Nonlinear Filtering Algorithm Research Articles

Local linear LUT method for spatial colour-correction algorithm speed-up

There is a class of nonlinear filtering algorithms for digital colour enhancement, characterised by data-driven local effects and high computational cost. A new method called LLL (local linear look-up table (LUT)) is presented, which speeds up these filters without losing their local effect. Usually, classic LUT-based methods are global whereas the approach presented here uses the principles of LUT transformation in a local way. The main idea of this method is to apply the colour-enhancement algorithm to a small sub-sampled version of the input image and to use a modified look-up table technique to maintain the local filtering effect of the colour-enhancement algorithm. The method increases the speed of colour-filtering algorithms, reducing the number of pixels involved in the computation by sub-sampling the input image. To overcome possible loss of detail due to sub-sampling, an optional, additional stage to maintain high-frequency content is shown. LLL with two of these filters, the Brownian Retinex implementation and the automatic colour equalisation algorithm, are tested. Results, comparison and conclusions are presented.

New Kalman filtering algorithm for narrowband interference suppression in spread spectrum systems

A new Kalman filtering algorithm based on estimation of spread spectrum signal before suppression of narrowband interference (NBI) in spread spectrum systems, using the dependence of autoregressive (AR) interference, is presented compared with performance of the ACM nonlinear filtering algorithm, simulation results show that the proposed algorithm has preferable performance, there is about 5 dB SNR improvement in average.

New Nonlinear Filtering Strategies for Eliminating Medium and Long Tailed Noise in Images with Edge Preservation Properties

Arithmetic filters are quite effective in recovering the images confounded by medium-tailed (Gaussian) noise. These filters, however, perform poorly in the presence of additive long-tailed (impulse) noise and they do not preserve edge structures. Median smoother discards outliers (impulses) effectively, but it fails to provide adequate smoothing for images corrupted with non-impulsive noise. In this paper, two new nonlinear techniques for image filtering, which we call New Filter I and New Filter II, are proposed based on a recently developed nonlinear highpass filter algorithm. New Filter I suppresses Gaussian noise quite well. New Filter II effectively eliminates impulses and filters out noise having Gaussian statistics. Both the Alters are shown to have good edge preserving characteristics. The proposed filters are evaluated for their performance on a test image and the results obtained are included.

A nonlinear filtering algorithm immune to singular errors

The problem of linear discrete filtering is resolved for the case when the observation channel contains piecewise continuous interference having a finite number of the first-kind discontinuities on the whole observation segment and is described, within the continuity intervals, by power polynomials with random coefficients. An illustrative example is included.

Multivariate analysis and classification of two-dimensional angular optical scattering patterns from aggregates

Two-dimensional light-scattering patterns from aggregates have undergone feature extraction followed by multivariate statistical analysis. The aggregates are comprised of primary particles of varying shape and size. Morphological descriptors (features) were extracted by a nonlinear filtering algorithm (spectrum enhancement) and then processed by principal component analysis and discriminant function analysis. The analysis was performed on two data sets, one in which the aggregates had a fixed primary particle size but varied in overall dimension and another in which the aggregate size was fixed but the primary particle size varied. Classification of the samples was performed adequately, providing some distinction among the limited classes that were analyzed.

Estimating a State-Space Model from Point Process Observations

A widely used signal processing paradigm is the state-space model. The state-space model is defined by two equations: an observation equation that describes how the hidden state or latent process is observed and a state equation that defines the evolution of the process through time. Inspired by neurophysiology experiments in which neural spiking activity is induced by an implicit (latent) stimulus, we develop an algorithm to estimate a state-space model observed through point process measurements. We represent the latent process modulating the neural spiking activity as a gaussian autoregressive model driven by an external stimulus. Given the latent process, neural spiking activity is characterized as a general point process defined by its conditional intensity function. We develop an approximate expectation-maximization (EM) algorithm to estimate the unobservable state-space process, its parameters, and the parameters of the point process. The EM algorithm combines a point process recursive nonlinear filter algorithm, the fixed interval smoothing algorithm, and the state-space covariance algorithm to compute the complete data log likelihood efficiently. We use a Kolmogorov-Smirnov test based on the time-rescaling theorem to evaluate agreement between the model and point process data. We illustrate the model with two simulated data examples: an ensemble of Poisson neurons driven by a common stimulus and a single neuron whose conditional intensity function is approximated as a local Bernoulli process.

