Modelling of non-stationary processes using radial basis function networks

This paper reports preliminary progress on a principled approach to modelling nonstationary phenomena using neural networks. We are concerned with both parameter and model order complexity estimation. The basic methodology assumes a Bayesian foundation. However to allow the construction of pragmatic models, successive approximations have to be made to permit computational tractibility. The lowest order corresponds to the (Extended) Kalman filter approach to parameter estimation which has already been applied to neural networks. We illustrate some of the deficiencies of the existing approaches and discuss our preliminary generalisations, by considering the application to nonstationary time series.

The accuracy of parameter estimation from noisy data, with application to resonance peak estimation in distributed Brillouin sensing

Distributed Brillouin sensing of strain and temperature works by making spatially resolved measurements of the position of the measurand-dependent extremum of the resonance curve associated with the scattering process in the weakly nonlinear regime. Typically, measurements of backscattered Stokes intensity (the dependent variable) are made at a number of predetermined fixed frequencies covering the design measurand range of the apparatus and combined to yield an estimate of the position of the extremum. The measurand can then be found because its relationship to the position of the extremum is assumed known. We present analytical expressions relating the relative error in the extremum position to experimental errors in the dependent variable. This is done for two cases: (i) a simple non-parametric estimate of the mean based on moments and (ii) the case in which a least squares technique is used to fit a Lorentzian to the data. The question of statistical bias in the estimates is discussed and in the second case we go further and present for the first time a general method by which the probability density function (PDF) of errors in the fitted parameters can be obtained in closed form in terms of the PDFs of the errors in the noisy data.

Multispectral retinal image analysis:a novel non-invasive tool for retinal imaging

Purpose-To develop a non-invasive method for quantification of blood and pigment distributions across the posterior pole of the fundus from multispectral images using a computer-generated reflectance model of the fundus. Methods - A computer model was developed to simulate light interaction with the fundus at different wavelengths. The distribution of macular pigment (MP) and retinal haemoglobins in the fundus was obtained by comparing the model predictions with multispectral image data at each pixel. Fundus images were acquired from 16 healthy subjects from various ethnic backgrounds and parametric maps showing the distribution of MP and of retinal haemoglobins throughout the posterior pole were computed. Results - The relative distributions of MP and retinal haemoglobins in the subjects were successfully derived from multispectral images acquired at wavelengths 507, 525, 552, 585, 596, and 611?nm, providing certain conditions were met and eye movement between exposures was minimal. Recovery of other fundus pigments was not feasible and further development of the imaging technique and refinement of the software are necessary to understand the full potential of multispectral retinal image analysis. Conclusion - The distributions of MP and retinal haemoglobins obtained in this preliminary investigation are in good agreement with published data on normal subjects. The ongoing development of the imaging system should allow for absolute parameter values to be computed. A further study will investigate subjects with known pathologies to determine the effectiveness of the method as a screening and diagnostic tool.

The slope of the psychometric function and non-stationarity of thresholds in spatiotemporal contrast vision

The slope of the two-interval, forced-choice psychometric function (e.g. the Weibull parameter, ß) provides valuable information about the relationship between contrast sensitivity and signal strength. However, little is known about how or whether ß varies with stimulus parameters such as spatiotemporal frequency and stimulus size and shape. A second unresolved issue concerns the best way to estimate the slope of the psychometric function. For example, if an observer is non-stationary (e.g. their threshold drifts between experimental sessions), ß will be underestimated if curve fitting is performed after collapsing the data across experimental sessions. We measured psychometric functions for 2 experienced observers for 14 different spatiotemporal configurations of pulsed or flickering grating patches and bars on each of 8 days. We found ß ˜ 3 to be fairly constant across almost all conditions, consistent with a fixed nonlinear contrast transducer and/or a constant level of intrinsic stimulus uncertainty (e.g. a square law transducer and a low level of intrinsic uncertainty). Our analysis showed that estimating a single ß from results averaged over several experimental sessions was slightly more accurate than averaging multiple estimates from several experimental sessions. However, the small levels of non-stationarity (SD ˜ 0.8 dB) meant that the difference between the estimates was, in practice, negligible.

The accuracy of parameter estimation from noisy data, with application to resonance peak estimation in distributed Brillouin sensing

Distributed Brillouin sensing of strain and temperature works by making spatially resolved measurements of the position of the measurand-dependent extremum of the resonance curve associated with the scattering process in the weakly nonlinear regime. Typically, measurements of backscattered Stokes intensity (the dependent variable) are made at a number of predetermined fixed frequencies covering the design measurand range of the apparatus and combined to yield an estimate of the position of the extremum. The measurand can then be found because its relationship to the position of the extremum is assumed known. We present analytical expressions relating the relative error in the extremum position to experimental errors in the dependent variable. This is done for two cases: (i) a simple non-parametric estimate of the mean based on moments and (ii) the case in which a least squares technique is used to fit a Lorentzian to the data. The question of statistical bias in the estimates is discussed and in the second case we go further and present for the first time a general method by which the probability density function (PDF) of errors in the fitted parameters can be obtained in closed form in terms of the PDFs of the errors in the noisy data.