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Showing papers on "Kernel adaptive filter published in 1991"


Journal ArticleDOI
TL;DR: In this article, a general analysis of multidimensional multirate filter banks is presented, which is applicable to discrete signal spaces of any dimension, to multi-dimensional systems based on arbitrary downsampling and upsampling lattices and for filter banks with any number of channels.
Abstract: A general analysis of multidimensional multirate filter banks is presented. The approach is applicable to discrete signal spaces of any dimension, to multirate systems based on arbitrary downsampling and upsampling lattices, and for filter banks with any number of channels. A new numerical design procedure is also presented for multidimensional multirate perfect reconstruction filter banks, which is based on methods of nonlinearly constrained numerical optimization. An error function that depends only on the analysis filter impulse response coefficients is minimized, subject to a set of quadratic equality constraints that involve both the analysis and synthesis filter coefficients. With this design framework, it is possible to design a wide variety of filter banks that have a number of desirable properties. The analysis and synthesis filters that result are finite impulse response (FIR) and of equal size. In addition, both paraunitary and nonparaunitary filter banks can be designed with this method. Unlike paraunitary filter banks, nonparaunitary filter banks are capable of performing analysis bank functions more general than band-splitting with flat passband filters. >

216 citations


Patent
18 Sep 1991
TL;DR: In this article, a method for processing a field of image data samples to provide for one or more of the functions of decimation, interpolation, and sharpening is accomplished by use of an array transform processor such as that employed in a JPEG compression system.
Abstract: A method for processing a field of image data samples to provide for one or more of the functions of decimation, interpolation, and sharpening is accomplished by use of an array transform processor such as that employed in a JPEG compression system. Blocks of data samples are transformed by the discrete even cosine transform (DECT) in both the decimation and interpolation processes, after which the number of frequency terms is altered. In the case of decimation, the number of frequency terms is reduced, this being followed by inverse transformation to produce a reduced-size matrix of sample points representing the original block of data. In the case of interpolation, additional frequency components of zero value are inserted into the array of frequency components after which inverse transformation produces an enlarged data sampling set without an increase in spectral bandwidth. In the case of sharpening, accomplished by a convolution or filtering operation involving multiplication of transforms of data and filter kernel in the frequency domain, there is provided an inverse transformation resulting in a set of blocks of processed data samples. The blocks are overlapped followed by a savings of designated samples, and a discarding of excess samples from regions of overlap. The spatial representation of the kernel is modified by reduction of the number of components, for a linear-phase filter, and zero-padded to equal the number of samples of a data block, this being followed by forming the discrete odd cosine transform (DOCT) of the padded kernel matrix.

156 citations


Journal ArticleDOI
TL;DR: The authors outline the design of an optimal, computationally efficient, infinite impulse response edge detection filter, computed based on Canny's high signal to noise ratio, good localization criteria, and a criterion on the spurious response of the filter to noise.
Abstract: The authors outline the design of an optimal, computationally efficient, infinite impulse response edge detection filter. The optimal filter is computed based on Canny's high signal to noise ratio, good localization criteria, and a criterion on the spurious response of the filter to noise. An expression for the width of the filter, which is appropriate for infinite-length filters, is incorporated directly in the expression for spurious responses. The three criteria are maximized using the variational method and nonlinear constrained optimization. The optimal filter parameters are tabulated for various values of the filter performance criteria. A complete methodology for implementing the optimal filter using approximating recursive digital filtering is presented. The approximating recursive digital filter is separable into two linear filters, operating in two orthogonal directions. The implementation is very simple and computationally efficient. has a constant time of execution for different sizes of the operator, and is readily amenable to real-time hardware implementation. >

156 citations


Journal ArticleDOI
TL;DR: In this paper, the convergence properties of the iterative Wiener filter are analyzed and an alternate iterative filter is proposed to correct for the convergence error, which is shown to give minimum mean-squared error.
Abstract: The iterative Wiener filter, which successively uses the Wiener-filtered signal as an improved prototype to update the covariance estimates, is investigated. The convergence properties of this iterative filter are analyzed. It has been shown that this iterative process converges to a signal which does not correspond to the minimum mean-squared-error solution. Based on the analysis, an alternate iterative filter is proposed to correct for the convergence error. The theoretical performance of the filter has been shown to give minimum mean-squared error. In practical implementation when there is unavoidable error in the covariance computation, the filter may still result in undesirable restoration. Its performance has been investigated and a number of experiments in a practical setting were conducted to demonstrate its effectiveness. >

