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Adaptive Weighted Myriad Filter Algorithms for Robust Signal Processing in alphaStable Noise Environments
, 1998
"... Stochastic gradientbased adaptive algorithms are developed for the optimization of Weighted Myriad Filters. Weighted Myriad Filters form a class of nonlinear filters, motivated by the properties of ffstable distributions, that have been proposed for robust nonGaussian signal processing in impulsi ..."
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Cited by 17 (8 self)
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Stochastic gradientbased adaptive algorithms are developed for the optimization of Weighted Myriad Filters. Weighted Myriad Filters form a class of nonlinear filters, motivated by the properties of ffstable distributions, that have been proposed for robust nonGaussian signal processing in impulsive noise environments. The weighted myriad for an Nlong data window is described by a set of nonnegative weights fw i g N i=1 and the socalled linearity parameter K ? 0. In the limit as K ! 1, the filter reduces to the familiar weighted mean filter (a constrained linear FIR filter). In this paper, necessary conditions are obtained for optimality of the filter weights under the mean absolute error criterion. An implicit formulation of the filter output is used to find an expression for the gradient of the cost function. Using instantaneous gradient estimates, an adaptive steepestdescent algorithm is then derived to optimize the weights. This algorithm involves a very simple update term t...
Selection Weighted Vector Directional Filters
"... In this paper, a class of Weighted Vector Directional Filters (WVDFs) based on the selection of the output sample from the multichannel input set is analyzed and optimized. The WVDF output minimizes the sum of weighted angular distances to other input samples from the filtering window. Dependent o ..."
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Cited by 11 (3 self)
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In this paper, a class of Weighted Vector Directional Filters (WVDFs) based on the selection of the output sample from the multichannel input set is analyzed and optimized. The WVDF output minimizes the sum of weighted angular distances to other input samples from the filtering window. Dependent on the weighting coefficients, the class of the WVDFs can be designed to perform a number of smoothing operations with different properties, which can be applied for specific filtering scenarios. In order to adapt the weighting coefficients to varying noise and image statistics, we introduce a methodology, which achieves an optimal tradeoff between smoothing and detail preserving characteristics. The proposed angular optimization algorithms take advantage of adaptive stack filters design and weighted median filtering framework. The optimized WVDFs are able to remove image noise, while maintaining excellent signaldetail preservation capabilities and sufficient robustness for a variety of signal and noise statistics.
Permutation Weighted Order Statistic Filter Lattices
 IEEE Transactions on Image Processing
, 1995
"... We introduce and analyze a new class of nonlinear filters called permutation weighted order statistic (PWOS) filters. These filters extend the concept of weighted order statistic (WOS) filters, in which filter weights associated with the input samples are used to replicate the corresponding sample ..."
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Cited by 5 (2 self)
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We introduce and analyze a new class of nonlinear filters called permutation weighted order statistic (PWOS) filters. These filters extend the concept of weighted order statistic (WOS) filters, in which filter weights associated with the input samples are used to replicate the corresponding samples, and an order statistic is chosen as the filter output. PWOS filters replicate each input sample according to weights determined by the temporalorder and rankorder of samples within a window. Hence, PWOS filters are in essence timevarying WOS filters. By varying the temporalrank order information used in selecting the output, for a given observation window size, we obtain a wide range of filters that are shown to comprise a complete lattice structure. At the simplest level in the lattice, PWOS filters reduce to the wellknown WOS filter, but for higher levels in the lattice, the obtained selection filters can model complex nonlinear systems and signal distortions. It is shown that PW...
Weighted Order Statistic Classifiers with Large RankOrder Margin
 in Proceedings of the Twentieth International Conference on Machine Learning
, 2003
"... We investigate how stack filter function classes like weighted order statistics can be applied to classification problems. This leads to a new design criteria for linear classifiers when inputs are binaryvalued and weights are positive. We present a rankbased measure of margin that is direct ..."
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We investigate how stack filter function classes like weighted order statistics can be applied to classification problems. This leads to a new design criteria for linear classifiers when inputs are binaryvalued and weights are positive. We present a rankbased measure of margin that is directly optimized as a standard linear program and investigate its relationship to regularization. Our approach can robustly combine large numbers of base hypothesis and has similar performance to other types of regularization.
Circuits and Systems Exposition Weighted Median Filters: A Tutorial
"... Abstract Weighted Median (WM) filters have attracted a growing number of interest in the past few years. They inherent the robustness and edge preserving capability of the classical median filter and resemble linear FIR filters in certain properties. Furthermore, WM filters belong to the broad clas ..."
