multi-target posterior distribution. While this reduces the dimensionality of the problem, the PHD filter still involves intractable integrals in many cases of interest. Several authors have proposed sequential Monte Carlo (SMC) implementations of the PHD filter. However these implementations are the equivalent of the bootstrap particle filter, and the latter is well known to be inefficient. Drawing on ideas from the auxiliary particle filter (APF), we present an SMC implementation of the PHD filter, which employs auxiliary variables to enhance its efficiency. Numerical examples are presented for two scenarios, including a challenging nonlinear observation model.

109 citations


Patent
30 Dec 2010
TL;DR: In this paper, the Schur-Cohn stability test is applied to the denominator coefficients of the HR filter transfer function to determine the stability of the noise cancellation system and the secondary path is identified in an on-line manner.
Abstract: Systems and methods for adaptive feed-forward noise cancellation. The system includes a plurality of reference microphones, an error microphone, a secondary path module, an adaptation controller, and a canceller filter. A finite impulse response ("FIR") based plant model is converted to an infinite impulse response ("HR") based plant model using balanced model reduction. Due to the inherent instability of the adaptive HR filter, the Schur-Cohn stability test is applied to the denominator coefficients of the HR filter transfer function to determine the stability of the noise cancellation system. A secondary path of the noise cancellation system is identified in an on-line manner in the secondary path module. If the energy level of the communication signal (e.g., a music signal) is strong, secondary path identification is performed. The adaptation controller controls the updating of the HR transfer function based on the stability determination and the secondary path. An anti-noise signal is then generated and added to the communication signal. The anti-noise signal is generated within approximately 60 or fewer micro-seconds.

90 citations


Journal ArticleDOI
TL;DR: The proposed neural- network method for EM behavior modeling of microwave filters that have many input variables can produce a much more accurate high-dimensional model compared to the conventional neural-network method and the resulting model is much faster than an EM model.
Abstract: Neural networks are useful for developing fast and accurate parametric model of electromagnetic (EM) structures. However, existing neural-network techniques are not suitable for developing models that have many input variables because data generation and model training become too expensive. In this paper, we propose an efficient neural-network method for EM behavior modeling of microwave filters that have many input variables. The decomposition approach is used to simplify the overall high-dimensional neural-network modeling problem into a set of low-dimensional sub-neural-network problems. By incorporating the knowledge of filter decomposition with neural-network decomposition, we formulate a set of neural-network submodels to learn filter subproblems. A new method to combine the submodels with a filter empirical/equivalent model is developed. An additional neural-network mapping model is formulated with the neural-network submodels and empirical/equivalent model to produce the final overall filter model. An H -plane waveguide filter model and a side-coupled circular waveguide dual-mode filter model are developed using the proposed method. The result shows that with a limited amount of data, the proposed method can produce a much more accurate high-dimensional model compared to the conventional neural-network method and the resulting model is much faster than an EM model.

77 citations


Journal ArticleDOI
TL;DR: This result confirms that the Gaussian assumption in the Kalman filter formulation, which is violated by most ensemble Kalman filters through the nonlinearity in the model, is a necessary condition to avoid catastrophic filter divergence.
Abstract: Two types of filtering failure are the well known filter divergence where errors may exceed the size of the corresponding true chaotic attractor and the much more severe catastrophic filter divergence where solutions diverge to machine infinity in finite time. In this paper, we demon- strate that these failures occur in filtering the L-96 model, a nonlinear chaotic dissipative dynamical system with the absorbing ball property and quasi-Gaussian unimodal statistics. In particular, catas- trophic filter divergence occurs in suitable parameter regimes for an ensemble Kalman filter when the noisy turbulent true solution signal is partially observed at sparse regular spatial locations. With the above documentation, the main theme of this paper is to show that we can suppress the catastrophic filter divergence with a judicious model error strategy, that is, through a suitable linear stochastic model. This result confirms that the Gaussian assumption in the Kalman filter formulation, which is violated by most ensemble Kalman filters through the nonlinearity in the model, is a necessary condition to avoid catastrophic filter divergence. In a suitable range of chaotic regimes, adding model errors is not the best strategy when the true model is known. However, we find that there are several parameter regimes where the filtering performance in the presence of model errors with the stochastic model supersedes the performance in the perfect model simulation of the best ensemble Kalman filter considered here. Secondly, we also show that the advantage of the reduced Fourier domain filtering strategy (A. Majda and M. Grote, Proceedings of the National Academy of Sciences, 104, 1124-1129, 2007), (E. Castronovo, J. Harlim and A. Majda, J. Comput. Phys., 227(7), 3678-3714, 2008), (J. Harlim and A. Majda, J. Comput. Phys., 227(10), 5304-5341, 2008) is not simply through its numerical efficiency, but significant filtering accuracy is also gained through ignoring the correlation between the appropriate Fourier coefficients when the sparse observations are available in regular space locations.

