Time-Domain Quantitative Decomposition of MRS FID Signals: Hankel Singular Value Decomposition (HSVD) and the Fast Padé Transform (FPT) Methods
Abstract
Purpose
Accurate quantitative magnetic resonance spectroscopy (MRS) is essential for metabolic imaging, yet conventional Fourier-based analysis fails when spectra exhibit extreme dynamic range, as commonly encountered in hyperpolarized 13C MRS. Dominant injected substrate signals prevent reliable phase correction and peak fitting, rendering quantification of weak downstream metabolites unreliable. This work investigates time-domain signal decomposition using Hankel singular value decomposition (HSVD) and the Fast Padé Transform (FPT) as practical, physics-based alternatives for robust MRS quantification.
Methods
Complex free induction decay (FID) signals were analyzed directly in the time domain using HSVD and FPT, without Fourier transformation or phase correction. Both methods model the FID as a sum of exponentially damped sinusoids and directly estimate spectral parameters including frequency, decay constant, and amplitude. HSVD allows explicit control of the number of retained signal components, while FPT identifies signal poles through rational approximation with subsequent filtering. Quantitative peak areas were computed analytically from the estimated amplitudes and decay constants. Results were compared against conventional FFT-based analysis.
Results
FFT-based spectra were dominated by the injected substrate resonance, with weak metabolites poorly resolved and unsuitable for reliable peak fitting. In contrast, HSVD and FPT consistently separated minor spectral components directly from the time-domain signal. Weak metabolites obscured in Fourier spectra were recovered with stable frequency and decay estimates. Quantitative peak areas derived from time-domain parameters were reproducible and consistent with expected metabolic relationships. Both methods remained robust even when the FID duration was reduced, demonstrating resilience to truncated acquisitions.
Conclusion
Time-domain decomposition using HSVD and Fast Padé Transform enables accurate, phase-independent quantification of MRS data with extreme dynamic range. By eliminating phase correction and empirical spectral fitting, these methods provide a robust and efficient framework for quantitative hyperpolarized MRS, with significant impact on metabolic imaging and clinical translation.