Showing papers on "Kernel adaptive filter published in 1996"

Optimal Surface Smoothing as Filter Design

Abstract: Smooth surfaces are approximated by polyhedral surfaces for a number of computational purposes. An inherent problem of these approximation algorithms is that the resulting polyhedral surfaces appear faceted. Within a recently introduced signal processing approach to solving this problem [7, 8], surface smoothing corresponds to low-pass filtering. In this paper we look at the filter design problem in more detail. We analyze the stability properties of the low-pass filter described in [7, 8], and show how to minimize its running time. We show that most classical techniques used to design finite impulse response (FIR) digital filters can also be used to design significantly faster surface smoothing filters. Finally, we describe an algorithm to estimate the power spectrum of a signal, and use it to evaluate the performance of the different filter design techniques described in the paper.

Incremental Least Squares Methods and the Extended Kalman Filter

Abstract: In this paper we propose and analyze nonlinear least squares methods which process the data incrementally, one data block at a time. Such methods are well suited for large data sets and real time operation and have received much attention in the context of neural network training problems. We focus on the extended Kalman filter, which may be viewed as an incremental version of the Gauss--Newton method. We provide a nonstochastic analysis of its convergence properties, and we discuss variants aimed at accelerating its convergence.

The theory and design of arbitrary-length cosine-modulated filter banks and wavelets, satisfying perfect reconstruction

Abstract: It is well known that FIR filter banks that satisfy the perfect-reconstruction (PR) property can be obtained by cosine modulation of a linear-phase prototype filter of length N=2mM, where M is the number of channels. In this paper, we present a PR cosine-modulated filter bank where the length of the prototype filter is arbitrary. The design is formulated as a quadratic-constrained least-squares optimization problem, where the optimized parameters are the prototype filter coefficients. Additional regularity conditions are imposed on the filter bank to obtain the cosine-modulated orthonormal bases of compactly supported wavelets. Design examples are given.

An adaptive noise cancelling arrangement, a noise reduction system and a transceiver

Abstract: Known is a so-called cross-coupled adaptive noise cancelling arrangement utilizing an adaptive noise filter and an adaptive cross-talk filter in a feedback loop for cancelling correlated noise at a primary signal input and reference input. The known cross-coupled ANC does not operate satisfactorily, particularly not for acoustic noise cancellation. This leads to reverberant-like sound singals, in particular in a typical office room with remote noise sources. A cross-coupled adaptive noise cancelling arrangement is proposed having a different configuration giving rise to a better performance. The adaptive cross-talk filter is split into a prefilter section and an adaptive filter section, the sections using different input signals. The prefilter section estimates the desired signal from the input signal of the noise cancelling arrangement, and the adaptive filter section has its input coupled to the output of the noise cancelling arrangement, a delay section being provided between the input and the output of the noise cancelling arrangement. In an embodiment, the prefilter section and the adaptive filter section are separate filters.

A new technique for nonlinear estimation

Abstract: A new nonlinear filter referred to as the state-dependent Riccati equation filter (SDREF) is presented. The SDREF is derived by constructing the dual of a little known nonlinear regulator control design technique which involves the solution of a state-dependent Riccati equation (SDRE) and which has been appropriately called the SDRE control method. The resulting SDREF has the same structure as the continuous steady-state linear Kalman filter. In contrast to the linearized Kalman filter (LKF) and the extended Kalman filter (EKF) which are based on linearization, the SDREF is based on a parameterization that brings the nonlinear system to a linear structure having state-dependent coefficients (SDC). In a deterministic setting, before stochastic uncertainties are introduced, the SDC parameterization fully captures the nonlinearities of the system, It was shown in Cloutier et al. (1996) that, in the multivariable case, the SDC parameterization is not unique and that the SDC parameterization itself can be parameterized. This latter parameterization creates extra degrees of freedom that are not available in traditional filtering methods. These additional degrees of freedom can be used to either enhance filter performance, avoid singularities, or avoid loss of observability. The main intent of this paper is to introduce the new nonlinear filter and to illustrate the behaviorial differences and similarities between the new filter, the LKF, and the EKF using a simple pendulum problem.

