The Continuous Wavelet Transform in MRS : Tutorial text, Marie Curie Research Training Network FAST

Suvichakorn, Aimamorn [UCL] Lemke, Christina [UCL] Schuck Jr., Adalberto [UCL] Antoine, Jean-Pierre [UCL]

This tutorial text reviews some applications of the Continuous Wavelet Transform (CWT) in Magnetic Resonance Spectroscopy (MRS), focusing on the problems of spectral line estimation, namely, apodization, random noise, baseline, solvent peak, nonstandard lineshapes. First, we use a standard wavelet, namely the Morlet wavelet. Next, we introduce a new type of wavelet, derived from the autocorrelation function of a model signal. Finally, we apply this new technique for constructing adapted wavelets, generated from the metabolite data themselves. A short compendium on the basics of the CWT and some explicit numerical programs are given in two Appendices.