Peter J. W. Rayner

Near optimal detection of signals in impulsive noise modeled with a symmetric /spl alpha/-stable distribution

There has been great interest in symmetric /spl alpha/-stable distributions which have proved to be very good models for impulsive noise. However, most of the classical non-Gaussian receiver design techniques cannot be extended to the symmetric /spl alpha/-stable noise case since these techniques require an explicit compact analytical form for the probability density function (PDF) of the noise distribution which /spl alpha/-stable distributions do not possess. A new analytical representation has been suggested for the symmetric /spl alpha/-stable PDF which is based on scale mixtures of Gaussians. Based on this new analytical representation, this paper introduces a novel near-optimal receiver for the detection of signals in symmetric /spl alpha/-stable noise. The performance of the new receiver is very close to the locally optimum receiver and is significantly better than the performance of previously suggested sub-optimum receivers. The new technique has important potential in radar, sonar, and other applications.

A Bayesian approach to the restoration of degraded audio signals

In this paper we derive the a posteriori probability for the location of bursts of noise additively superimposed on a Gaussian AR process. The theory is developed to give a sequentially based restoration algorithm suitable for real-time applications. The algorithm is particularly appropriate for digital audio restoration, where clicks and scratches may be modelled as additive bursts of noise. Experiments are carried out on both real audio data and synthetic AR processes and significant improvements are demonstrated over existing restoration techniques. >

Polyphonic pitch tracking using joint Bayesian estimation of multiple frame parameters

We present a novel approach to pitch estimation and note detection in polyphonic audio signals. We pose the problem in a Bayesian probabilistic framework, which allows us to incorporate prior knowledge about the nature of musical data into the model. We exploit the high correlation between model parameters in adjacent frames of data by explicitly modelling the frequency variation over time using latent variables. Parameters are estimated jointly across a number of adjacent frames to increase the robustness of the estimation against transient events. Individual frames of data are modelled as the sum of harmonic sinusoids. Parameter estimation is performed using Markov chain Monte Carlo (MCMC) methods.

Blind single channel deconvolution using nonstationary signal processing

Blind deconvolution is fundamental in signal processing applications and, in particular, the single channel case remains a challenging and formidable problem. This paper considers single channel blind deconvolution in the case where the degraded observed signal may be modeled as the convolution of a nonstationary source signal with a stationary distortion operator. The important feature that the source is nonstationary while the channel is stationary facilitates the unambiguous identification of either the source or channel, and deconvolution is possible, whereas if the source and channel are both stationary, identification is ambiguous. The parameters for the channel are estimated by modeling the source as a time-varyng AR process and the distortion by an all-pole filter, and using the Bayesian framework for parameter estimation. This estimate can then be used to deconvolve the observed signal. In contrast to the classical histogram approach for estimating the channel poles, where the technique merely relies on the fact that the channel is actually stationary rather than modeling it as so, the proposed Bayesian method does take account for the channels stationarity in the model and, consequently, is more robust. The properties of this model are investigated, and the advantage of utilizing the nonstationarity of a system rather than considering it as a curse is discussed.

Unsupervised image segmentation using Markov random field models

Abstract We present two unsupervised segmentation algorithms based on hierarchical Markov random field models for segmenting both noisy images and textured images. Each algorithm finds the the most likely number of classes, their associated model parameters and generates a corresponding segmentation of the image into these classes. This is achieved according to the maximum a posteriori criterion. To facilitate this, an MCMC algorithm is formulated to allow the direct sampling of all the above parameters from the posterior distribution of the image. To allow the number of classes to be sampled, a reversible jump is incorporated into the Markov Chain. Experimental results are presented showing rapid convergence of the algorithm to accurate solutions.

