Rate distortion optimal signal compression using second order polynomial approximation

In this paper we present a time domain signal compression algorithm based on the coding of line segments which are used to approximate the signal. These segments are fit in a way that is optimal in the rate distortion sense. The approach is applicable to many types of signals, but in this paper we focus on the compression of ElectroCardioGram (ECG) signals. As opposed to traditional time-domain algorithms, where heuristics are used to extract representative signal samples from the original signal, an optimization algorithm is formulated in [1, 2, 3] for sample selection using graph theory, with linear interpolation applied to the reconstruction of the signal. In this paper the algorithm in [1, 2, 3] is generalized by using second order polynomial interpolation for the reconstruction of the signal from the extracted signal samples. The polynomials are fitted in a way that guarantees minimum reconstruction error given an upper bound on the number of bits. The method achieves good performance compared both to the case where linear interpolation is used in reconstruction of the signal and to other state-of-the-art ECG coders.