144 citations


Proceedings ArticleDOI
14 Apr 1991
TL;DR: The proposed image contrast enhancement technique is based on combining the original image with its filtered version obtained using one of the two nonlinear filters.
Abstract: Two types of very simple two-dimensional nonlinear filters are introduced and applied to image contrast enhancement. The first type is based on a generalization of the Teager's algorithm. A theoretical analysis has shown that this type of nonlinear filter works like a local-mean-weighted highpass filter. Based on this analysis, a second type of nonlinear filter has been developed which works like local-mean-weighted bandpass filter. The proposed image contrast enhancement technique is based on combining the original image with its filtered version obtained using one of the two nonlinear filters. Very high quality enhancement has been achieved for natural images. >

142 citations


Journal ArticleDOI
TL;DR: The feedback-cancellation system described updates the estimated feedback path whenever changes are detected in the feedback behavior, and a least-mean square adaptive filter and a Wiener filter are investigated for computing the filter coefficients.
Abstract: Feedback cancellation in hearing aids involves estimating the feedback signal and subtracting it from the microphone input signal. The feedback-cancellation system described updates the estimated feedback path whenever changes are detected in the feedback behavior. When a change is detected, the normal hearing-aid processing is interrupted, a pseudorandom probe signal is injected into the system, and a set of filter coefficients is adjusted to give an estimate of the feedback path. The hearing aid is then returned to normal operation with the feedback-cancellation filter as part of the system. Two approaches are investigated for computing the filter coefficients: a least-mean square (LMS) adaptive filter and a Wiener filter. Test results are presented for a computer simulation of an in-the-ear (ITE) hearing aid. The simulation results indicate that more than 10 dB of cancellation can be obtained and that the Wiener filter is more effective in the presence of strong interference. >

125 citations


Patent
03 Sep 1991
TL;DR: In this paper, a fixed transversal filter is used to adaptively filter a TDMA RF received signal for compensating for a time varying impulse response of the channel, and the adaptive filtering is performed initially during a synchronizing portion (preamble) of the filtered signal in accordance with a fast recursive least squares algorithm.
Abstract: A TDMA RF received signal is demodulated by first being filtered with a fixed transversal filter having a characteristic selected for matching a fixed square root raised cosine pulse characteristic of the received signal. The filtered signal is then adaptively filtered for compensating for a time varying impulse response of the channel. The adaptive filtering is performed initially during a synchronizing portion (preamble) of the filtered signal in accordance with a fast recursive least squares algorithm. Subsequent filter adaptation to a data portion of the filtered signal is accomplished in accordance with a computationally less expensive normalized least mean square procedure. The adaptive filter repetitively applies a modified Viterbi algorithm to blocks of 2D symbols, such that D symbols are released for adapting the adaptive filter means during the data portion of the filtered signal and the signal. The released symbols are also employed for adapting elements required in computing a metric for the modified Viterbi algorithm and the reconstructed signal used to form an error signal that drives the adaptation algorithms.

96 citations


Patent
30 Aug 1991
TL;DR: In this article, the authors proposed to suppress the increment of arithmetic load on an arithmetic unit and attain noise reduction precisely by predicting the divergence of a control sound source based on the update quantity of the filter coefficient of an adaptive filter.
Abstract: PURPOSE:To suppress the increment of arithmetic load on an arithmetic unit and to attain noise reduction precisely by predicting the divergence of a control sound source based on the update quantity of the filter coefficient of an adaptive filter. CONSTITUTION:The filter coefficient is computed so as to minimize the square e of sound pressure based on a reference signal r1m to which filter processing is applied corresponding to the number of combination of transfer relation between microphones 8a-8h and speakers 7a-7d by a microprocessor 16, and the sum computation of the square e of the sound pressure, and the filter processing is applied to a reference signal from a frequency-voltage conversion circuit 11 by the filter coefficient as updating that of the adaptive filter 13 adaptively, and the speakers 7a-7d can be driven. Therefore, since it is possible to predict the divergence of the control sound source and to operate a divergence regulation means 22, divergence phenomenon can be suppressed even when the mechanical characteristics of the speakers 7a-7d and the microphones 8a-8h are changed due to the lapse of time, or the temperature change of control space occurs, etc. Also, it is possible to suppress the increment of arithmetic load on the arithmetic unit.

