A fast memory-saving method for the Morlet wavelet-based transform and its application to in vivo assessment of microcirculation dynamics

We propose an approach to the fast numerical evaluation of the continuous wavelet transform with the Morlet wavelet based on the replacement of the Gaussian factor in the latter by a hierarchical sequence of B-splines and their application to the image formed by the analyzed signal multiplied by a set of periodic functions. We show that the suggested approach results in a significant reduction of the resulting data storage (almost linear dependence on the sample length vs. the quadratic one required by conventional methods). In order to illustrate the workability of the proposed technique we applied it to the analysis of the data on the blood flow velocity data obtained in vivo from chorioallantoic membrane of chicken embryo, which exhibit non-stationarity, bi- or multirhythmicity.