A fast least-squares algorithm for linearly constrained adaptive filtering

Abstract: An extension of the field of fast least-squares techniques is presented. It is shown that the adaptation gain, which is updated with a number of operations proportional to the number of transversal filter coefficients, can be used to update the coefficients of a linearly constrained adaptive filter. An algorithm that is robust to round-off errors is derived. It is general and flexible. It can handle multiple constraints and multichannel signals. Its performance is illustrated by simulations and compared with the classical LMS-based Frost (1972) algorithm.

On a class of computationally efficient, rapidly converging, generalized NLMS algorithms

Abstract: Over the last decade, a certain computationally efficient, rapidly converging adaptive filtering algorithm has been independently discovered many times. The algorithm can be viewed as a generalization of the normalized LMS (NLMS) algorithm that updates on the basis of multiple input signal vectors. This article compares and discusses the different approaches to and embellishments of the basic algorithm, and contrasts the various interpretations from different perspectives.

Image decoder using adjustable filtering

Abstract: Noise contained in a reproducing image signal is suppressed by performing a filtering operation on an image signal obtained by decoding data that has been coded with a unit of a block consisting of m×n pixels. A filter circuit having a plurality of filter characteristics suppresses noise, and a characteristics selection circuit switches the filter characteristics of the filter circuit by use of a quantizing parameter employed for coding the image signal.

Adaptive edge-preserving smoothing filter

Abstract: An adaptive edge-preserving smoothing filter effectively reduces noise levels while preserving fine structures in data. The behavior of the filter is controlled easily by two control parameters. To adaptively control the behavior of the filter, the control parameter, α, can be set as a function of the local directional variances. The control parameter, β, can be set as a function of all of the directional variances and directional means. The filter includes; a compute means which receives the filter window size, the number of filter directions and input data, adaptive weighting parameter map means which receives the control parameter, α, adaptive weighting process means, adaptive combination parameter map means which receives the control parameter, β, and final compute means which provides the filtered output data.

Theory and design of two-dimensional filter banks: a review

Abstract: There has been considerable interest in the design of multidimensional (MD) filter banks. MD filter banks find application in subband coding of images and video data. MD filter banks can be designed by cascading one-dimensional (1D) filter banks in the form of a tree structure. In this case, the individual analysis and synthesis filters are separable and the filter bank is called a separable filter bank. MD filter banks with nonseparable filters offer more flexibility and usually provide better performance. Nonetheless, their design is considerably more difficult than separable filter banks. The purpose of this paper is to provide an overview of developments in this field on the design techniques for MD filter banks, mostly two-dimensional (2D) filter banks. In some image coding applications, the 2D two-channel filter banks are of great importance, particularly the filter bank with diamond-shaped filters. We will present several design techniques for the 2D two-channel nonseparable filter banks. As the design of MD filters are not as tractable as that of 1D filters, we seek design techniques that do not involve direct optimization of MD filters. To facilitate this, transformations that turn a separable MD filter bank into a nonseparable one are developed. Also, transformations of 1D filter banks to MD filter banks are investigated. We will review some designs of MD filter banks using transformations. In the context of 1D filter bank design, the cosine modulated filter bank (CMFB) is well-known for its design and implementation efficiency. All the analysis filters are cosine modulated versions of a prototype filter. The design cost of the filter bank is equivalent to that of the prototype and the implementation complexity is comparable to that of the prototype plus a low-complexity matrix. The success with 1D CMFB motivate the generalization to the 2D case. We will construct the 2D CMFB by following a very close analogy of 1D case. It is well-known that the 1D lossless systems can be characterized by state space description. In 1D, the connection between the losslessness of a transfer matrix and the unitariness of the realization matrix is well-established. We will present the developments on the study of 2D lossless systems. As in 1D case, the 2D FIR lossless systems can be characterized in terms of state space realizations. We will review this, and then address the factorizability of 2D FIR lossless systems by using the properties of state space realizations.

