James R. Hopgood

Blind Image Restoration Using a Block-Stationary Signal Model

We present a novel method for blind image restoration which is a multidimensional extension of an approach used successfully for audio restoration. A nonstationary image model is used to increase reliability of blur estimates. This source model consists of a separate autoregressive model in each region of the image. A hierarchical Bayesian model for the observations is used, and a maximum marginalised a posteriori (MMAP) blur estimate is obtained by optimising the resulting probability density function

Nonstationary Blind Image Restoration using Variational Methods

The variational Bayesian approach has recently been proposed to tackle the blind image restoration (BIR) problem. We consider extending the procedures to include realistic boundary modelling and non-stationary image restoration. Correctly modelling the boundaries is essential for achieving accurate blind restorations of photographic images, whilst nonstationary models allow for better adaptation to local image features, and therefore improvements in quality.

Blind restoration of blurred photographs via AR modelling and MCMC

We propose a new image and blur prior model, based on non-stationary autoregressive (AR) models, and use these to blindly deconvolve blurred photographic images, using the Gibbs sampler. As far as we are aware, this is the first attempt to tackle a real-world blind image deconvolution (BID) problem using Markov chain Monte Carlo (MCMC) methods. We give examples with simulated and real out-of-focus images, which show the state-of-the-art results that the proposed approach provides.

Nonconcurrent multiple speakers tracking based on extended Kalman particle filter

Acoustic reverberation introduces multipath components into an audio signal, and therefore changes the source signal statistical properties. This causes problems for source localisation and tracking since reverberation generates spurious peaks in the time delay functions, and makes the subsequent location estimator hard to track the motion trajectory. Previous time delay based tracking methods, such as the extended Kalman filter and the particle filter, are sensitive to reverberation and are unable to follow sharp changes in the source positions. In this paper, the extended Kalman filter and the particle filter are combined to solve this problem. One of the advantages of this approach is that the optimal importance function can be obtained after extended Kalman filtering. Thus, the position samples are distributed in a more accurate area than using a prior importance function. Experiment results show that the proposed algorithm outperforms the sequential importance resampling particle filter by reducing the estimation error and following the switch of speakers quickly under a moderate reverberant environment (reverberation time T60 < 0.3s).

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.

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.

Single channel separation using linear time varying filters: separability of non-stationary stochastic signals

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 generalised Wiener filter, the degree of separability can be deduced from the filter structure. To identify this structure, the processes are represented on an arbitrary 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.

Bayesian formulation of subband autoregressive modelling with boundary continuity constraints

The all-pole model is often used to approximate rational transfer functions parsimoniously. In many applications, such as single channel blind deconvolution, an estimate of the channel is required. However, in general, attempting to model the entire channel spectrum by a single all-pole model leads to a large computational load. Hence, it is better to model a particular frequency band of the spectrum by an all-pole model, reducing a single high-dimensional optimisation to a number of low-dimensional ones. If each subband is completely decoupled from the others, and does not enforce any continuity, there are discontinuities in the spectrum at the subband boundaries. Continuity is ensured by constraining the subband parameters such that the end points at one subband boundary are matched to the spectrum in the adjacent subbands. This is formulated in the Bayesian probabilistic framework.

Bayesian single channel blind deconvolution using parametric signal and channel models

This paper considers single channel blind deconvolution, in which a degraded observed signal is modelled as the convolution of a non-stationary source signal with a stationary distortion operator. Recovery of the source signal from the observed signal is achieved by modelling the source signal as a time-varying autoregressive process, the distortion operator by a IIR filter, and then using a Bayesian framework to estimate the parameters of the distorting filter, which can be used to deconvolve the observed signal. The paper also discusses how the non-stationary properties of the source signal allow the identification of the distortion operator to be uniquely determined.

A probabilistic framework for subband autoregressive models applied to room acoustics

Real room acoustic impulse responses (AIRs) modelled by infinite impulse response (IIR) filters require high model orders. Many problems involving the estimation of AIRs reduce to high dimensional optimisation problems. Subband autoregressive (AR) modelling techniques reduce this difficult optimisation problem to a number of simpler low dimensional optimisations. This paper introduces a formulation for subband AR modelling in a probabilistic framework which facilitates robust Bayesian parameter estimation. The paper also provides new results to show that the subband AR representation accurately models typical AIRs and, therefore, is suitable for modelling room reverberation.