Machine accurate quantification in magnetic resonance spectroscopy

A powerful and invaluable complement to anatomical diagnostics, Magnetic Resonance Spectroscopy (MRS) provides bio-chemical information about the viability and overall functionality of the scanned tissue. This latter information is not available directly from time signals encoded from patients via MRS. Rather, time signals need to be spectrally analysed by considering the quantification problem. By solving this problem, one can reconstruct the fundamental frequencies and the corresponding amplitudes as well as their total number. Such parameters yield directly the diagnostically most relevant quantities that are the concentrations of the identified metabolites.All these key spectral parameters can unequivocally be reconstructed from the input time signal by using the fast Padé transform (FPT). The present computations demonstrate that the FPT can achieve the “spectral convergence”, i.e. the exponential convergence rate as a function of the signal length for a fixed bandwidth. This is illustrated to within machine accuracy by the exact reconstruction of all the parameters of every physical resonance from a synthesised noiseless time signal with 25 complex damped exponentials, including those for tightly overlapped and nearly degenerate resonances. Overlapped resonances are abundant in spectra from in vivo MRS and, moreover, they are often of utmost relevance for diagnostics, especially in clinical oncology.