Wavelet-based deconvolution

A fast computational algorithm for deconvolution of signals in the form of peaks with exponentially falling fronts in the presence of noise is proposed. The filter bank coefficients are constructed on the basis of new wavelets called quasi-wavelets, which are derived from the instrument's pulse response (instrument function) or similar functions defined analytically. A regularization procedure is offered based on selecting the sampling interval of the observed signal and the smoothing parameter of the restoring filter. This method ensures separation of completely overlapping peaks (without any noticeable saddle between them). The systematic error of restoration with an exactly known instrument function is a few tenths of a percent at three-to fourfold noise suppression.