Journal ArticleDOI
TL;DR: In this article, the properties of the Kolmogorov-Zurbenko (KZ) filter and its extensions with applications in high-resolution signal and image processing are reviewed.
Abstract: We reviewed the properties of the Kolmogorov–Zurbenko (KZ) filter and its extensions with applications in high resolution signal and image processing. The KZ filter is defined as an iteration of a moving average (MA) filter. The impulse response function of the KZ filter is a convolution of the rectangular window being used in a MA filter. Zero derivatives at the edges of the impulse response function make it a sharply declining function, providing high frequency resolution. The KZ Fourier transform (KZFT) is derived from the KZ filter by applying it to Fourier transform. Extensions of the KZ filter and the KZFT are demonstrated with examples. Copyright © 2010 John Wiley & Sons, Inc. For further resources related to this article, please visit the WIREs website.

Journal ArticleDOI
TL;DR: A complex adaptive notch filter is developed, for tracking single-sided tones immersed in background noise, which inherits useful properties from its real counterpart and is faster convergence and tracking than a gradient descent algorithm.
Abstract: A complex adaptive notch filter is developed, for tracking single-sided (a.k.a. analytic or complex) tones immersed in background noise. A complex all-pass based realization is pursued which inherits useful properties from its real counterpart: independent tuning of the notch frequency and attenuation bandwidth, easy realization of the complementary band-pass filter, unbiased frequency estimation, and faster convergence and tracking than a gradient descent algorithm.

Journal ArticleDOI
TL;DR: A novel approach to visual tracking called the harmony filter, based on the Harmony Search algorithm, which models the target as a colour histogram and searches for the best estimated target location using the Bhattacharyya coefficient as a fitness metric.

Patent
01 Dec 2010
TL;DR: In this paper, the first real valued adaptive filter is configured to estimate a first intermodulation noise component (e.g., an in-phase component) in a desired signal and to cancel the estimated noise.
Abstract: One embodiment of the present invention relates to an adaptive filtering apparatus comprising first and second real valued adaptive filters, respectively configured to receive an adaptive filter input signal based upon a transmission signal in a transmission path. The first real valued adaptive filter is configured to operate a real valued adaptive filter algorithm on the input signal to estimate a first intermodulation noise component (e.g., an in-phase component) in a desired signal and to cancel the estimated noise. The second real valued adaptive filter is configured to operate a real valued adaptive filter algorithm on the input signal to estimate a second intermodulation noise component (e.g., a quadrature phase component) in the desired signal and to cancel the estimated noise. Accordingly, each filter operates a real valued adaptive algorithm to cancel a noise component, thereby removing complex cross terms between the components from the adaptive filtering process.

Journal ArticleDOI
Jingen Ni1, Feng Li1
TL;DR: Experimental results show that the proposed adaptive combination scheme can obtain both fast convergence rate and small steady-state mean-square error.
Abstract: In hands-free telephones and teleconferencing systems, acoustic echo cancellers are required, which are often implemented by adaptive filters. In these applications, the speech input signal of the adaptive filter is highly correlated and the impulse response of the echo path is very long. These characteristics will slow down the convergence rate of the adaptive filter if the well-known normalized least-mean-square (NLMS) algorithm is used. The normalized subband adaptive filter (NSAF) offers a good solution to this problem because of its decorrelating property. However, similar to the NLMS-based adaptive filter, the NSAF requires a tradeoff between fast convergence rate and small steady-state mean-square error (MSE). In this paper, we propose an adaptive combination scheme to address this tradeoff. The combination is carried out in subband domain and the mixing parameter that controls the combination is adapted by means of a stochastic gradient algorithm which employs the sum of squared subband errors as the cost function. The performance of the proposed combination scheme is evaluated in the context of acoustic echo cancellation (AEC). Experimental results show that the combination scheme can obtain both fast convergence rate and small steady-state MSE.

