Modélisations polynomiales des signaux ECG : applications à la compression

Abstract : Developing new ECG data compression methods has become more important with the implementation of telemedicine. In fact, compression schemes could considerably reduce the cost of medical data transmission through modern telecommunication networks. Our aim in this thesis is to elaborate compression algorithms for ECG data, using orthogonal polynomials. To start, we studied ECG physiological origin, analysed this signal patterns, including characteristic waves and some signal processing procedures generally applied ECG. We also made an exhaustive review of ECG data compression algorithms, putting special emphasis on methods based on polynomial approximations or polynomials interpolations. We next dealt with the theory of orthogonal polynomials. We tackled on the mathematical construction and studied various and interesting properties of orthogonal polynomials. The modelling of ECG signals with orthogonal polynomials includes two stages: Firstly, ECG signal should be divided into blocks after QRS detection. These blocks must match with cardiac cycles. The second stage is the decomposition of blocks into polynomial bases. Decomposition let to coefficients which will be used to synthesize reconstructed signal. Compression is the fact of using a small number of coefficients to represent a block made of large number of signal samples. We realised ECG signals decompositions into some orthogonal polynomials bases: Laguerre polynomials and Hermite polynomials did not bring out good signal reconstruction. Interesting results were recorded with Legendre polynomials and Tchebychev polynomials. Consequently, our first algorithm for ECG data compression was designed using Jacobi polynomials. This algorithm could be optimized by suppression of boundary effects, it then becomes universal and could be used to compress other types of signal such as audio and image signals. Although Laguerre polynomials and Hermite functions could not individually let to good signal reconstruction, we imagined an association of both systems of functions to realize ECG compression. For that matter, every block of ECG signal that matches with a cardiac cycle is split in two parts. The first part consisting of the baseline section of ECG is decomposed in a series of Laguerre polynomials. The second part made of P-QRS-T waves is modelled with Hermite functions. This second algorithm for ECG data compression is robust and very competitive
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Daniel Tchiotsop. Modélisations polynomiales des signaux ECG : applications à la compression. Autre [cond-mat.other]. Institut National Polytechnique de Lorraine, 2007. Français. ⟨NNT : 2007INPL088N⟩. ⟨tel-01752958⟩

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