Training analysis of adaptive interference suppression for direct-sequence code-division multiple-access systems

Abstract: This paper studies the transient behavior of an adaptive near-far resistant receiver for direct-sequence (DS) code-division multiple-access (CDMA) known as the minimum mean-squared error (MMSE) receiver. This receiver structure is known to be near-far resistant and yet does not require the large amounts of side information that are typically required for other near-far resistant receivers. In fact, this receiver only requires code timing on the one desired signal. The MMSE receiver uses an adaptive filter which is operated in a manner similar to adaptive equalizers. Initially there is a training period where the filter locks onto the signal that is sending a known training sequence. After training, the system can then switch to a decision-directed mode and send actual data. This work examines the length of the training period needed as a function of the number of interfering users and the severity of the near-far problem. A standard least mean-square (LMS) algorithm is used to adapt the filter and so the trade-off between convergence and excess mean-squared error is studied. It is found that in almost all cases a step size near 1.0/(total input power) gives the best speed of convergence with a reasonable excess mean-squared error. Also, it is shown that the MMSE receiver can tolerate a 30-40 dB near-far problem without excessively long convergence time.

Adaptive noise removal from biomedical signals using warped polynomials

Abstract: Presents the time-warped polynomial filter (TWPF), a new interval-adaptive filter for removing stationary noise from nonstationary biomedical signals. The filter fits warped polynomials to large segments of such signals. This can be interpreted as low-pass filtering with a time-varying cutoff frequency. In optimal operation, the filter's cut-off frequency equals the local signal bandwidth. However, the author also presents an iterative filter adaptation algorithm, which does not rely on the (complicated) computation of the local bandwidth. The TWPF has some important advantages over existing adaptive noise removal techniques: it reacts immediately to changes in the signal's properties, independently of the desired noise reduction; it does not require a reference signal and can be applied to nonperiodical signals. In case of quasiperiodical signals, applying the TWPF to the individual signal periods leads to an optimal noise reduction. However, the TWPF can also be applied to intervals of fixed size, at the expense of a slightly lower noise reduction. This is the way nonquasiperiodical signals are filtered. The author presents experimental results which demonstrate the usefulness of the interval-adaptive filter in several biomedical applications: noise removal from ECG, respiratory and blood pressure signals, and base-line restoration of electroencephalograms (EEGs).

Fractional Wiener filter

Abstract: The fractional correlation is a new operation that can easily be implemented by optical means. This operation might be useful for shift-variant pattern recognition and for image restoration. The Wiener filter is the optimal filter according to the minimal square-error criterion. For a given spectral noise that distorts the reference image, this filter is optimal for restoring an image in noise. A fractional Wiener filter is suggested for restoring reference objects in a fractional correlation system. The new filter sometimes performs better than the conventional Wiener filter.

Optimal Recursive Iterative Algorithm for Discrete Nonlinear Least-Squares Estimation

Abstract: The estimation algorithm developed offers an alternative to standard recursive nonlinear estimators such as the extended Kalman filter and the iterated extended Kalman filter. The algorithm, which is developed from a quadratic cost function basis, splits the problem of cost function minimization into a linear first step and a nonlinear second step by defining new first-step states that are nonlinear combinations of the unknown states. Estimates of the firststep states are obtained by minimizing the first-step cost function using a Kalman filter formulation. Estimates of the unknown, or second-step, states are obtained by minimizing the second-step cost function using an iterative Gauss-Newton algorithm. The two-step estimator is shown to be optimal for static problems in which the time variation of the measurement equation can be separated from the unknowns. This method is then generalized by approximating the nonlinearity as a perturbation of the dynamic update, while keeping the measurement cost function the same. In contrast, the extended Kalman filter and the iterated extended Kalman filter linearize the measurement cost function, resulting in suboptimal estimates. Two example applications confirm these analytical results.

Method and apparatus for adjusting a spectrum shape of a speech signal

Abstract: Adjusting the shape of a spectrum of a speech signal includes the steps of using a first filter with pole-zero transfer function A(z)/B(z) for subjecting a speech signal to a spectrum envelop emphasis and a second filter cascade-connected with the first filter, for compensating for a spectral tilt due to the first filter, independently deriving two filter coefficients used in the second filter for compensating for the spectral tilt from the pole-zero transfer function, and compensating for the spectral tilt corresponding to the pole-zero transfer function according to the derived filter coefficients.

