New Class Of Nonlinear Filters Research Articles

Nonlinear acoustic echo cancellation based on pipelined Hermite filters

This paper introduces a new class of nonlinear filters for nonlinear acoustic echo cancellation (NLAEC) based on Hermite nonlinear filters (HNFs), which is a sub-class of linear-in-the-parameters nonlinear filters (LIPNFs). Specifically, the basis functions of HNFs include cross-terms of the expanded inputs at different time instants, and are mutually orthogonal for white normally distributed input signals. Although HNFs yield good performance for NLAEC, they suffer from high computational complexity. To tackle this problem, a computationally efficient pipelined variant of HNFs is introduced. The pipelined HNFs (PHNFs) include a nonlinear part followed by a linear one such that the input space is first expanded nonlinearly and then cast by a linear mapping to the output space. Experimental results using both synthesized and real data, and involving several nonlinear scenarios show the effectiveness of the proposed approach.

A new method for the design of energy transfer filters

This paper is concerned with the development of a new method for the design of energy transfer filters (ETFs). ETFs are a new class of non-linear filters recently proposed by the authors, which employ non-linear effects to transfer signal energy from one frequency band to a different frequency location. The new method uses the powerful orthogonal least squares (OLS) algorithm to solve the least squares problem associated with the design and compared with previous methods achieves much better filtering performance.

Vector Directional Distance Rational Hybrid Filters for Color Image Restoration

A new class of nonlinear filters, called vector-directional distance rational hybrid filters (VDDRHF) for multispectral image processing, is introduced and applied to color image-filtering problems. These filters are based on rational functions (RF). The VDDRHF filter is a two-stage filter, which exploits the features of the vector directional distance filter (VDDF), the center weighted vector directional distance filter (CWVDDF) and those of the rational operator. The filter output is a result of vector rational function (VRF) operating on the output of three sub-functions. Two vector directional distance (VDDF) filters and one center weighted vector directional distance filter (CWVDDF) are proposed to be used in the first stage due to their desirable properties, such as, noise attenuation, chromaticity retention, and edges and details preservation. Experimental results show that the new VDDRHF outperforms a number of widely known nonlinear filters for multi-spectral image processing such as the vector median filter (VMF), the generalized vector directional filters (GVDF) and distance directional filters (DDF) with respect to all criteria used. 

Parallel computations for Yau filters

In the early 1990s, Yau developed a new class of nonlinear filters, called the Yau Filterswhich contain the Kalman-Bucy filters and the Benes filters as special cases. It has been shown that, from the Lie algebraic point of view, the Yau filters are the most general finite-dimensional filters. Yau and Hu proved that the DMZ equation for a Yau filter can be reduced to a Kolmogorov type partial differential equation and a system of linear differential equations. They noticed that the PDE is independent of the observed data and hence can be solved off-line. An efficient parallel algorithm for the system of ODEs would lead to fast solutions of Yau filters and hence their suitability for real-life applications. In this paper, we have proposed several parallel methods suitable for this system of ODEs.

ECG baseline wander and powerline interference reduction using nonlinear filter bank

Methods of noise reduction have decisive influence on performance of all electrocardiographic (ECG) signal processing systems. This work deals with problems of baseline wander and powerline interference reduction. It is impossible to reduce effectively these disturbances without signal distortion using a linear filtering approach. Another disadvantage of the linear filters is their long impulse response. This leads to inadmissibly large delay in ECG signal analysis in monitoring and exercise electrocardiography. This work presents a new class of nonlinear filters without these disadvantages. Additionally, using a bank of these filters, powerline interference reduction is possible. Performance of the new method is experimentally compared with the traditional methods of baseline wander reduction using synthetic as well as the signals from the CTS-ECG database.

Generalised class of nonlinear-type hybrid filters

A new class of nonlinear filters called the generalised directional distance rational hybrid filters (GDDRHF) for multidimensional signal processing is described. The application at hand is colour image filtering problems. The GDDRHF filter is a two-stage filter, which exploits the features of a new directional distance filter, where the temporal information related to the central sample is expressed by its weight, and those of the rational operator. This weight is incorporated to a sum of vector distances and vector angles. It is shown that the new GDDRHF outperforms a number of widely known nonlinear filters with respect to all criteria used.

