Prof. Dr. Volker M. Koch, Switzerland

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Doctoral Dissertation



Series in Signal and Information Processing, Vol. 18
edited by Hans-Andrea Loeliger

Volker M. Koch
A Factor Graph Approach to Model-Based Signal Separation

First edition 2007, Hartung-Gorre Verlag Konstanz, 328 pages, 
ISBN-10: 3-86628-140-4, ISBN-13: 978-3866281400, 64 €


This doctoral thesis is about a rather new model-based signal processing methodology that is based on factor graphs and message-passing algorithms. Using this, we have developed exemplary signal processing algorithms for various biomedical applications. The main application to evaluate and demonstrate this new methodology was in the field of electromyographic (EMG) signal analysis. EMG signals are electrical signals that are generated during muscle contractions. They can be measured using various kinds of electrodes, e.g., needle or fine-wire electrodes. Their analysis provides valuable information for the diagnosis of neuromuscular disorders, the study of neuromuscular control mechanisms, and the verification of anatomic hypotheses.

EMG signals are essentially made up of superimposed action potential trains from several sources. For a thorough analysis, the measured EMG signals need to be decomposed into their constituent trains. However, this task can become difficult if action potentials from different sources overlap. Many EMG signal decomposition methods have been proposed. Traditional algorithms often use heuristic segmentation and clustering approaches. Especially in the case of difficult superpositions with many overlapping action potentials, these algorithms could often not decompose muscle signals correctly. Many other approaches are computationally not feasible when superpositions of many action potentials are to be resolved.

To be able to decompose EMG signals with difficult superpositions, new signal processing algorithms based on factor graphs were developed. Factor graphs allow the systematic derivation of advanced model-based signal processing algorithms. A factor graph is a graphical model that represents a factorization of a function. Instead of starting with such a function, we explain how a factor graph for EMG signal decomposition can intuitively be obtained from a block diagram. Here, the block diagram is a simulation model for EMG signals. The factor graph approach allowed us to integrate action potential shape information, firing statistics, and other properties of EMG signals into the same model.

Finally, we show how decomposition is achieved by means of the sum-product algorithm. It performs inference by passing messages along the edges of a factor graph. Since our factor graphs have cycles, we get sub-optimal iterative algorithms that allow handling complex models, which could not be used just a few years ago. We have developed several algorithms that differ, e.g., in the representation of the messages propagating in factor graphs. Our new algorithms allow the fast resolution of single and multi-channel superpositions consisting of many overlapping action potentials.

We have also used the factor graph language to derive novel message-passing algorithms for several other biomedical applications. One example is the extraction of heart beats from pressure sensors that are located under bedposts (seismosomnography). The advantage of this method is that the signals can be recorded without attaching electrodes to a human subject while sleeping. Other examples include the important topic of multi-channel neural spike sorting and blind-source separation for electroencephalographic signals. We present exemplary factor graphs for all these applications.



Graphical models, factor graphs, signal modeling, model-based signal processing, sum-product algorithm, message passing, superpositions, signal decomposition, resolving superpositions, electromyography, seismosomnography, multi-channel neural spike sorting, blind source separation.



My examiner was Professor Dr. Hans-Andrea Loeliger of ETH Zurich and my co-examiner was Professor Dr. Kevin C. McGill of Stanford University.  


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