ABSTRACT
This chapter examines the most difficult numerical aspects in solving the quantification problem in magnetic resonance spectroscopy (MRS). For clinical diagnostics via MRS, the most relevant quantities are metabolite concentrations that are proportional to the reconstructed peak areas. Therefore, metabolite concentrations of the examined tissue can be extracted from the spectrally analyzed time signal. Hence the clinical importance of the quantification problem in MRS. The chapter demonstrates that when the fast Pade transform (FPT) is near the convergence region, an unparalleled “phase transition” takes place, because literally two additional signal points are sufficient to attain the full 12 digit accuracy with the exponentially fast rate of convergence. The average number of fundamental frequencies in the window of interest defines the resolution of the FPT. In the FPT(+) the true and spurious resonances are completely separated from each other in two disjoint portions of the complex frequency plane.
