Pareto optimal nonlinear filters for image enhancement

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

An analytic solution for real optimal filters is known, and the special case of optimal binary phase-only filters can be solved by a fast binning algorithm but no analytic solution is known. We establish a geometric solution for the design of optimal binary amplitude filters (OBAF's) and optimal binary phase-only filters (OBPOF's) for any object. The optimal filter is found in terms of maximizing the field strength at the origin in the correlation plane. We found that it is possible to construct a unique convex polygon by using an ordered set of phasors from the filter object's Fourier transform. This process leads eventually to an exact solution for the filter-design problem. We show that the maximum distance across the polygon divides the phasors into two groups: For the OBAF, it determines the group that is passed or blocked; for the OBPOF, it determines which group is passed with a zero or a pi phase shift. The shape of the convex polygon gives qualitative information on the criticalness and the tightness needed in the design process. It provides good insight into the binning-process algorithm and permits us to bound the error in the binning process. Design examples through computer simulation and applications in fingerprint identification are presented.

An efficient method is proposed for the design of finite impulse response (FIR) filter with arbitrary pass band edge, stop band edge frequencies and transition width. The proposed FIR band stop filter is designed using craziness based particle swarm optimization (CRPSO) approach. Given the filter specifications to be realized, the CRPSO algorithm generates a set of optimal filter coefficients and tries to meet the ideal frequency response characteristics. In this paper, for the given problem, the realizations of the optimal FIR band pass filters of different orders have been performed. The simulation results have been compared with those obtained by the well accepted evolutionary algorithms, such as Parks and McClellan algorithm (PMA), genetic algorithm (GA) and classical particle swarm optimization (PSO). Several numerical design examples justify that the proposed optimal filter design approach using CRPSO outperforms PMA and PSO, not only in the accuracy of the designed filter but also in the convergence speed and solution quality.

The theory of optimum nonlinear filters outlined in this paper is based on the consideration of a sequence of classes of nonlinear filters, designated as 𝔑1, 𝔑2, 𝔑3, …, such that each class in the sequence includes all the preceding classes and, furthermore, the class of linear filters is a subclass of every class in the sequence. A filter of class 𝔑m is described in terms of a characteristic function which involves m age variables and m values of the input time-function. The input-output relationship for a filter of class 𝔑m has the form of an m-fold integral of the characteristic function with respect to the m age variables. It is shown that the characteristic function of the optimum filter (in the least squares sense) within the class 𝔑m satisfies a linear integral equation of 2mth order. The optimization of filters of class 𝔑1 is treated in detail, and methods of approximate realization of such filters in the form of nonlinear delay line filters and power series filters are indicated. The results are extended to the case of nonstationary time series.

Stator frame radial vibrations of an induction motor are composed of the sum of three different components: aerodynamic, mechanical and electromagnetic vibrations. The separation of these components could be useful in order to quantify their respective vibratory influence. Moreover, each of these components carrying different physical informations, such a processing could be interesting to further analyze each component independently, and finally diagnose induction machine faults more easily. This paper deals with a new processing algorithm able to extract electro-magnetic vibrations of an induction motor from measured signals. To this end, a nonlinear quadratic optimal filter is used to estimate these vibratory components from stator currents and radial vibrations measured at one location on the stator frame. This algorithm is based on the physical quadratic link between stator currents and electromagnetic vibrations, which is first detailed. The algorithm used to estimate the optimal nonlinear quadratic filter is then determined and analyzed. Finally, the proposed algorithm is applied to real signals, and is shown to be very efficient, whatever frequency band.

Robust fault detection for a class of nonlinear time-delay systems

Filters are important building blocks in signal processing circuits. Some researcher had successfully utilized genetic algorithm (GA) in design of filters. Nevertheless, filters obtained by GA are always complex and require lengthy computations. Ant colony optimization (ACO) is a novel searching technique used in optimization problems. In this paper, an ACO approach for optimization of analog filters is presented. In a design example, the order of a lowpass filter and the parameters of its components have been optimized in a discrete search space. AC analysis of the optimized filter has been conducted, and the results have been compared with a filter obtained by GA. The results show that filters obtained by ACO have simpler structures and better performance.

