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

A new class of nonlinear filters, the so-called class of Multi-Directional Infinite Impulse Response Median Hybrid Filters (MIMH), 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 (including impulse removal, step preservation, and noise suppression). >

Thee Median-Rational Hybrid Filter (MRHF) has been recently introduced as a new class of nonlinear filters and successfully applied to image filtering problems. The main characteristics of the MRHF are the good noise attenuation property in smooth areas and the preservation of edges end details. In fact, in changing areas the noise attenuation is traded for a good response to the change. Moreover, the median filters effectively remove the impulsive noise while the rational filter performs well in relatively high SNR Gaussian contaminated environments. Another relevant characteristic is that MRHF's usually act on small windows and thus require a reduced number of operations, resulting in simple and fast filtering structures. In this paper we present a programmable hardware implementation for the MRHF's. Exploiting the features of the dynamic logic families it is possible to achieve high speed and compactness, while keeping the power dissipation very low.

A new class of nonlinear filters called FIR-weighted myriad hybrid (FIR-WMyH) filters was introduced. These filters have a combination structure of linear FIR filters and weighted myriad filter, and can efficiently utilize the special strongpoint of two filters. Through the backpropagation algorithm used in the neural networks, we derive a stochastic gradient-based adaptive algorithm for determining optimal FIR-WMyH filters under the mean square error (MSE) criterion. In two impulsive noise models, the robust performance of this adaptive algorithm is demonstrated through the computer simulation results. © 2006 IEEE.

A new method for a design of polynomial filters based on the Volterra series expansion is presented. The problem of nonlinear filter design is considered as a multi-objective problem and is solved by using an optimization approach. A theoretical background of the proposed method is stated. The obtained results allow one to design Pareto optimal filters in the presence of several conflicting criteria. In this case, the optimal nonlinear filter is characterized by a filter plane, which is tangent to a convex optimal decision function. The issue of reasonable choice of the design parameters defining the nonlinear filter performance is discussed. Examples of design, together with a performance comparison with other known nonlinear operators on simulated images, complete the article.

Simulation of a non-Gaussian stochastic process based on a combined distribution of the UHPM and the GBD

A novel nonlinear filter, which incorporates the concept of exponential sinusoidal models into nonlinear filters based on functional link networks (FLNs) has been developed in this paper. The proposed filter is designed to provide improved convergence characteristics over traditional FLN filters. The conventional trigonometric FLN may be considered as a special case of the proposed adaptive exponential FLN (AEFLN). An adaptive exponential least mean square (AELMS) algorithm has been derived and the same has been successfully applied for identification of a couple of nonlinear plants. The AEFLN-based nonlinear active noise control (ANC) system has also been designed and an adaptive exponential filtered-s least mean square (AEFsLMS) algorithm has been developed to update the weights as well as the exponential factor. Simulation study has revealed the improved noise mitigation offered by the AEFLN-based nonlinear ANC system.

Through the combination of linear finite impulse response (FIR) filters and weighted order statistic (WOS) filters, the authors introduce a new class of nonlinear filters called FIR-WOS hybrid (FWH) filters. This class of filters, including FIR filters, WOS filters, and various kinds of FIR median hybrid (FMH) filters, consists of a few linear FIR subfilters and a WOS filter operated over the outputs of the subfilters. Motivated by the backpropagation algorithm used in neural networks, an adaptive algorithm is derived in the binary domain for determining optimal FWH filters under the mean absolute error criterion. Simulation results in image processing demonstrate that adaptive FWH filters perform as well as linear filters in Gaussian noise and better than adaptive WOS filters in impulsive noise. >

LIDAR (Laser Integrated Radar) is an engineering problem of great practical importance in environmental monitoring sciences. Signal processing for LIDAR applications involves highly nonlinear models and consequently nonlinear filtering. Optimal nonlinear filters, however, are practically unrealizable. In this paper, the Lainiotis′s multi‐model partitioning methodology and the related approximate but effective nonlinear filtering algorithms are reviewed and applied to LIDAR signal processing. Extensive simulation and performance evaluation of the multi‐model partitioning approach and its application to LIDAR signal processing shows that the nonlinear partitioning methods are very effective and significantly superior to the nonlinear extended Kalman filter (EKF), which has been the standard nonlinear filter in past engineering applications.

A simulator to aid in the design of nonlinear image processing filters is developed. This simulator assists the filter design by determining parameters manually by trial-and-error. The method is also useful for improving the results of the learning optimization methods. An example of the application of the technique to improve a resultant filter by a learning method of a mathematical morphological filter is shown.

In this paper we propose a generalized method of structural identification of biomedical signals with locally concentrated properties using a digital non-linear filter. The experimental verification of the detecting function was performed by using different ways to describe the model of the desired class of structural elements.

In the light of an increasing share in the electrical grid, wind turbines must be enabled to provide grid stabilizing behavior. This can be achieved by a variation of the turbine’s power output depending on the current state of the electrical grid. However, changes of power output excite oscillations in the turbine structure. To reduce the loading caused by the considered frequency droop scheme, in this paper a nonlinear model-based filter design in a Takagi-Sugeno structure is proposed. The design uses Lyapunov function-based linear matrix inequalities for deriving the necessary feedback gains of the filter. The results are obtained for NREL’s 5 MW reference turbine. By connecting FAST to an analytic power system model, we study the effects on turbine loading as a result of frequency stabilization in case of a load imbalance. The proposed filter is designed and implemented to reduce the damage equivalent load of the tower fore-aft motion, and its influence on the frequency trajectory is studied.

Linear filtering techniques have serious limitations in dealing with signals that have been created or processed by a system exhibiting some degree of nonlinearity, or, in general, situations where the relevance of information cannot be specified in the frequency domain. In image processing, many of these characteristics are often present, and it is no wonder that image processing is the field where nonlinear filtering techniques have first shown clear superiority over linear filters. Since nonlinear filters are all of those filters that are not linear, there is a large variety of different filters in use, and no common theory can exist. This makes filter design challenging, and optimization is meaningful only after restricting the class. It can be done in several conceptually different ways and, in this paper, we consider these techniques and the optimization methods that go together with the particular restriction. We review polynomial and rational filter classes and the optimization of stack filters under structural constraints and statistical constraints.

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.

RESPONSE STATISTICS OF OCEAN STRUCTURES TO NON-LINEAR HYDRODYNAMIC LOADING PART II: NON-GAUSSIAN OCEAN WAVES

We study the effects of linear and nonlinear filter distortions on MSK modulated signals. The linear filter distortions considered include bandlimiting and impairments described by a polynomial decomposition of the amplitude and phase response, i.e., linear amplitude, parabolic amplitude, residual amplitude, parabolic phase, cubic phase and residual phase. The nonlinear distortions considered are memoryless AM/AM and AM/PM conversions. The class of nonlinear filters that can be modeled by a linear distortion followed by memoryless AM/AM and AM/PM conversions can be understood by studying the combined effects of these individual distortions. This model can be used for modeling TWTAs and other nonlinear amplifiers. Using this approach we show how certain linear filter distortions can precompensate for subsequent nonlinear distortions. Specifically, we demonstrate that when the phase shift vs. input power curve exhibits a negative slope, i.e. AM/PM 0, the negative parabolic phase reduces the net phase variation as compared to the positive parabolic phase.