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A. C. Fisher, A. Small, R. P. Hagan, M. C. Brown; A Robust 6 Parameter Wavelet-Based Model for the Clinical PERG. Invest. Ophthalmol. Vis. Sci. 2008;49(13):5818.
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To describe a robust minimum parameter graphical model of the clinical PERG waveform for optimal recovery from recordings of poor signal-to-noise ratio (SNR)Introduction: The PERG waveform as described in the ISCEV Standard is usually characterised by 3 coordinates pairs (‘cardinal points’) in time ~[35, 50, 95]ms and amplitude, requiring just 6 numbers. However, even with a conservative bandwidth of [1 … 45]Hz, Fourier Series decomposition requires a minimum of 15 numbers (to describe the DC-term and the first 7 harmonics). Further, recent artificial neural network models (e.g. SPoC www.liverpooleye.org) have required ≥ 16 numbers. Clearly, without a system of constraints, the standard practice of reporting the PERG with only 3 cardinal points is under-determined and consequently ambiguous. In the model presented here, such constraints are provided by a single simple template applied to a two-level wavelet decomposition of the data.
A reference structure is constructed from the ISCEV PERG model comprising: i. a detrended bandlimited zero-extended template; ii. a weighting vector emphasising ‘regions of interest’ close to cardinal point times. The data are decomposed into low-frequency (high scale) and high-frequency (low scale) components by discrete wavelet transformation. Each of these decompositions are Pearson crosscorrelated under scale, time-displacement and amplitude perturbation with the template weighted by the weighting vector. This results in 2 x 3 numbers which define the 6 parameter model.This model was tested against noise-free clinical PERG waveforms (with unequivocal ‘cardinal points’) to which realistic 1/f Gaussian noise [white … Brownian] over a range of SNRs was added.
In all trials the 6 parameter model recovered the cardinal points as least as effectively as the SPoC Expert System but additionally reproduced the underlying waveform 'exactly' as judged by the human eye.
The model can be effectively applied during data acquisition to recover the underlying PERG. Its 6 parameters can be tested in real-time using bootstrap statistical sampling to optimise the recovery process and minimise recording times.The MatLab program is 'open source'. An interactive demo will be available over the Internet via MatSoap (www.matsoap.org.uk) at www.liverpooleye.org
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