Reviewed conference papers

• P.Kidmose, Independent Component Analysis Using the Spectral Measure for Alpha-Stable Distributions [0.4Mb], Proceedings of IEEE-EURASIP Workshop on Nonlinear Signal and Image Processing, NSIP2001.
• T.Fabricius, P.Kidmose and L.K.Hansen, Dynamic Components of Linear Stable Mixtures from Fractional Low Order Moments [1.7Mb], Proceedings of International Conference on Acoustics, Speech and Signal Processing, ICASSP2001, pp. 3957-3960.
• P.Kidmose, Alpha-Stable Distributions in Signal Processing of Audio Signals [4.0Mb], 41st Conference on Simulation and Modelling, Scandinavian Simulation Society, SIMS2000, pp. 87-94.
• P.Kidmose, Adaptive Filtering for Non-Gaussian Processes [0.5Mb], Proceedings of International Conference on Acoustics, Speech and Signal Processing, ICASSP2000, pp. 424-427.

Ph.D. Thesis

A postscript-version of my Ph.D. Thesis "Blind Separation of Heavy Tail Signals" is available thesis.ps [48Mb], thesis.ps.gz [9.8Mb]. The thesis has been submitted in partial fulfillment of the requirements for the Ph.D. degree in electrical engineering to Informatics and Mathematical Modelling, Technical University of Denmark.

The Ph.D. thesis is on methods for blind signal separation of signals with heavy tail distributions. The thesis is partly motivated by applications in digital signal processing of audio signals, and partly by the theoretical basis for blind separation of heavy tail signals. Initially an introduction to blind signal separation and the inherent problems are given, the signal models are introduced, and the models are discussed in relation to different applications.

The thesis introduces different heavy tailed distributions that have potential application in the field of signal processing, and special emphasis is on a certain class of distributions - the stable distributions. The class of stable distributions have some attractive analytical characteristics and it turns out that they are suitable for modelling many physical signals. Many of the fundamental assumptions in classical statistical signal processing does not apply to heavy tail signals in general. The thesis establishes the necessary theoretical basis for statistical signal processing and for blind separation of heavy tail signals.

The thesis introduces the most important existing methods for blind signal separation and the methods are discussed in relation to signals with heavy tail distributions. One of the most important methods for blind signal separation is based on the maximum likelihood principle. It turns out that blind signal separation methods based on the maximum likelihood method is appropriate to deal with heavy tail signals, that the method is relatively robust to deviations in the model of the distributions of the signals, and that the methods work even for stable distributions. A class of methods for blind signal separation is based on joint diagonalization of matrices; the thesis propose some variants of these methods and a unifying presentation of these methods are given. Finally a new method for blind signal separation of heavy tail signals, that is based on the spectral measure for stable distributions is proposed. The method has two remarkable properties, the number of independent signals and the corresponding basis vectors in a general rectangular mixing matrix can be identified.

The thesis focuses on applications in processing of audio signals, and an empirical examination of a broad class of audio signals shows that the class of stable distributions are suitable for modelling audio signals. The methods for blind signal separation are evaluated on various audio signals from synthetic mixtures and from signals from an experimental teleconference system.

Miscellaneous

• Master Thesis. P.Kidmose and J.B.Pedersen, Beamformer til støjredution i høreapparater, IMM-EKS-1998-37, Department of Mathematical Modelling, Technical University of Denmark.
• Patent resulting from B.Sc. Thesis. WO 97/10884, A Method for Adjusting a Separation Process and an Apparatus for use by the Method.