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Abstract Weighted Median (WM) filters have attracted a growing number of interest in the past few years. They inherent the robustness and edge preserving capability of the classical median filter and resemble linear FIR filters in certain properties. Furthermore, WM filters belong to the broad class of nonlinear filters called stack filters. This enables the use of the tools developed for the latter class in characterizing and analyzing the behavior and properties of WM filters, e.g. noise attenuation capability. The fact that WM filters are threshold functions allows the use of neural network training methods to obtain adaptive WM filters. In this tutorial paper we trace the development of the theory of WM filtering from its beginnings in the median filter to the recently developed theory of optimal weighted median filtering. The following one and multidimensional applications are presented in this paper: idempotent weighted median filters for speech processing, adaptive weighted median and optimal weighted median filters for image and image sequence restoration, weighted medians as robust predictors in DPCM coding and Quincunx coding, and weighted median filters in scan rate conversion in normal TV and HDTV systems. I.
A Parallel Programmable Architecture for Linear and Nonlinear Filtering
"... In this paper we introduce a parallel, programmable architecture capable of supporting both linear and nonlinear filtering. The proposed architecture consists of a ring of processors which can be configured to operate like a sorter for order statistic based filters, and like a systolic array for lin ..."
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In this paper we introduce a parallel, programmable architecture capable of supporting both linear and nonlinear filtering. The proposed architecture consists of a ring of processors which can be configured to operate like a sorter for order statistic based filters, and like a systolic array for linear filters. Such a structure also supports combination filters that are obtained by cascading linear and nonlinear flters. In addition, this architecture efficiently computes filters with window sizes larger than the number of processors. 1 Introduction In digital signal and image processing applications, removal of noise is achieved by nonlinear filters, linear filters, and a combination of these two filters. Each of these filters are effective in removing certain types of noise distributions. For instance, linear filters effectively remove Gaussian noise. Nonlinear filters, based on order statistics, effectively remove impulsive noise and noise with a heavytailed distribution. In the p...
Algebraic Characterizations of Nonlinear Digital Filters
"... The book, Fundamentals of Nonlinear Digital Filtering, by Jaako Astola and Pauli Kuosmanen presents both a useful selection guide for practitioners seeking a signal processing solution and a valuable panoramic perspective for theoreticians interested in the underlying principles on which nonlinear d ..."
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The book, Fundamentals of Nonlinear Digital Filtering, by Jaako Astola and Pauli Kuosmanen presents both a useful selection guide for practitioners seeking a signal processing solution and a valuable panoramic perspective for theoreticians interested in the underlying principles on which nonlinear digital filters are based. For example, the results presented in their book make it clear that most popular nonlinear filters exhibit homogeneous scaling behavior, and are mostly based on nonsmooth (i.e., “medianlike”) functions, rendering the Taylor series expansions popular in many engineering disciplines largely useless. What is less obvious is that these two characteristics are closely related, a result that comes from the theory of functional equations. This paper examines a range of algebraic ideas (e.g., categories, groupoids, clones, etc.) that can be useful in characterizing and designing nonlinear filters, building in part on our past joint work with Jaakko Astola. 1
Weighted Median Filters with SigmaDelta Modulation Encoding
"... Oversampled SigmaDelta modulation (SDM) is becoming a standard method for implementing highresolution A/D and D/A converters in silicon. Digital decimation filters play a fundamental role in Oversampled SigmaDelta A/D decoders. In this paper, we first show that Weighted Median Filters (WMF) can b ..."
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Oversampled SigmaDelta modulation (SDM) is becoming a standard method for implementing highresolution A/D and D/A converters in silicon. Digital decimation filters play a fundamental role in Oversampled SigmaDelta A/D decoders. In this paper, we first show that Weighted Median Filters (WMF) can be used for SDM decimation filters and that these filters are readily implemented in the SDM binary domain. A very promising characteristic SDM converters equipped with weighted median decimating filters is that sharp discontinuities (edges) can be preserved and acquired. Thus, the bandlimited constraint imposed on the input signals could be relaxed making SDM more attractive to A/D conversion of signals containing sharp transitions. Secondly, we show that weighted median filtering of a demodulated sequence (at the Nyquist rate) can be implemented concurrently in the A/D decoder. Thus, by a simple modification of the binary timeseries outputted by the A/D modulator, the sequence obtained aft...
SESSION IIB MULTIMEDIA STORAGE, COMPRESSION AND APPLICATION THREEDIMENSIONAL SHAPE MODELING WITH A RASTER SCAN FORMAT
"... Abstract: A simple and robust procedure of threedimensional shape modeling for an object approximation has been developed based on a raster scan modeling algorithm. A prototypical surface or solid model with desired meshing is first prepared and then transferred to the model that approximates the s ..."
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Abstract: A simple and robust procedure of threedimensional shape modeling for an object approximation has been developed based on a raster scan modeling algorithm. A prototypical surface or solid model with desired meshing is first prepared and then transferred to the model that approximates the shape of the real object. The vertex geometry of the prototypical mesh is modified based on the multidirectional silhouettes, light stripe projection and position measurement using triangulation. Topology of the prototype is conserved throughout the process. Stable meshing, and hence, accurate shape approximation is developed. This also eliminates the laborious modeling procedures, the sophisticated camera calibrations, and complicated geometric model data transmission protocols, enabling the remote and quasireal time monitoring and modeling.