Journal ArticleDOI
TL;DR: A modified particle filter algorithm that combines intensity and edge cues is proposed that can track the infrared pedestrian more effectively and reliably than the traditional particle filter algorithms.

Journal ArticleDOI
TL;DR: Results are given that show that the proposed configuration is able to provide a convenient bias versus variance tradeoff, leading to reductions in the filter mean-square error, especially in situations with a low signal-to-noise ratio (SNR).
Abstract: It is a well-known result of estimation theory that biased estimators can outperform unbiased ones in terms of expected quadratic error. In steady state, many adaptive filtering algorithms offer an unbiased estimation of both the reference signal and the unknown true parameter vector. In this correspondence, we propose a simple yet effective scheme for adaptively biasing the weights of adaptive filters using an output multiplicative factor. We give theoretical results that show that the proposed configuration is able to provide a convenient bias versus variance tradeoff, leading to reductions in the filter mean-square error, especially in situations with a low signal-to-noise ratio (SNR). After reinterpreting the biased estimator as the combination of the original filter and a filter with constant output equal to 0, we propose practical schemes to adaptively adjust the multiplicative factor. Experiments are carried out for the normalized least-mean-squares (NLMS) adaptive filter, improving its mean-square performance in stationary situations and during the convergence phase.

Proceedings ArticleDOI
Fred Daum1, Jim Huang1
TL;DR: The theory of particle flow is generalized to stabilize the nonlinear filter and implements Bayes' rule using particle flow rather than with a pointwise multiplication of two functions, avoiding one of the fundamental and well known problems in particle filters, namely "particle degeneracy".
Abstract: We generalize the theory of particle flow to stabilize the nonlinear filter. We have invented a new nonlinear filter that is vastly superior to the classic particle filter and the extended Kalman filter (EKF). In particular, the computational complexity of the new filter is many orders of magnitude less than the classic particle filter with optimal estimation accuracy for problems with dimension greater than 4. Our accuracy is typically several orders of magnitude better than the EKF for nonlinear problems. We do not resample, and we do not use any proposal density from an EKF or UKF or other filter. Moreover, our new algorithm is deterministic, and we do not use any MCMC methods; this is a radical departure from other particle filters. The new filter implements Bayes' rule using particle flow rather than with a pointwise multiplication of two functions; this avoids one of the fundamental and well known problems in particle filters, namely "particle degeneracy." In addition, we explicitly stabilize our particle filter using negative feedback, unlike standard particle filters, which are generally very inaccurate for plants with slow mixing or unstable dynamics. This stabilization improves performance by several orders of magnitude for difficult problems.

Proceedings ArticleDOI
14 Mar 2010
TL;DR: This paper develops a new widely linear noise-reduction Wiener filter based on the variance and pseudo-variance of the short-time Fourier transform coefficients of speech signals that causes less speech distortion and its minimum mean-squared error is smaller than that of the classicalWiener filter.
Abstract: This paper develops a new widely linear noise-reduction Wiener filter based on the variance and pseudo-variance of the short-time Fourier transform coefficients of speech signals. We show that this new noise-reduction filter has many interesting properties, including but not limited to: 1) it causes less speech distortion as compared to the classical noise-reduction Wiener filter; 2) its minimum mean-squared error (MSE) is smaller than that of the classical Wiener filter; 3) it can increase the subband signal-to-noise ratio (SNR), while the classical Wiener filter has no effect on the subband SNR for any given signal frame and subband.

Journal ArticleDOI
TL;DR: In this paper, a maximum likelihood algorithm for simultaneous estimation of state and parameter values in nonlinear stochastic state-space models is proposed, which uses a combination of expectation maximization, nonlinear filtering and smoothing algorithms.