94 citations


Patent
07 Feb 1991
TL;DR: In this article, a digital virtual earth active cancellation system with an adaptive filter (44) was proposed, in which the adaptive filter is adapted by the system impulse response (c) to cancel the residual signal.
Abstract: A digital virtual earth active cancellation system (14) which receives a phenomena input signal (r) representing residual phenomena to be cancelled and has an adaptive filter (44) which generates a cancellation signal (y). A system impulse response (c) is convolved with the cancellation signal (y) and is subtracted from the input signal (r) to produce an estimate of noise (x). The adaptive filter (44) produces the cancellation signal (y) by filtering the estimated noise (x) with a filter weight (a) that is adapted by the system impulse response (c). By convolving the estimate of noise (x) with the system impulse (c) to adapt the filter (44), the values sent to an adapter (50) for the adaptive filter (44) are kept within 90° phase of the residual signal (r). This substantially eliminates the problems associated with destructive feedback due to phase shifts without the need for external reference signals.

78 citations


Journal ArticleDOI
TL;DR: The transversal variable-length stochastic gradient algorithm is described, a modification of the stochastically gradient algorithm that allows dynamic allocation of coefficients of an adaptive filter, which results in fast convergence, typical of low-order filters, and good steady-state performance, Typical of high- order filters.
Abstract: The transversal variable-length stochastic gradient algorithm is described. It is a modification of the stochastic gradient algorithm that allows dynamic allocation of coefficients of an adaptive filter. The order of the filter and the adaptation step size are changed automatically when an appropriate level of performance is reached during the course of the adaptation process. In this way, the algorithm results in fast convergence, typical of low-order filters, and good steady-state performance, typical of high-order filters. >

69 citations


Journal ArticleDOI
TL;DR: In this article, a simulation of a singly terminated ladder filter is used to obtain a filter bank with a complexity of O(N) for adaptive line enhancement, which has the necessary conditions for global convergence and to yield uncorrelated sinusoidal enhanced outputs that are undistorted versions of the corresponding frequency components of the input.
Abstract: The filter-bank structure proposed is based on a digital simulation of a singly terminated ladder filter. This filter bank can also be arrived at from a filter described by G Peceli (1989) and represents an extremely hardware efficient structure, having a complexity of O(N). The main application examined is adaptive line enhancement. The filter-bank-based line enhancer is shown to have the necessary conditions for global convergence and to yield uncorrelated sinusoidal enhanced outputs that are undistorted versions of the corresponding frequency components of the input. A number of additional possible applications for the filter-bank are described. These include the tracking of periodic signals, subband coding, frequency-domain adaptive noise-cancellation, and frequency-domain processing of signals from phased arrays. >

Book
01 Jan 1991
TL;DR: In this article, Kalman filtering theory structure and parameter adaptive estimation asymptotic and convergence properties of partitioned adaptive systems partitioning filter - probabilistic approach partitioning estimators - scattering approach pseudolinear partitioning filtering and tracking motion analysis two-stage bias correction estimators based on generalized partitioning filters in discrete-time systems multiple model adaptive filtering and control for Markovian jump system
Abstract: Review of Kalman filtering theory structure and parameter adaptive estimation asymptotic and convergence properties of partitioned adaptive systems partitioning filter - probabilistic approach partitioning estimators - scattering approach pseudolinear partitioning filter and tracking motion analysis two-stage bias correction estimators based on generalized partitioning filter forward-pass fixed-interval smoother in discrete-time systems multiple model adaptive filtering and control for Markovian jump system.

Journal ArticleDOI
TL;DR: An adaptive filter structure which is based on linear combinations of order statistics which can adapt well to a variety of noise probability distributions, including impulsive noise and is suitable for image-processing applications.
Abstract: An adaptive filter structure which is based on linear combinations of order statistics is proposed. An efficient method to update the filter coefficients is presented, which is based on the minimal mean-square error criterion and which is similar to the Widrow algorithm for the linear adaptive filters. Another method for coefficient update is presented, which is similar to the recursive least squares (RLS) algorithm and which has faster convergence properties. The proposed-filter can adapt well to a variety of noise probability distributions, including impulsive noise. It also performs well in the case of nonstationary signals and, therefore, it is suitable for image-processing applications. >

Journal ArticleDOI
TL;DR: In this article, an adaptive filter technique for tuning continuous-time integrated filters is presented based on model-matching configuration and tunes both the poles and zeros of the transfer function.
Abstract: An adaptive filter technique for tuning continuous-time integrated filters is presented. This technique is based on the model-matching configuration and tunes both the poles and zeros of the transfer function. Circuit details of an experimental prototype are given. The experimental prototype consists of an integrated third-order filter that is automatically tuned by off-chip circuitry realizing the adaptive tuning system. Both experimental and simulation results are presented to confirm the viability of the proposed approach. >

