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

Abstract

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.

Feasibility study for applying the lower-order derivative fast Padé transform to measured time signals

“…This was done in Refs. [6,15]. Both processors performed envelope estimations using the same noisy time signal points {c n +r n } where {c n } are the noiseless time signal points.…”

“…[18], the concept of iterative spectra averaging from Refs. [4,6] was employed. The total number of iterations in averaging was 12 and 3 of them have been explicitly shown and analyzed in detail.…”

“…We have herein applied the dFPT to process MRS time signals encoded in vivo on a 1.5 T MR clinical scanner from a pediatric patient with cerebral asphyxia [4,6,18]. This problem was selected, in part, because MR spectra associated with ischemia or asphyxia are very dense and, thus, have represented a great challenge for resolution and interpretation.…”

“…One of such mathematical transforms in MRS is the fast Padé transform (FPT) [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. It can perform both shape and parameter estimations.…”

“…The most recent upgrade of the FPT is the derivative fast Padé transform (dFPT) [6,[15][16][17]. This processor can provide quantification by exclusive reliance upon shape estimation.…”