Fast Padé transform for optimal quantification of time signals from magnetic resonance spectroscopy

Abstract

AbstractThe fast Padé transform (FPT) is both a parametric and a nonparametric estimator that is capable of quantifying the input raw time signals without any fitting. The FPT simultaneously interpolates as well as extrapolates, and this is expected to mitigate truncation artifacts. To assess performance, it is necessary to compare the main features of the FPT with the characteristics of other parametric estimators, as well as with the fast Fourier transform (FFT), which can yield only shape spectra. The FPT can also give the shape of a spectrum, but accomplishes this in two totally different ways, with and without computing the spectral parameters (complex frequencies and amplitudes). A number of other parametric estimators used in signal processing are unable to yield shape spectra without prior extraction of the fundamental frequencies and the corresponding amplitudes. The primary goal of the present study is to assess the accuracy, robustness, and efficiency of the FPT for parametric and nonparametric estimations of experimentally measured time signals from in vivo magnetic resonance spectroscopy (MRS). Robustness and steadiness of the FPT are assessed relative to the FFT by monitoring the convergence rates of these two processors through a systematic and gradual decrease of the truncation level of the full signal length. Accuracy of the FPT is verified by performing error analysis of proven validity, using a gold standard, if available. Alternatively, comparison is made between the two complementary variants of the FPT that converge inside and outside the unit circle. Efficiency of the FPT is checked with respect to the FFT for estimation of the shape of a spectrum, as well as relative to other parametric processors, in the case of quantifications. To establish the accuracy, robustness, and efficiency of the FPT within the outlined multi‐level strategy, we use a time signal encoded via MRS at 4T from the brain of a healthy volunteer. We also assess the overall usefulness of the FPT for signal processing of data acquired from patients, in light of the emerging appreciation that spectroscopy of the tissue metabolites offers a number of vital advantages over the corresponding anatomical imaging in diagnostics. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005