Journal ArticleDOI
TL;DR: In this article, the authors proposed an adaptive filtering method based on the Kalman filter, a linear recursive estimator, to perform parameter estimation with erroneous models, which has a number of applications in analytical chemistry.
Abstract: The increased power of small computers makes the use of parameter estimation methods attractive. Such methods have a number of uses in analytical chemistry. When valid models are available, many methods work well, but when models used in the estimation are in error, most methods fail. Methods based on the Kalman filter, a linear recursive estimator, may be modified to perform parameter estimation with erroneous models. Modifications to the filter involve allowing the filter to adapt the measurement model to theexperimental data through matching the theoretical and observed covoriance of the filter innovations sequence. The adaptive filtering methods that result have a number of applications in analytical chemistry.

Journal ArticleDOI
TL;DR: A decision feedback equalizer containing a feedback filter with both poles and zeros is proposed for high-speed digital communications over the subscriber loop and results show that the pole-zero DFE offers a significant improvement in mean squared error relative to the conventional DFE.
Abstract: A decision feedback equalizer (DFE) containing a feedback filter with both poles and zeros is proposed for high-speed digital communications over the subscriber loop. The feedback filter is composed of a relatively short FIR filter that cancels the initial part of the channel impulse response, which may contain rapid variations due to bridge taps, and a pole-zero, or IIR, filter that cancels the smoothly decaying tail of the impulse response. Modifications of an adaptive IIR algorithm, based on the Steiglitz-McBride (1965) identification scheme, are proposed to adapt the feedback filter. A measured subscriber loop impulse response is used to compare the performance of the adaptive pole-zero DFE, assuming a two-pole feedback filter, with a conventional DFE having the same number of coefficients. Results show that the pole-zero DFE offers a significant improvement in mean squared error relative to the conventional DFE. The speed convergence of the adaptive pole-zero DFE is comparable to that of the conventional DFE using the standard least mean square (LMS) adaptive algorithm. >

Patent
Erik Ordentlich1, Yair Shoham1
20 Jun 1991
TL;DR: In this article, a CELP code/decoder based system is improved for use with a wide-band signal such as a high-quality speech signal by modifying the noise weighting filter used in such systems to include a filter section which affects primarily the spectral tilt of the weighting filters in addition to a filter component reflecting formant frequency information in the input signal.
Abstract: An improved digital communication system, e.g., a CELP code/decoder based system, is improved for use with a wide-band signal such as a high-quality speech signal by modifying the noise weighting filter used in such systems to include a filter section which affects primarily the spectral tilt of the weighting filter in addition to a filter component reflecting formant frequency information in the input signal. Alternatively, the weighting is modified to reflect perceptual transform techniques.

Journal ArticleDOI
TL;DR: Computer simulations in which the proposed adaptive filter structure is used to identify actual acoustic echo path impulse responses show that the Legendre ADF has better convergence performance than the transversal ADF when identifying systems with long impulse response.
Abstract: An adaptive filter (ADF) structure is proposed for applications in which large-order ADFs are required. It is based on modeling the impulse response of the system to be identified as a linear combination of a set of discrete Legendre orthogonal functions. The proposed adaptive filter structure has desirable stability features and a unimodal mean-square error surface as well as a modular structure that permits an easy increase of the filter order without changing the previous stages. Computer simulations in which the proposed structure is used to identify actual acoustic echo path impulse responses show that the Legendre ADF has better convergence performance than the transversal ADF when identifying systems with long impulse response. >

Journal ArticleDOI
TL;DR: The main advantage of the MSS algorithm over the conventional LMS algorithm is that better performance is achieved without the knowledge of the input signal characteristics, such as signal power, degree of nonstationarity, signal-to-noise ratio, and stability bounds.
Abstract: A multistep size frequency-domain adaptive filter capable of tracking both stationary and nonstationary signals is proposed. This algorithm makes use of the simple structure of the least mean square error algorithm to update the filter coefficients and process the signal. It then proceeds further by incorporating a set of three step sizes and a knowledge-based strategy to select the best set of filter coefficients and the optimum step size iteratively. The main advantage of the MSS algorithm over the conventional LMS algorithm is that better performance is achieved without the knowledge of the input signal characteristics, such as signal power, degree of nonstationarity, signal-to-noise ratio, and stability bounds. Experimentally, the MSS algorithm is tested under various signal environments. The transient characteristics of the step sizes are found to be in agreement with previous theoretical studies of nonstationary characteristics of the LMS algorithm. In order to reduce the complexity, the conventional frequency-domain block LMS structure is also modified so that the MSS algorithm can be embedded more efficiently by exploiting the block structure. >

