Metabolite-sensitive analysis of magnetic resonance spectroscopic signals using the continuous wavelet transform

We introduce a new class of wavelets, called metabolite-based autocorrelation wavelets, for the analysis of magnetic resonance spectroscopic (MRS) signals by means of the continuous wavelet transform (CWT). Each MRS signal consists of a number of frequency components typical for the active nuclei and the chemical environment around them in a particular voxel. Identifying individual metabolite components is crucial for the evolving field of MRS for clinical applications. In a first step, we develop the theoretical analysis, considering continuous wavelets derived from (Lorentzian lineshape) signal models. With this analytical approach, we can not only tailor individual wavelets but also determine signal parameters such as the damping factor of the Lorentzian lineshape. Then, we design more complex wavelets numerically from discrete metabolite profiles. As the resulting wavelets are discrete, too, they require an extra step of up- and downsampling in order to perform a proper CWT. The outcome is that the present analysis indicates without ambiguity the presence of a given metabolite in a MRS signal