Vector median-rational hybrid filters for multichannel image processing

In this letter, a new class of nonlinear filters called vector median-rational hybrid filters (VMRHFs) for multispectral image processing is introduced and applied to the color image filtering problem. These filters are based on rational functions (RFs) offering a number of advantages. First, a rational function is a universal approximator and a good extrapolator. Second, it can be trained by a linear adaptive algorithm. Third, it produces the best approximation (w.r.t. a given cost function) for some specific functions. The output is the result of a vector rational operation over the output of three subfilters, such as two vector median (VM) subfilters and one center weighted vector median filter (CWVMF). These filters exhibit desirable properties, such as edge and details preservation and accurate chromaticity estimation.

Nonlinear filtering by threshold decomposition

A new threshold decomposition architecture is introduced to implement stack filters. The architecture is also generalized to a new class of nonlinear filters known as threshold decomposition (TD) filters which are shown to be equivalent to the class of L1-filters under certain conditions. Another new class of filters known as linear and order statistic (LOS) filters result from the intersection of the class of TD and L1-filters. Performance comparisons among several filters are then presented. It was found that TD is compatible with L1, LOS, and linear filters in suppressing Gaussian noise, and is superior in suppressing salt-and-pepper noise. LOS filters, however, provide a better compromise in performance and complexity.

Median-rational hybrid filters for image restoration

A new class of nonlinear filters is introduced, called median-rational hybrid filters (MRHFs), based on rational functions (RFs). The output is the result of rational operation taking into account three sub-functions. It is shown that every sub-function will preserve details within its sub-windows. The proposed MRHF filters have the inherent property that on smooth areas they provide good noise attenuation whereas on changing areas the noise attenuation is traded for good response to change. It is shown that a consistent reduction in the objectively measured mean absolute error and mean square error is obtained.

Smoothing of discontinuous signals: the competitive approach

Discontinuous signals buried in noise cannot be recovered by linear filtering methods. This paper presents a new class of nonlinear filters in which sets of forward and backward linear predictors and smoothers compete with each other at each timestep. The winner of each competition is granted the right to produce the smoothed estimate at that timestep. This conceptually simple approach to nonlinear filtering, called the competitive smoothing approach, is justified by considering sets of Kalman filters (corresponding to the hypotheses used in the Bayesian framework) which are used to derive model credibility coefficients. These are shown to essentially "switch" between the various models. We argue that the concept of competitive smoothing is considerably more general than just the Kalman setting, and can be used with almost any predictors and/or smoothers. Several examples are presented which demonstrate the efficacy of the approach at both smoothing and preserving jump discontinuities. Comparisons are made with the other main nonlinear filtering approach, the median filter.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Permutation weighted order statistic filter lattices

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 temporal-order and rank-order of samples within a window. Hence, PWOS filters are in essence time-varying WOS filters. By varying the amount of temporal-rank 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 well-known 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 PWOS filters are realizable by a N! piecewise linear threshold logic gate where the coefficients within each partition can be easily optimized using stack filter theory. Simulations are included to show the advantages of PWOS filters for the processing of image and video signals.

Permutation filters: a class of nonlinear filters based on set permutations

Introduces and analyzes a new class of nonlinear filters that have their roots in permutation theory. The authors show that a large body of nonlinear filters proposed to date constitute a proper subset of permutation filters (/spl Pscr/ filters). In particular, rank-order filters, weighted rank-order filters, and stack filters embody limited permutation transformations of a set. Indeed, by using the full potential of a permutation group transformation, one can design very efficient estimation algorithms. Permutation groups inherently utilize both rank-order and temporal-order information; thus, the estimation of nonstationary processes in Gaussian/nonGaussian environments with frequency selection can be effectively addressed. An adaptive design algorithm that minimizes the mean absolute error criterion is described as well as a more flexible adaptive algorithm that attains the optimal permutation filter under a deterministic least normed error criterion. Simulation results are presented to illustrate the performance of permutation filters in comparison with other widely used filters. >

