Author: Aleš Holobar
Mentor: Prof. Dr.  Damjan Zazula
Date: Oct. 26, 2004

Blind decomposition of convolutive mixtures of close-to-orthogonal pulse sources applied to surface electromyograms

Keywords: digital signal processing, blind source separation, multi-channel blind deconvolution, pulse sources, time-frequency analysis, higher-order statistics, w-slices, Newton-Gauss optimization, inverse correlation matrix based method, MIMO system identification, surface electromyographic signals, surface EMG decomposition, motor unit, innervation pulse train, motor unit action potential

UDK: 621.391:61(043.3)

Abstract: In this doctoral dissertation blind decomposition of convolutive mixtures of close-toorthogonal pulse source signals is addressed. Three novel decomposition approaches based on the time-frequency analysis, higher-order statistics and algebraic approach are developed. Furthermore, necessary conditions for the reconstruction of complete pulse sequences and their impulse responses are investigated and a thorough and detailed study of the factors influencing its performance, such as noise and non-orthogonality of sources, are carried out. Although derived in the case of more measurements than sources (overdetermined system), the algebraic approach is extended to slightly underdetermined systems (with more sources than measurements). In contrast with other decomposition techniques, the proposed approaches work well also in the case of not completely orthogonal source signals. Finally, all the proposed solutions are applied to the surface electromyographic (EMG) signals.

The thesis begins with an overview of existing methods and techniques for blind source separation. The methods for both multiplicative and convolutive cases are critically assessed and mutually compared. Next, a brief introduction to the physiology of the human muscles is given. In order to provide the basis for evaluation of the decomposition results on the real surface EMG signals, the properties of the motor unit (MU) innervation pulse trains, and generation of the motor unit action potentials (MUAPs) at the end-plate are explained. The factors influencing the shape and amplitudes of MUAPs, detected at the skin surface, are also identified. Afterwards, the decomposition methods for both intra-muscular and surface EMG signals are critically evaluated and the influence of the superimposed MUAPs studied. Finally, the assumed data model of surface EMG signals is introduced and its main limitations and assumption clarified. Surface EMG signals are modelled as a multi-channel, linear, shift-invariant multipleinput- multiple-output (MIMO) system.

In the second part of this dissertation, three different approaches to blind source separation of the convolutive mixtures of general pulse source signals are derived. Firstly, the over-determined case is assumed (the case with more measurements than sources) and two novel approaches introduced. The first one utilizes the Wigner-Ville time-frequency distributions and enables the reconstruction of both the pulse source signals and the corresponding MIMO system responses. The second approach enables automatic reconstruction of the MIMO system responses and is based on higher-order cumulants. Next, the decomposition is extended to the underdetermined case (the case with more sources than measurements) and a completely novel approach to blind deconvolution of pulse source signals, so called inverse correlation matrix based method, is derived. The introduced approaches are tested on both synthetic and real surface EMG signals. Firstly, the impacts of the number of active MUs, their firing frequencies, depth in the muscle tissue, etc., as well as the influence of noise are evaluated on the synthetic signals. The results prove the superiority of the inverse correlation based method. Applying it to the over-determined case at a high signal to noise ratio (SNR), almost all simulated MU innervation pulse trains are completely reconstructed. In the under-determined case with number of sources exceeding the number of measurements by factor 1.4, approximately a half of the simulated MUs are completely identified. The performance also drops with the SNR. At SNR of 0 dB, approximately 30 % of the MUs identified at SNR = 20 dB are reconstructed. In all cases, the decomposed innervation pulse trains exhibit a perfect match with the reference synthetic source signals. The other two methods are significantly less efficient.

Finally, all three decomposition approaches are applied to the real surface EMG signals, recorded during an isometric 5 % and 10 % contractions of the dominant biceps brachii muscle of 9 healthy young male subjects. Again, the inverse correlation based method proves to be superior. Altogether, 30 and 56 MUs’ innervation pulse trains are completely reconstructed from the 5 % and 10 % muscle contraction measurements, respectively. The reconstructed MU firing patterns are compared against various physiologically induced limitations and prove to be in agreement with expectations and careful visual analysis.