Proceedings ArticleDOI
03 Dec 2010
TL;DR: A new approach to Gabor filter bank design is proposed, by incorporating feature selection, i.e. filter selection, into the design process, and this in turn leads to improved performance of texture classification.
Abstract: Texture feature has been widely used in object recognition, image content analysis and many others. Among various approaches to texture feature extraction, Gabor filter has emerged as one of the most popular ones. Gabor filter-based feature extractor is in fact a Gabor filter bank defined by its parameters including frequencies, orientations and smooth parameters of Gaussian envelope. In the literature, different parameter settings have been suggested, and filter banks created by these parameter settings work well in general. From the perspective of pattern classification, however, filter banks thus designed may not be ideal. In the present study, we propose a new approach to Gabor filter bank design, by incorporating feature selection, i.e. filter selection, into the design process. The merits of incorporating filter selection in filter bank design are twofold. Firstly, filter selection produces a compact Gabor filter bank and hence reduces computational complexity of texture feature extraction. Secondly, Gabor filter bank thus designed produces low-dimensional feature representation with improved sample-to-feature ratio, and this in turn leads to improved performance of texture classification. Experiment results on benchmark datasets and a real application have demonstrated the effectiveness of the proposed method.

Journal ArticleDOI
TL;DR: Results show that with the same accuracy, the processing time of the second-order nonlinear regression filters for a dataset of 1024*1024 points has been reduced to several seconds from the several hours of traditional algorithms.
Abstract: In this paper, the general model of the Gaussian regression filter for areal surface analysis is explored. The intrinsic relationships between the linear Gaussian filter and the robust filter are addressed. A general mathematical solution for this model is presented. Based on this technique, a fast algorithm is created. Both simulated and practical engineering data (stochastic and structured) have been used in the testing of the fast algorithm. Results show that with the same accuracy, the processing time of the second-order nonlinear regression filters for a dataset of 1024*1024 points has been reduced to several seconds from the several hours of traditional algorithms.

Journal ArticleDOI
TL;DR: This paper proposes a novel spatial filter for biomagnetic source imaging that is derived based on a modified version of the minimum-norm spatial filter and is designed to have a performance close to that of the adaptive minimum-variance spatial filter through the use of an estimated covariance matrix.
Abstract: This paper proposes a novel spatial filter for biomagnetic source imaging. The proposed spatial filter is derived based on a modified version of the minimum-norm spatial filter and is designed to have a performance close to that of the adaptive minimum-variance spatial filter through the use of an estimated covariance matrix. In this method, the theoretical form of the measurement covariance matrix is estimated as an updated gram matrix in a recursive procedure. Since the proposed method does not use the sample covariance matrix, it is free of the well-known weaknesses of the minimum-variance spatial filter, namely, the proposed spatial filter does not require a large number of time samples, and it can even be applied to single-time-sample data. It is also robust to source correlation. We have validated the method's effectiveness by our computer simulations as well as through experiments using auditory-evoked magnetoencephalographic data.

Patent
03 Aug 2010
TL;DR: In this article, a blind adaptive filter for narrowband interference cancellation is proposed, which includes an adaptive filter, a delay unit coupled to the adaptive filter to generate a delayed signal with a predetermined delay length.
Abstract: The present invention relates to a blind adaptive filter for narrowband interference cancellation, which includes an adaptive filter, a delay unit coupled to the adaptive filter for generating a delayed signal with a predetermined delay length from the output signal of the adaptive filter, and an error calculation unit coupled to the adaptive filter and the delay unit. The error calculation unit compares the output signal from the adaptive filter and the delayed signal from the delay unit to extract error information, and feedback the first error information to the adaptive filter. The first error information is formed of a transfer function including a number of coefficients, and used to adjust the adaptive filter and remove interference in the next input signal. The disclosed technique is also applicable in wideband receivers, as well as resisting multiple strong narrowband interferences having a frequency sweep rate of tens of milliseconds.

Journal ArticleDOI
TL;DR: A novel adaptive filter is proposed using a recurrent cerebellar-model-articulation-controller (CMAC) that has favorable properties of small size, good generalization, rapid learning, and dynamic response, thus it is more suitable for high-speed signal processing.
Abstract: A novel adaptive filter is proposed using a recurrent cerebellar-model-articulation-controller (CMAC). The proposed locally recurrent globally feedforward recurrent CMAC (RCMAC) has favorable properties of small size, good generalization, rapid learning, and dynamic response, thus it is more suitable for high-speed signal processing. To provide fast training, an efficient parameter learning algorithm based on the normalized gradient descent method is presented, in which the learning rates are on-line adapted. Then the Lyapunov function is utilized to derive the conditions of the adaptive learning rates, so the stability of the filtering error can be guaranteed. To demonstrate the performance of the proposed adaptive RCMAC filter, it is applied to a nonlinear channel equalization system and an adaptive noise cancelation system. The advantages of the proposed filter over other adaptive filters are verified through simulations.