This paper presents an alternative approach for the design of linear phase digital high pass FIR filter using Particle Swarm Optimization with Constriction Factor and Inertia Weight Approach (PSOCFIWA). FIR filter design is a multi-modal optimization problem. The conventional gradient based optimization techniques are not efficient for digital filter design. Given the filter specifications to be realized, PSO algorithm generates a set of optimal filter coefficients and tries to meet the ideal frequency characteristic. In this paper, for the given problem, the realization of the optimal FIR high pass filters of different orders has been performed. The simulation results have been compared to those obtained by the well accepted evolutionary algorithm such as genetic algorithm (GA). The results justify that the proposed optimal filter design approach using PSOCFIWA outperforms GA, not only in the accuracy of the designed filter but also in the convergence speed and solution quality.

Three adaptive linearization schemes are proposed. In the first scheme, linearization is performed by canceling nonlinearity at the output of a physical system. In the second, a nonlinear postprocessor is employed to postdistort signals. In the third, a preprocessor is used. The schemes using a postprocessor and a preprocessor are designed for weakly nonlinear systems, whereas the scheme of linearization by cancellation at the output can be applied to problems with stronger nonlinearities. In all three methods, necessary estimates of linear and nonlinear operators are provided by adaptive linear and nonlinear filters. Typical simulation results for a physical system modeled by a Volterra series with a linear term, a quadratic term, and a cubic term are presented and are judged encouraging. >

This paper considers the nonlinear system filtering with packet dropouts. We assume that the packet arrived rate is known in advance but the sequence of packet dropouts is unknown. At first, we use the probability-weighted method to achieve a pseudo measurement sequence, and every pseudo measurement is the weighted value of the measurements acquired at the current time step and the prior time step. Some classical nonlinear filtering methods can be used via the pseudo measurement sequence and the dynamic equation of the system, and then the pseudo measurement unscented Kalman filter (PM_UKF) and the pseudo measurement particle filter (PM_PF) are given. This pseudo measurement sequence can be also used in the linear system, and its time complexity is lower than that of Sun's optimal filter at this time. Simulation results show the effectiveness of the proposed algorithms.

In this paper, an optimal multilevel stack filtering algorithm (the stack filters used at each level are designed to be optimal) is introduced. Optimal multilevel stack filter is capable of considering a larger window mask than an optimal stack filter. Multilevel unidirectional stack filters and multilevel bidirectional stack filters are studied in particular. Design of an optimal multilevel stack filter is similar to the design of an optimal stack filter where the compare-and- select algorithm can be used. However, the design procedure needs to be adapted to operation on more than one level. Several design examples are presented showing the good performance of the proposed method.

A comparison of various low-pass filter architectures that are commonly used in Sigma-Delta(/spl Sigma/-/spl Delta/) demodulators is presented in the paper. In this comparison the conventional demodulator filter architectures such as the optimal FIR filter, Sinc/sup k/ filter and non-linear Zoomer filter are considered. It is shown that the optimum FIR filter provides the most attractive properties among the conventional demodulator low-pass filters. As an alternative to the optimal FIR filter, optimal Laguerre IIR filter architecture is then proposed in the paper. A design scheme for the optimal IIR filter is presented via the use of orthonormal Laguerre functions. In comparison with the conventional FIR filter approach, this design offers several attractive features. The proposed IIR filter design problem is easy to solve and numerically robust. Furthermore, the optimal IIR filter is easy to implement because it needs only a small number of components and therefore well suited for VLSI implementations.

Optimal duration-bandwidth localized antisymmetric biorthogonal wavelet filters

A training framework is developed in this paper to design optimal nonlinear filters for various signal and image processing tasks. The targeted families of nonlinear filters are the Boolean filters and stack filters. The main merit of this framework at the implementation level is perhaps the absence of constraining models, making it nearly universal in terms of application areas. We develop fast procedures to design optimal or close to optimal filters, based on some representative training set. Furthermore, the training framework shows explicitly the essential part of the initial specification and how it affects the resulting optimal solution. Symmetry constraints are imposed on the data and, consequently, on the resulting optimal solutions for improved performance and ease of implementation. The case study is dedicated to natural images. The properties of optimal Boolean and stack filters, when the desired signal in the training set is the image of a natural scene, are analyzed. Specifically, the effect of changing the desired signal (using various natural images) and the characteristics of the noise (the probability distribution function, the mean, and the variance) is analyzed. Elaborate experimental conditions were selected to investigate the robustness of the optimal solutions using a sensitivity measure computed on data sets. A remarkably low sensitivity and, consequently, a good generalization power of Boolean and stack filters are revealed. Boolean-based filters are thus shown to be not only suitable for image restoration but also robust, making it possible to build libraries of "optimal" filters, which are suitable for a set of applications.