Iterative averaging of spectra as a powerful way of suppressing spurious resonances in signal processing

Abstract

The fast Padé transform (FPT) was applied to magnetic resonance spectroscopic (MRS) time signals encoded in vivo on a 1.5 T scanner from the parietal-temporal brain region of a pediatric patient who had suffered cerebral asphyxia. An iterative averaging procedure was implemented to the 9th iteration, whereby spurious structures on the total shape spectra were effectively suppressed. The parametric and non-parametric hbox {FPT}^{(pm )} were verified to reconstruct equivalent total shape spectra. Via the parametric FPT, the spectral region of interest was chosen to bypass the giant water resonance, automatically generating spectral envelopes without the need for windowing. The dense component spectra were reliably reconstructed by the hbox {FPT}^{(+)}, in the “usual” mode (mixture of absorption and dispersion components) and “ersatz” mode (reconstructed phases set to zero). Via the latter, interference effects were well-visualized for closely-overlapping and hidden resonances. The most stringent test was performed for the complex frequencies and associated complex amplitudes reconstructed by the hbox {FPT}^{(+)}. Exceedingly small variances were obtained for all four Padé-reconstructed parameters per genuine resonance, once convergence was achieved at the 7th to 9th iterated averages. This now fully-validated methodology can generate denoised spectra and accurate spectral parameters for in vivo MRS data encoded within neurodiagnostics. Such a multi-faceted Padé-based strategy for processing the dense spectra of the brain could vitally improve pediatric neurodiagnostics. A wider range of clinical applications becomes within reach, including areas of cancer diagnostics where the added value of in vivo MRS is urgently needed. The broad theoretical underpinnings of incorporating quantum mechanics into signal processing provide the basis for these innovative advances.