New nonlinear algorithms for estimating and suppressing narrowband interference in DS spread spectrum systems

Abstract: It has been shown that the narrowband (NB) interference suppression capability of a direct-sequence (DS) spread spectrum system can be enhanced considerably by processing the received signal via a prediction error filter. The conventional approach to this problem makes use of a linear filter. However, the binary DS signal, that acts as noise in the prediction process, is highly non-Gaussian. Thus, linear filtering is not optimal. Vijayan and Poor (1990) first proposed using a nonlinear approximate conditional mean (ACM) filter of the Masreliez (1975) type and obtained significant results. This paper proposes a number of new nonlinear algorithms. Our work consists of three parts. (1) We develop a decision-directed Kalman (DDK) filter, that has the same performance as the ACM filter but a simpler structure. (2) Using the nonlinear function in the ACM and the DDK filters, we develop other nonlinear least mean square (LMS) filters with improved performance. (3) We further use the nonlinear functions to develop nonlinear recursive least squares (RLS) filters that can be used independently as predictors or as interference identifiers so that the ACM or the DDK filter can be applied. Simulations show that our nonlinear algorithms outperform conventional ones.

Nonhomogeneity detection method and apparatus for improved adaptive signal processing

Abstract: Apparatus and method for improving detection of targets in a radar system that employs adaptive filtering. A nonhomogeneity detector eliminates nonhomogeneous signals from the population of signals received. An adaptive filter weight controller estimates covariance matrices from only homogenous signals. Thus the apparatus and method improves the probability of detecting the presence or absence of a target at the same time that it decreases the probability of a false alarm by improving the performance of an adaptive filter. Though developed for airborne radar, the apparatus and method may be applied to the processing of any image.

Effort constraints in adaptive feedforward control

Abstract: Adaptive algorithms are presented for constrained multichannel feedforward control. They minimize the sum of squared error signals while limiting the value of either the sum of squared control signals (total effort) or the mean square value of each individual control signal (individual efforts). It is shown that the exact least squares solutions for these problems have a simple form, which can be approached with an adaptive algorithm. The properties of the resulting algorithm are illustrated by simulation.

Globally convergent adaptive IIR filters based on fixed pole locations

Abstract: A new class of adaptive filters, dubbed fixed pole adaptive filters (FPAF's), is introduced. These adaptive filters have infinite impulse responses, yet their adaptation exhibits provable global convergence. Good filter performance with a relatively small number of adapted parameters is permitted by the new filter structure, thus reducing the computational burden needed to implement adaptive filters. The implementation and computational complexity of the FPAF is described, and its modeling capabilities are determined. Excitation conditions on the filter input are established that guarantee global convergence of a standard set of adaptive algorithms. Some methods are described for selecting the fixed pole locations based on a priori information regarding the operating environment of the adaptive filter. The FPAF is tailored to applications by such a procedure, enabling improved performance. In examples, the FPAF is shown to achieve a smaller minimum mean square error, given an equal number of adapted parameters, in comparison with adaptive FIR filters and adaptive filters based on Laguerre and Kautz models.

Adaptive filter to detect rounded convex regions: iris filter

Abstract: This paper proposes a unique filter, called "iris filter", which evaluates the degree of convergence of gradient vectors in the neighborhood of the pixel of interest. The generalized iris filter and its simplified one are given. The degree of convergence is related to the distribution of orientations of gradient vectors. The region of support of the iris filter is controlled so that the degree of convergence of gradient vectors in it becomes maximum. It means that the size and the shape of the region of support changes adaptively according to the distribution pattern of gradient vectors around the pixel of interest. Theoretical analysis using models of a rounded convex region and a semi-cylindrical region is given. It shows that rounded convex regions are mostly enhanced even if their original contrasts to their background are weak and elongated objects are suppressed. However, the filter output is 1//spl pi/ at the boundaries of rounded convex regions and semi-cylindrical ones in spite of their contrast. This absolute value can be used to detect boundaries of those objects. The proposed filter is effective to enhance and detect rounded convex regions with various sizes and contrasts.

