Compressing ECG signals by piecewise polynomial approximation

Compression of digital electrocardiogram (ECG) signals has traditionally been tackled by heuristical approaches. It has been demonstrated that exact optimization algorithms outclass these heuristical approaches by a wide margin with respect to the reconstruction error. As opposed to traditional time-domain algorithms, where some heuristic is used to extract representative signal samples from the original signal, the exact optimization algorithm proposed by Haugland, Heber and Husoy (see Medical & Biological Engineering & Computing, vol.35, p.420-24, 1997) formulates the sample selection problem as a graph theory problem. Thus well known optimization theory can be applied in order to yield optimal compression. Haughland et al. applied linear interpolation in the reconstruction of the signal. This paper generalizes the optimization algorithm such that reconstruction can be made by second order polynomial interpolation in the extracted signal samples. The polynomials are fitted in a way that guarantees minimal reconstruction error, and the method proves the good performance compared to the case where linear interpolation is used in the reconstruction of the signal.