On the parameterization of Hermite transform with application to the compression of QRS complexes

The concentration and sparsity of signal representation in the Hermite transform (HT) basis may highly depend on a properly chosen scaling factor and discrete time shift parameter. In that sense, we propose a simple and efficient iterative procedure for automatic determination of the optimal scaling factor. The optimization criterion is based on the ℓ1-norm acting as a measure of signal concentration in the HT domain. Instead of centering the signal at the zero time instant, we also propose to shift the center for a few points left or right, which will additionally improve the concentration. An important application of the proposed optimization approach is the compression of QRS complexes, where properly chosen scaling factor and time-shift increase the compression performance. The results are verified using synthetic and real examples and compared with the existing approach for the compression of QRS complexes.