Journal ArticleDOI
TL;DR: In this article, a linear matrix inequality (LMI)-based robust-stability condition is derived for fixed state-feedback gains, and an iterative algorithm that combines these two robuststability conditions is designed that yields the largest bandwidth while guaranteeing closed-loop robust stability.
Abstract: A low-pass filter is inserted in a repetitive controller to guarantee the stability of the modified repetitive-control system. The control precision strongly depends on the parameter of the filter. This study presents a method of simultaneously optimising the parameters of the low-pass filter and state feedback of a modified repetitive-control system in which the plant contains a class of uncertainties. First, the relationship between the control precision of a repetitive-control system and a low-pass filter is explained. Next, a linear matrix inequality (LMI)-based robust-stability condition is derived for fixed state-feedback gains. This condition is transformed into a generalised eigenvalue problem and is used to calculate the maximum cut-off angular frequency of the low-pass filter. Then, another LMI-based robust-stability condition is derived for a fixed low-pass filter, and is employed to find H∞ static-state-feedback gains. Moreover, an iterative algorithm that combines these two robust-stability conditions is designed that yields the largest bandwidth while guaranteeing closed-loop robust stability. The conservativeness of the result produced by the algorithm is the same as that of the less conservative of the two robust-stability conditions. Finally, two numerical examples demonstrate the validity of the method.

Journal ArticleDOI
TL;DR: In this paper, Gaussian regression filter that works without running-in and running-out profile fragments as well as profile spline filter was developed. And Gaussian robust profile filtering technique was established.
Abstract: Various components of surface texture are identified, namely form, waviness and roughness. Separation of these components is done by digital filtering. Gaussian regression filter that works without running-in and running-out profile fragments as well as profile spline filter was developed. The performance of conventional Gaussian digital filter was compared with those of Gaussian regression filter and spline filter. The modelled deterministic and random one-process profiles are the objects of investigation. We found that the performance of Gaussian regression filter was better than that of spline filter. Gaussian robust profile filtering technique was established. Valley suppression Rk filter was also included. These filters were compared and some of them were recommended. This paper is given in two parts. Part I focuses on the analysis of one-process surfaces. Part II discusses mainly digital filtering of stratified textures.

Patent
30 Jun 2010
TL;DR: In this article, an in-loop filtering apparatus for deblocking-filtered image data in an encoder of image data is presented. Butler et al. proposed an inloop filtering algorithm for eliminating an error of deblocking filtered image data.
Abstract: An in-loop filtering apparatus for eliminating an error of deblocking-filtered image data in an encoder of image data, the apparatus including: an in-loop filter generator which generates in-loop filters using different filter coefficients for a block boundary and a block inside of the deblocking-filtered image; an in-loop filter applier which performs selective filtering on at least one of the block boundary and the block inside using the generated in-loop filters; and an in-loop filter information generator which generates in-loop filter information including at least one of coefficients of the generated in-loop filters, information indicating an area to which in-loop filtering is applied between the block boundary and the block inside, a size of a block to which in-loop filtering is applied, and a flag indicating whether to use an in-loop filter generated for a current frame or an in-loop filter generated for a previous frame.

Book ChapterDOI
20 Sep 2010
TL;DR: This work proposes an adaptive version of the Linear Minimum Mean Square Error estimator that applies an adaptive filtering kernel that is based on a space-variant estimate of the noise level and a weight consisting of the product of a Gaussian kernel and the diffusion similarity with respect to the central voxel.
Abstract: Measuring the diffusion properties of crossing fibers is very challenging due to the high number of model parameters involved and the intrinsically low SNR of Diffusion Weighted MR Images. Noise filtering aims at suppressing the noise while pertaining the data distribution. We propose an adaptive version of the Linear Minimum Mean Square Error (LMMSE) estimator to achieve this. Our filter applies an adaptive filtering kernel that is based on a space-variant estimate of the noise level and a weight consisting of the product of a Gaussian kernel and the diffusion similarity with respect to the central voxel. The experiments show that the data distribution after filtering is still Rician and that the diffusivity values are estimated with a higher precision while pertaining an equal accuracy. We demonstrate on brain data that our adaptive approach performs better than the initial LMMSE estimator.