Proceedings ArticleDOI
14 Apr 1991
TL;DR: The authors present a general, direct method for designing perfect reconstruction filter banks with rational sampling rate changes, and the regularity question is addressed, and a regular filter is shown for a dilation factor of 3/2.
Abstract: The authors present a general, direct method for designing perfect reconstruction filter banks with rational sampling rate changes. Such filter banks have N branches, each one having a sampling factor of p/sub i//q/sub i/ and their sum equal to one. A design example showing the advantage of using the direct over the indirect method is given. Due to recent results pointing to the relationship between filter banks and wavelet theory, the regularity question is addressed as well, and a regular filter is shown for a dilation factor of 3/2. >

Journal ArticleDOI
TL;DR: A new tracking filter is presented that copes with the problems associated with the synthesis of target trackers for air-to-air missiles and is based on the time scale separation inherent in the tracking dynamics.
Abstract: A critical phase during air-to-air interception is the homing phase. It is characterized by a short time to go and low bearing rates on the homing path. The phase is critical because any misconception with respect to the target maneuver may result in a substantial miss distance. This is essentially due to the lack of time to perform path corrections when the target produces a collision course error by an evasive maneuver. The estimation of the target acceleration is therefore crucial to the design of guidance laws that allow a fast response to target maneuvers. There are, however, severe problems associated with the synthesis of target trackers for air-to-air missiles. These problems include the lack of observability, modeling errors, and the restriction of the computation time due to high sampling rates. In this paper, a new tracking filter is presented that copes with the problems just mentioned. It is based on the time scale separation inherent in the tracking dynamics. In conjunction with a simple adaption scheme, this filter is able to track a large class of target maneuvers in a computationally efficient manner.

Journal ArticleDOI
TL;DR: A simplified algorithm is presented for computing the gradient in adaptive IIR (infinite impulse response) lattice filters, and it is concluded that the proposed method allows the development of robust adaptation IIR algorithms with a cost proportional to the filter order.
Abstract: A simplified algorithm is presented for computing the gradient in adaptive IIR (infinite impulse response) lattice filters. For a filter with N zeros and N poles, this algorithm requires only order N computations. Several computer simulations were performed to compare the performance of the proposed O(N) formulation and the conventional O(N/sup 2/) formulation, and no difference in their behavior was found. In these simulations the full Hessian and the diagonal Hessian adaptive algorithms were used in a system-identification configuration. It is concluded that the proposed method allows the development of robust adaptive IIR algorithms with a cost proportional to the filter order. >

Journal ArticleDOI
TL;DR: An algorithm is developed for computing the mean-square-optimal values for small, image-restoration kernels that can restore images with fidelity comparable to images restored with the unconstrained Wiener filter.
Abstract: An algorithm is developed for computing the mean-square-optimal values for small, image-restoration kernels. The algorithm is based on a comprehensive, end-to-end imaging system model that accounts for the important components of the imaging process: the statistics of the scene, the point-spread function of the image-gathering device, sampling effects, noise, and display reconstruction. Subject to constraints on the spatial support of the kernel, the algorithm generates the kernel values that restore the image with maximum fidelity, that is, the kernel minimizes the expected mean-square restoration error. The algorithm is consistent with the derivation of the spatially unconstrained Wiener filter, but leads to a small, spatially constrained kernel that, unlike the unconstrained filter, can be efficiently implemented by convolution. Simulation experiments demonstrate that for a wide range of imaging systems these small kernels can restore images with fidelity comparable to images restored with the unconstrained Wiener filter. >

Journal ArticleDOI
TL;DR: In this paper, a numerically well-conditioned, quasi-extended Kalman filter is proposed, which is numerically described and shown to have superior estimation performance for short distances compared with the widely used linear tracking filters.
Abstract: A numerically well-conditioned, quasi-extended Kalman filter is proposed. The filter is numerically described. The simulation results presented show that the estimation performance of the quasi-extended filter is superior, for short distances, compared with the widely used linear tracking filters. In addition, the simplicity of the quasi-extended filter makes it very easy to implement. >

Journal ArticleDOI
TL;DR: In this paper, a rotation-invariant correlation filter is proposed to minimize correlation plane energy and produce a sharp and easily detected peak, which uses symmetry requirements to achieve rotation invariance and hence is generalized.
Abstract: A rotation-invariant correlation filter to minimize correlation plane energy and produce a sharp and easily detected peak is addressed. The filter uses symmetry requirements to achieve rotation invariance and hence is generalized. Full mathematical detail of the filter synthesis and initial test results are presented. Drawbacks of the existing circular harmonic function (CHF) and other rotation-invariant filters are noted and used as motivation for these new filters.