Method and apparatus for coding an input signal based on characteristics of the input signal

Abstract: An interframe coding system which eliminates higher frequency components contained in an image signal effectively and adaptively with an adaptive filter provided in a coding loop. The adaptive filter eliminates the higher frequency components with the optimal filtering intensity for an image signal specified with a filtering coefficient which is decided by a filter controller. The filtering coefficient is decided by normalization of the difference between an input image signal and a predictive signal from a frame memory by the "Activity" of the input image signal or the predictive signal. The "Activity" can be based upon the sum of the absolute or squared difference values based upon the mean value of luminance intensity of pixels of the image signal.

Optimization of filter banks using cyclostationary spectral analysis

Abstract: This paper proposes a design method of optimal biorthogonal FIR filter banks that minimize the time-averaged mean squared error (TAMSE) when the high-frequency subband signal is dropped. To study filter banks from a statistical point of view, cyclostationary spectral analysis is used since the output of the filter bank for a wide-sense stationary input is cyclostationary. First, the cyclic spectral density of the output signal is derived, and an expression for the TAMSE is presented. Then, optimal filter banks are given by minimizing the TAMSE with respect to the coefficients of the filters under the biorthogonality condition. By imposing the additional constraints on the coefficients, the optimal biorthogonal linear phase filter bank can be obtained.

Advanced Concepts in Adaptive Signal Processing

Abstract: Preface. 1: Introduction and Background. 1.1. Common Adaptive Concepts from Different Disciplines. 1.2. Generic Applications of Adaptive Methods. 1.3. Performance Measures in Adaptive Systems. 1.4. The Minimum Mean Squared Error Solution. 1.5. Adaptive Algorithms for FIR Systems. 1.6. Adaptive Algorithms for IIR Systems. 1.7. New Horizons in Adaptive Signal Processing. 1.8. Notation and Conventions. 2: Advanced Algorithms for 1-D Adaptive Filtering. 2.2. Data- Reusing LMS Algorithms. 2.3. Orthogonalization by PR Modulation. 2.3. The Gauss-Newton Adaptive Filtering algorithm. 2.4. Block Adaptive IIR Filters Using the PCG Method. 3: Structures and Algorithms for Two-Dimensional Adaptive Signal Processing. 3.1. Applications of Two-Dimensional Adaptive Filtering. 3.2. Two- Dimensional FIR Adaptive Filtering. 3.3. Two-Dimensional IIR Adaptive Filters. 3.4. Two-Dimensional IIR Adaptive Filtering Experiments. 3.5. Uniqueness Characteristics of the 2-D IIR MSE Minimization. 4: Adaptive Fault Tolerance. 4.1. Application of AFT to FIR Adaptive Filters. 4.2. Adaptive Filter Structures. 4.3. A Simple Fault Tolerant FIR Adaptive Filter. 4.4. The Transform Domain FTAF. 4.5. The DFT-Based TDFTAF with the Conjugate Gradient. 4.6. Robust and Practical TDFTAFs. 4.7. Full Fault Tolerance Transforms. 4.8. Discussion. 5: Adaptive Polynomial Filters. 5.1. The Volterra Series. 5.2. Gradient Based Adaptive Volterra Filters. 5.3. RLSSecond-Order Volterra Adaptive Filter. 5.4. LS Lattice Second-Order Volterra Adaptive Filter. 5.5. QR-Based LS Lattice Second Order Volterra Filter. 5.6. The Adaptive Volterra Filter for Gaussian Signals. 5.7. Other Polynomial-Based Nonlinear Adaptive Filters. 5.8. Discussion. Appendix. Subject Index.

Biorthogonal cosine-modulated filter bank

Abstract: Cosine-modulated filter banks have been studied extensively because of their design ease and efficient implementation. These filter banks either have restricted lengths or assume the paraunitary property for the polyphase matrices. In this paper, the biorthogonal cosine-modulated filter bank with arbitrary length is considered and the perfect reconstruction (PR) conditions are derived. These conditions are the general form of the PR conditions reported in the literature. Examples of PR systems with variable overall delay are designed using the quadratic constrained least squares formulation.