Generalization and PAC learning: some new results for the class of generalized single-layer networks

The ability of connectionist networks to generalize is often cited as one of their most important properties. We analyze the generalization ability of the class of generalized single-layer networks (GSLNs), which includes Volterra networks, radial basis function networks, regularization networks, and the modified Kanerva model, using techniques based on the theory of probably approximately correct (PAC) learning which have previously been used to analyze the generalization ability of feedforward networks of linear threshold elements (LTEs). An introduction to the relevant computational learning theory is included. We derive necessary and sufficient conditions on the number of training examples required by a GSLN to guarantee a particular generalization performance. We compare our results to those given previously for feedforward networks of LTEs and show that, on the basis of the currently available bounds, the sufficient number of training examples for GSLNs is typically considerably less than for feedforward networks of LTEs with the same number of weights. We show that the use of self-structuring techniques for GSLNs may reduce the number of training examples sufficient to guarantee good generalization performance, and we provide an explanation for the fact that GSLNs can require a relatively large number of weights.

Generalized feature extraction for time-varying autoregressive models

In this paper, a feature extraction scheme for a general type of nonstationary time series is described. A non-stationary time series is one in which the statistics of the process are a function of time; this time dependency makes it impossible to utilize standard globally derived statistical attributes such as autocorrelations, partial correlations, and higher order moments as features. In order to overcome this difficulty, the time series vectors are considered within a finite-time interval and are modeled as time-varying autoregressive (AR) processes. The AR coefficients that characterize the process are functions of time that may be represented by a family of basis vectors. A novel Bayesian formulation is developed that allows the model order of a time-varying AR process as well as the form of the family of basis vectors used in the representation of each of the AR coefficients to be determined. The corresponding basis coefficients are then invariant over the time window and, since they directly relate to the time-varying AR coefficients, are suitable features for discrimination. Results illustrate the effectiveness of the method.

Least l p -norm impulsive noise cancellation with polynomial filters

Abstract It is a common experience in signal processing that impulsive noise observed in various natural environments cannot be described with the Gaussian distribution. Recently, a heavy tailed distribution namely the α - stable distribution has become a popular model for impulsive noise since it agrees very well with empirical data and is also theoretically justified with the generalised central limit theorem. Although, it is a generalisation of the Gaussian distribution and shares important properties with it, the non-Gaussian α -stable distribution differs from the Gaussian distribution in many ways, the most notable of which is the lack of finite second-order statistics. Therefore, the classical techniques based on linear least-squares estimation perform very poorly in impulsive noise elimination. In this paper, motivated by some properties of the α -stable distribution, new techniques based on linear and nonlinear least l p -norm estimation are introduced and several simulation results are presented which show that least l p -norm estimation with a Volterra-type prediction filter performs significantly better than the conventional linear techniques such as linear least-squares estimation and than nonlinear least-squares estimation. A new measure for signal distortion in impulsive noise, namely fractional order signal-to-noise ratio (FSNR) is also introduced to quantify the performance of various impulsive noise cancellation algorithms.

System for the removal of impulsive noise in image sequences

This paper presents a system for the restoration of image sequences that are degraded by impulsive noise such as scratches or dropouts. The proposed system uses a multilevel block matching algorithm to estimate the motion between frames and considers the use of an impulsive noise detector to improve the quality of restoration as compared to a global median operation. The detector considers the temporal continuity of motion compensated image information and makes a decision as to whether a suspected discontinuity is due to an impulsive distortion or occlusion in the sequence. When a corrupted portion of the image is detected a motion compensated median filter is used to remove the distortion. The paper introduces an extended multistage filter for image sequence processing. It is found that the use of the detector cannot adversely affect the filtered image when compared to the globally filtered image, and the detail preservation is generally better. The speed of processing is also increased since the number of median filtering operations is considerably reduced.

Single channel nonstationary stochastic signal separation using linear time-varying filters

Separability of signal mixtures given only one mixture observation is defined as the identification of the accuracy to which the signals can be separated. The paper shows that when signals are separated using the generalized Wiener filter, the degree of separability can be deduced from the signal structure. To identify this structure, the processes are represented on an general spectral domain, and a sufficient solution to the Wiener filter is obtained. The filter is composed of a term independent of the signal values, corresponding to regions in the spectral domain where the desired signal components are not distorted by interfering noise components, and a term dependent on the signal correlations, corresponding to the region where components overlap. An example of determining perfect separability of modulated random signals is given with application in radar and speech processing.