A convex optimization-based nonlinear filtering algorithm with applications to real-time sensing for patterned wafers

The paper is concerned with nonlinear filtering under unknown dynamics and high-complexity observations. We propose a convex optimization-based filtering algorithm, and show that the algorithm yields a bounded error if the disturbances are small and bounded, and if the observations are redundant. An experimental result is presented to demonstrate that the algorithm is capable of accurate real-time estimation of patterned wafer parameters in a plasma etching process with optical observation.

Fuzzy Ordering Theory and Its Use in Filter Generalization

The rank ordering of samples is widely used in robust nonlinear signal processing. Recent advances in nonlinear filtering algorithms have focused on combining spatial and rank (SR) order information into the filtering process to allow spatial correlations to be exploited while retaining the robust characteristics of strict rank order methods. Further generalization can be achieved by replacing the crisp, or binary, SR information utilized by most methods with more general fuzzy SR information. Indeed, by exploiting fuzzy methodologies real-valued SR orderings can be defined that not only relate the spatial and rank orderings of samples, but also includes information on sample spread. This paper utilizes this approach to define fuzzy ranking and fuzzy order statistics. Properties of these concepts are discussed and several previously defined filters are generalized by including fuzzy concepts. Specifically, the fuzzy median, fuzzy rank conditioned rank selection, and fuzzy weighted median filters are defined. Optimization of the parameters for these filters are discussed. Simulation results are presented to show the advantages of these fuzzy filters over their crisp counterparts.

Elimination of interference terms of the discrete Wigner distribution using nonlinear filtering

This paper introduces a new nonlinear filtering approach for the removal of cross terms in the discrete Wigner distribution. Realizing that linear smoothing kernels are unable to completely cancel the cross-terms without compromising time-frequency concentration and resolution of the auto-terms, a nonlinear filtering algorithm is devised where the filter automatically adapts to the rapidly changing nature of the Wigner distribution plane. Varying the filter behavior from an identity operation at one extreme to a low pass linear filter at the other, a near optimal removal of cross terms is achieved. Unlike traditional smoothing and optimal kernel design techniques, this algorithm does not reduce the time-frequency resolution and concentration of the auto-terms.

The application of matrix differential calculus for the derivation of simplified expressions in approximate non-linear filtering algorithms

It is shown how matrix differential calculus can be used to obtain simplified expressions for higher-order terms that appear in standard approximate non-linear filtering algorithms such as the first-order bias-corrected filter, the truncated second-order filter, and the modified Gaussian second-order filter. These terms are much simpler and more compact than the standard expressions given in the literature; particularly, no element-by-element computations are necessary. For comparison, the approximate version of the Daum filter is also included.

A Statistical Paradigm for Neural Spike Train Decoding Applied to Position Prediction from Ensemble Firing Patterns of Rat Hippocampal Place Cells

The problem of predicting the position of a freely foraging rat based on the ensemble firing patterns of place cells recorded from the CA1 region of its hippocampus is used to develop a two-stage statistical paradigm for neural spike train decoding. In the first, or encoding stage, place cell spiking activity is modeled as an inhomogeneous Poisson process whose instantaneous rate is a function of the animal's position in space and phase of its theta rhythm. The animal's path is modeled as a Gaussian random walk. In the second, or decoding stage, a Bayesian statistical paradigm is used to derive a nonlinear recursive causal filter algorithm for predicting the position of the animal from the place cell ensemble firing patterns. The algebra of the decoding algorithm defines an explicit map of the discrete spike trains into the position prediction. The confidence regions for the position predictions quantify spike train information in terms of the most probable locations of the animal given the ensemble firing pattern. Under our inhomogeneous Poisson model position was a three to five times stronger modulator of the place cell spiking activity than theta phase in an open circular environment. For animal 1 (2) the median decoding error based on 34 (33) place cells recorded during 10 min of foraging was 8.0 (7.7) cm. Our statistical paradigm provides a reliable approach for quantifying the spatial information in the ensemble place cell firing patterns and defines a generally applicable framework for studying information encoding in neural systems.

A new class of efficient adaptive nonlinear filters (ANLF)

A multilinearization procedure is described, with the use of which a new class of algorithms for nonlinear filtering can be realized. The methodology targets on adaptively selecting the best reference points for linearization from an ensemble of generated trajectories that span the whole state space of the desired signal. Through simulations, the approach is shown to be significantly superior to the classical extended Kalman filter and comparable in computational burden.

