Relation between wavelet-biopotential likeness and wavelet compression of biopotential trains

The wavelet transform (WT) gains ground every day over other methods of biosignal processing. Yet there is still much ambiguity when deciding which particular wavelet to use. The aim of this work is to consider the relationship between (a) the likeness of a wavelet to a transitory signal (the Hodgkin-Huxley action potential), and (b) the performance of the WT compressing a train of said signal. In order to achieve this, a new method of quantifying likeness is developed. The method is insensitive to amplitude, DC level, frequency and phase of the signals it is comparing. The compression performance of the WT is evaluated for several number of thresholding schemes (soft, hard, global, level, etc.). For all evaluations, the wavelet most alike the transitory signal yielded the best compression results. This study opens the door and establishes a methodology for many possible future researches.