Extraction of efficient and characteristic features of multidimensional time series

In numerous signal processing applications one disposes of multiple probes, delivering simultaneously information about one or multiple observed processes. The resulting multidimensional time series are often highly redundant and may contain stochastic contributions. The perception of the useful information becomes therefore very difficult and sometimes impossible. Thus, the major issue of concern of this thesis resides in the development of novel algorithms for the extraction of the salient and characteristic features of multidimensional time series. The proposed algorithms are based on parametric signal processing, namely we assume that the features of the experimental data can be represented efficiently by a specific model. We present a global framework for the selection of a specific model out of the large span of techniques proposed in the literature. For the selection of the model classes we use, in addition to prior knowledge about the particular applicatio, the principle of independent component analysis. More precisely, the model classes are selected in order to provide a separate analysis of signal components issued from different independent subsystems. Within a given model class, the specific model parameterization by a particular set of non-zero parameters is based on Rissanens Minimum Description Length (MDL) criterion. Thus, we obtain a very parsimonious modeling, avoid overparametrization and ensure an efficient representation of the observed data. In regard to this model selection framework, various algorithms are developed throughout this thesis. A subband model is proposed for data, containing signal components from different subsystems which manifest themselves in different frequency bands. Classical blind source separation techniques are applied to multidimensional time series, which can be considered as noiseless mixtures of some independent elementary signals. Noisy time series are enhanced by an automatic noise reduction algorithm based on local principal component analysis in the space of delayed coordinates. Eventually, algorithms are also proposed for the analysis of multidimensional time series, which can be considered as noisy mixtures of some independent elementary signals. Generally, we have developed and validated the algorithms for a large class of signals.The class comprises signals of interest issued from linear or nonlinear dynamical systems and various distributions of additive white noise. The algorithms are generally equipped with an automatic parameter selection method based on the MDL principle. Therefore they do not necessitate a troublesome and hazardous parameter tuning of the operator and constitute promising signal processing tools for the practical user. In what concerns the experimental aspect of this thesis, the presented algorithms are mainly applied of to cardiovascular signals, such as heart beat and QT-intervals, arterial blood pressure and instantaneous lung volume. In this contex, we aimed at developing feature extraction algorithms which are able to distinguish different functional states of the cardiovascular system in regard to some aspects of the neural regulation. Two specific algorithms have been developed to obtain an observer of the modulatory effect of the autonomic cardiac outflow on cardiovascular parameters. These algorithms have been deduced from linearized small-signal models of the cardiovascular system. They have been based on the fundamental assumption about the independence the two antagonistic parts of the autonomic cardiac outfow, namely the sympathetic (CSNA) and parasympathetic (CPNA) cardiac outflows. A first algorithm has been based on non-causal blind source separation of heart beat intervals and arterial blood pressure. The reliability of this observer has been assessed by verification of the independence assumption for clinical data. Qualitative validations have demonstrated that the observer reconstructs a very statisfying approximation of sympathetic activity. Quantitative validations have pointed out that the observer is able to highlight changes in the level of the sympathetic and parasympathetic activities. The drawback of this observer resides in the fact that it requires simultaneous recordings of the electrocardiogram and the arterial blood pressure. Therefore we present a second algorithm, based on blind source separation of heart beat and QT intervals and which requires only electrocardiogram recordings. Its reliability has also been assesed in qualitative validations on clinical data. A further application of the presented algorithms is the field of noise reduction. We present algorithms for nonlinear noise reduction of chaotic signals as well as for speech enhancement. The algorithms are equipped with automatic parameter selection methods based on the MDL principle and do require a troublesome parameter tuning of the operator. The nonlinear noise reduction algorithm is validated on time series from Lorenz, Roessler and Henon attractors which have been contaminated by various additive noises. The proposed speech enhancement algorithm is based on a novel subspace partitioning which allows to minimize signal distortion and maximize noise reduction. An objective evaluation of the performance has been based on phonetically equilibrated French sentences with several noises from the Noisex-92 Database. A further validation is performed by using the proposed algorithm as a pre-processing unit to automatic speech recognition system.