Review of recent applications of the conventional and derivative fast Padé transform for magnetic resonance spectroscopy

This review is on the fast Padé transform (FPT) for magnetic resonance spectroscopy (MRS). It is structured into two portions. Firstly, we give an introductory overview, emphasizing the conceptual framework. Secondly, we cover the specific, concrete accomplishments with detailed analysis and selected illustrations. Key advances have been achieved by the FPT for MRS in the most recent period. These consist of direct applications of the FPT to time signals encoded by in vivo MRS from tumorous tissues. We focus on the robust and comprehensive Padé-based solutions for the thorniest problems (overlapping resonances, resolution, noise) that have hampered progress of in vivo MRS for a very long time. Both parametric and non-parametric aspects of signal processing in the FPT are thoroughly covered. The FPT, as a parameter estimator, solves exactly the quantification problem by reconstructing the positions, widths, heights and phases of all the physical peaks. This gives the component lineshapes of all the true resonances. The non-parametric FPT, as a shape estimator, has thus far predicted the total lineshapes alone without separating the individual components. Finally, we discuss the most recent advances in signal processing for MRS using the derivative fast Padé transform (dFPT). This upgrade is of utmost importance, as the dFPT exactly reconstructs all the peak parameters for every physical resonance by carrying out estimation of total shape spectra alone. The derivative operator within the dFPT narrows the linewidths and concomitantly enhances the peak heights, while simultaneously suppressing noise. This leads to separation of overlapping peaks, resolution improvement and noise reduction. Far-reaching ramifications of such an achievement within MRS are highlighted with the prospects for further explorations to the benefit particularly of cancer medicine.