Tree-structured nonlinear filters in digital mammography

A new class of nonlinear filters with more robust characteristics for noise suppression and detail preservation is proposed for processing digital mammographic images. The new algorithm consists of two major filtering blocks: (a) a multistage tree-structured filter for image enhancement that uses central weighted median filters as basic sub-filtering blocks and (b) a dispersion edge detector. The design of the algorithm also included the use of linear and curved windows to determine whether variable shape windowing could improve detail preservation. First, the noise-suppressing properties of the tree-structured filter were compared to single filters, namely the median and the central weighted median with conventional square and variable shape adaptive windows; simulated images were used for this purpose. Second, the edge detection properties of the tree-structured filter cascaded with the dispersion edge detector were compared to the performance of the dispersion edge detector alone, the Sobel operator, and the single median filter cascaded with the dispersion edge detector. Selected mammographic images with representative biopsy-proven malignancies were processed with all methods and the results were visually evaluated by an expert mammographer. In all applications, the proposed filter suggested better detail preservation, noise suppression, and edge detection than all other approaches and it may prove to be a useful tool for computer-assisted diagnosis in digital mammography.

An IIR median hybrid filter

A new class of nonlinear filters, the multidirectional infinite impulse response median hybrid (MIMH) filters, is presented and analyzed. The input signal is processed twice using a linear shift-invariant (LSI) infinite impulse response (IIR) filtering module: once with normal causality and a second time with inverted causality. The final output of the MIMH filter is the median of the two-directional outputs and the original input signal. Thus, the MIMH filter is a concatenation of linear filtering (a LSI IIR filtering module) and nonlinear filtering (a median filtering module). Because of this unique scheme, the MIMH filter possesses many desirable properties which are both proven and analyzed (including impulse removal, step preservation, and noise suppression). A comparison to other medium-type filters is also provided.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Algorithms and architectures for a class of non-linear hybrid filters

Non-linear filters based on ranked order statistics form an important class of filters for image enhancement. They can smooth noisy images while retaining edge structures. Recently, a new class of non-linear filters called FIR-median hybrid (FMH) filters were proposed. They are more computationally efficient than the conventional median filter as the size of the window increases, since the number of ordering operations is independent of the size of window. Also, they can preserve fine details such as lines. In real time applications such as industrial inspection, techniques for fast computation of image processing filters, especially using parallel architectures, are of great interest. Recently there have been several inspection systems using pipeline architectures and various new algorithms have been proposed. In this paper, we describe algorithms for computing various classes of FMH filters using a pipeline image processing system equipped with hardware comparators, which are available on most commercial pipeline machines. These include the unidirectional, the bidirectional, and the multilevel FMH filters. The correctness of the algorithms is proven. The time and space complexities of the algorithms are analyzed.

A class of solvable nonlinear filters

The purpose of this paper is to present a new class of nonlinear filters that can be explicitly computed. The systems have drift satisfying a Riccati equation f + f 2 = V where V is Fourier transform of an arbitrary complex even Borel measure on U and we give an explicit formula for the unnormalized conditional density, as a convergent series each term of which depends only on a finite number of statistics.

A Linear Method for the Design of Optimal Nonlinear Filters for Non-Gaussian Processes

Attention is devoted in the present paper to obtaining the optimal mean square estimate X^(t) of X(t) given the observations {Y(s): t0≤ s≤ t }, where X and Y are jointly defined second-order non-Gaussian (i.e., not necessarily Gaussian) real-valued stochastic processes on an interval I: t0≤ t ≤ tf of the real line with known statistics. The underlying filter is represented by a Volterra functional series belonging to a generalized Fock space Fρ. Generalized Fock spaces are reproducing kernel Hilbert spaces of nonlinear functionals introduced by de Figueiredo and Dwyer (1980). In such a setting. a new linearequation in the space Fρ, which the optimal nonlinear filter must satisfy. is derived. This equation reduces to the Wiener-Hopf equation in the linear Gaussian case. Finally. a new class of nonlinear filters is presented which is optimal for a wide class of non-Gaussian stochastic processes. and is simple to implement.