LAUSR

The fast Padé transform (FPT) is further optimized for encoded in vivo MRS time signals. This is achieved by a judicious combination of spectra averaging and time signal extrapolation. The motivation is in strengthening suppression of the over-sensitivity of signal processing to changes in model order K. Implementation is carried out in the FPT variant $$\hbox {FPT}^{(+)}$$FPT(+) which, by numerically performed analytical continuation, converts divergent into convergent series. Convergence of reconstructions is monitored for a sequence of successive values of K. Comparison is made with the corresponding retrieval without spectra averaging and time signal extrapolation. Variances are dramatically reduced for the reconstructed parameters (complex frequencies and complex amplitudes) when spectra averaging and extrapolation are performed. Negligible variances imply convergence, which is accomplished herein using a single averaging procedure (no iterations). This has important implications in practice with encoded MRS data, providing remarkable efficiency, robustness and accuracy of Padé-based quantification. Algorithmically, spectra averaging and time signal extrapolation consist of four steps. First, the encoded time signal is used to compute total shape spectra (envelopes) for a sequence of model orders K, which is the number of resonances. Second, these envelopes are averaged (spectra averaging). All the spectra are computed at the same sweep frequencies whose number considerably exceeds the number of data points in the encoded time signal. Third, the complex average envelope is inverted to yield a new time signal which is longer than the encoded data (time signal extrapolation). Fourth, the Padé extrapolated time signal is quantified for a sequence of K to monitor convergence of the reconstructed parameters. All four steps are applied to in vivo MRS data encoded on a 3 T scanner from a borderline serous cystic ovarian tumor. We focus on this clinical problem to help develop effective methods for early detection of ovarian cancer, in order to improve survival for women afflicted with this malignancy. It is anticipated that the presently refined, multi-purpose Padé-based methodology with its practical advantages for in vivo MRS can contribute to this goal.