Proceedings ArticleDOI
14 Apr 1991
TL;DR: An algorithm for efficiently computing the eigenvector associated with the minimum eigenvalue of a correlation matrix is designed and can be used to compute the total least squares (TLS) solution to the linear regression problem which yields unbiased equation-error infinite impulse response (IIR) adaptive filters.
Abstract: An algorithm for efficiently computing the eigenvector associated with the minimum eigenvalue of a correlation matrix is designed. This algorithm can be used to compute the total least squares (TLS) solution to the linear regression problem which yields unbiased equation-error infinite impulse response (IIR) adaptive filters. The algorithm utilizes a two-channel fast Kalman filter and requires only inner products involving L*1 vectors where L is one greater than the total number of filter coefficients. The TLS solution also results in unbiased finite impulse response (FIR) adaptive filters when the filter input is distributed by additive noise, a condition which is usually ignored but may often occur in practice. >

Journal ArticleDOI
TL;DR: The calculation of a phase-encoded inverse filter allows compromises between discrimination capability and diffraction efficiency and phase quantization facilitates the materialization of the filter.
Abstract: Optical pattern recognition can profit from the progress in coding theory and technology that has been made in digital holography. The calculation of a phase-encoded inverse filter is described. This filter allows compromises between discrimination capability and diffraction efficiency. Phase quantization facilitates the materialization of the filter.

Journal ArticleDOI
TL;DR: In this article, a non-linear adaptive fault detection filter (NAFDF) is proposed to detect on-line and isolate the faults of a class of nonlinear systems arising from accidental jumps of the process parameters.
Abstract: A novel non-linear adaptive fault detection filter (NAFDF) is proposed. It can be used to detect on-line and isolate the faults of a class of non-linear systems arising from accidental jumps of the process parameters. The extended Kalman filter and weighted sum-squared residual method are first combined to delect the faults rapidly. A non-linear filter is then proposed and used for joint state and parameter estimation of the system, resulting in a series of parameters. Based on them, Bayes' decision algorithm is modified and used to isolate and classify the faults. An alternate initialization method is also presented, which makes it possible to detect and isolate the faults repeatedly. Finally, the effectiveness of the NAFDF is demonstrated by a simulation study.

Journal ArticleDOI
TL;DR: Two methods are proposed to modify the linear program (LP) developed by E.J. Coyle and J.-H.
Abstract: Two methods are proposed to modify the linear program (LP) developed by E.J. Coyle and J.-H. Lin (1988) to find a stack filter which minimizes the mean absolute error (MAE). In the first approach, the number of constraints is substantially reduced at the expense of requiring a zero-one LP to solve for an optimal filter. This scheme reduces the number of constraints from O(n2/sup n/) to O(28/sup n/), which is exactly the cardinality of the set of possible binary vectors which can appear in the window of the filter. In the second approach, the LP is transformed into a max-flow problem. This guarantees that the problem can be solved in time which is a polynomial function of the number of variables in the LP, as opposed to the worst-case exponential time that may occur with the simplex method. It also allows the many fast algorithms for the max-flow problem to be used to find an optimal stack filter. Recursive algorithms for construction of the window width n constraint matrix for both the original LP and the max-flow modification are also provided. >

Proceedings ArticleDOI
01 Apr 1991
TL;DR: An algorithm is provided that proceeds by changing the conditional expectation into a morphological filter while at the same time increasing the mean-square error a minimal amount, thereby providing a filter design that can be used online for structuring-element updating.
Abstract: Even in the binary case, designing optimal morphological filters involves a time-consuming search procedure that, in practice, can be intractable. The present paper provides an algorithm for filter design that is based upon the relationship between the optimal morphological filter and the conditional expectation. In effect, the algorithm proceeds by changing the conditional expectation into a morphological filter while at the same time increasing the mean-square error a minimal amount. Under many noise environments, the new algorithm is extremely efficient, thereby providing a filter design that can be used online for structuring-element updating.© (1991) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.