Recursive nonlinear filter for a continuous discrete-time model: separation of parameters and observations

A new nonlinear filtering algorithm is proposed for the model where the state is a randomly perturbed nonlinear dynamical system and the measurements are made at discrete-time moments in Gaussian noise. It is shown that the approximate scheme based on the algorithm converges to the optimal filter, and the error of the approximation is computed. The algorithm makes it possible to shift offline the most time-consuming operations related to solving the Fokker-Planck equations and computing the integrals with respect to the filtering density.

Estimation of Dynamic Reactivity Using anH∞Optimal Filter with a Nonlinear Term

A method of nonlinear filtering is applied to the problem of estimating the dynamic reactivity of a nonlinear reactor system. The nonlinear filtering algorithm developed is a simple modification of...

Nonlinear filters based on taylor series expansions∗

We have been dealing with the linear transition and measurement equations. The equations derived from economic theories, however, are nonlinear in general. Unless the distributions are normal and the measurement and transition equations are linear, we cannot derive the explicit expression for the filtering algorithm. Therefore, some approximation is necessary for estimation. In Chapter 3, the nonlinear filtering algorithms are derived by approximating the nonlinear measurement and transition equations, based on the Taylor series expansion.

State Space Modelling of Contaminant Transport Processes by Extending Discrete Vortex Simulations-1. Horizontal Dispersion.

In order to diagnose and predict the contaminant transport process in large scale geosystems using a nonlinear filtering strategy the state space model has been derived from simulating horizontal contaminant dispersion by extending the discrete vortex method. The dispersion area S and the dispersion rate S have been taken into account for evolving the state space model of the horizontal contaminant transport process. Eventually, S/S has been found to be represented by a function composed of exponential decay terms, which is transformed to the autonomous state equation and serves as the state space model accompanied with the observation equation. The state equation is extended to involve a noise process corresponding to disturbances such as viscous diffusion and inhomogeneity of the vortex strength as observed in real systems. The parameters involved in the state equation are adaptively estimated from the current state observations using a non-linear filtering algorithm. The state space model has been verified by a series of numerical demonstrations carried out using the discrete vortex method.

Nonlinear filtering for LIDAR signal processing

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.

Probabilistic linear models for multiresolution estimation in gray-level images

A multiresolution analysis of digital gray-level images is presented. A gray-level multi-scale framework is determined from two main assumptions: the gray scale is binary at the finest spatial resolution, and the gray levels of composed regions are obtained additively. In order to interrelate the gray-level histograms of the same image at different resolutions, probabilistic linear models are developed, which are then applied for estimation. Linear-optimization theory is used as a way of constructing such models. A general procedure for image processing is sketched, based on gray-level estimation. A versatile algorithm for nonlinear filtering is derived. Some examples of prospective applications are given.

An investigation into Kalman filter target tracking algorithms and their real time parallel transputer implementation

For target tracking applications, a Kalman filter is generally used to estimate the kinematic components of a manoeuvring target (position, velocity and acceleration) from noisy measurements. The tracking algorithm is selected according to a trade-off between its performance and real-time computational requirements when choosing the level of complexity of the model. According to the application, either a linear or a nonlinear Kalman filter algorithm can be used to track manoeuvring targets. However, although excellent accuracy estimates can be achieved with any chosen algorithm, it requires a huge amount of calculation thus making real-time processing impossible. This paper investigates the parallel implementation of tracking Kalman filters (EKF, GRF, LDKF and MGEKF) in both 2- and 3-D frames onto a range of transputer topologies to enable practical realisations. The partitioning strategies are highlighted, real-time implementation results are presented, and the relative speedup and efficiency are calculated to evaluate the performance of each parallel implementation.

A nonlinear filter algorithm for the detection of jumps in patch-clamp data.

This paper presents a new algorithm for the detection of channel openings and closures from noisy current signals, especially for the correct generation and interpretation of open-time and closed-time histograms. The Hinkley detector is a nonlinear off-line jump detection algorithm from the field of fault detection. Here, an improved version, the higher-order Hinkley detector H.O.H.D., is developed. A general description of the sensitivity of a detector is introduced by the time resolution tres. This allows a comparison of the nonlinear detectors with the standard threshold detectors preceded by a low-pass filter for noise suppression. By means of application to simulated and real data, the performance of the detection algorithms is investigated. The higher-order Hinkley detector gave the best results with respect to correct reconstruction of the event length, to a small amount of missed brief events as well as to the ability to achieve short time resolution without pretending false events, especially in the presence of colored noise.