Convergence characteristics of two algorithms in non-linear stimulus artefact cancellation for electrically evoked potential enhancement

Somatosensory evoked potentials (SEPs) are a sub-class of evoked potentials (EPs) that are very useful in diagnosing various neuromuscular disorders and in spinal cord and peripheral-nerve monitoring. Most often, the measurements of these signals are contaminated by stimulus-evoked artefact. Conventional stimulus-artifact (SA) reduction schemes are primarily hardware-based and rely on some form of input blanking during the SA phase. This procedure can result in partial SEP loss if the tail of the SA interferes with the SEP. Adaptive filters offer an attractive solution to this problem by iteratively reducing the SA waveform while leaving the SEP intact. Owing to the inherent non-linearities in the SA generation system, non-linear adaptive filters (NAFs) are most suitable. SA reduction using NAFs based on truncated second-order Volterra expansion series is investigated. The focus is on the performance of two main adaptation algorithms, the least mean square (LMS) and recursive least squares (RLS) algorithms, in the context of non-linear adaptive filtering. A comparison between the convergence and performance characteristics of these two algorithms is made by processing both simulated and experimental SA data. It is found that, in high artefact-to-noise ratio (ANR) SA cancellation, owing to the large eigenvalue spreads, the RLS-based NAF is more efficient than the LMS-based NAF. However, in low-ANR scenarios, the RLS- and LMS-based NAFs exhibit similar convergence properties, and the computational simplicity of the LMS-based NAFs makes them the preferred option.