Magnetic resonance spectroscopy (MRS), as a powerful and versatile diagnostic modality in physics, chemistry, medicine and other basic and applied sciences, depends critically upon reliable signal processing. It provides time signals by encoding, but cannot quantify on its own. Mathematical methods do so. The signal processor of choice for MRS is the fast Padé transform (FPT). The spectrum in the FPT is the unique polynomial quotient for the given Maclaurin expansion. The parametric FPT (parameter estimator) performs quantification of time signals encoded with MRS by explicitly solving the spectral analysis problem. Thus far, the non-parametric FPT (shape estimator) could not quantify. However, the non-parametric derivative fast Padé transform (dFPT) can quantify despite performing shape estimation alone. The dFPT was successfully benchmarked on synthesized MRS time signals for derivative orders ranging from 1 to 50. It simultaneously improved resolution (by splitting apart tightly overlapped peaks) and enhanced signal-to-noise ratio (by suppressing the background baseline). The same advantageous features of improving both resolution and signal-to-noise ratio are presently found to be upheld with encoded MRS time signals. Moreover, it is demonstrated that the dFPT hugely outperforms the derivative fast Fourier transform even for derivatives of orders as low as four. The clinical implications are discussed.

中文翻译：

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将低阶导数快速 Padé 变换应用于测量时间信号的可行性研究

磁共振波谱 (MRS) 作为物理学、化学、医学和其他基础科学和应用科学中一种强大且通用的诊断方式，严重依赖于可靠的信号处理。它通过编码提供时间信号，但不能自行量化。数学方法就是这样做的。MRS 选择的信号处理器是快速 Padé 变换 (FPT)。FPT 中的频谱是给定麦克劳林展开式的唯一多项式商。参数化 FPT（参数估计器）通过明确解决频谱分析问题来对使用 MRS 编码的时间信号进行量化。到目前为止，非参数 FPT（形状估计器）无法量化。然而，尽管单独执行形状估计，但非参数导数快速 Padé 变换 (dFPT) 可以量化。dFPT 在合成 MRS 时间信号上成功地进行了基准测试，其导数阶数从 1 到 50。它同时提高了分辨率（通过分离紧密重叠的峰）和增强的信噪比（通过抑制背景基线）。目前发现改进分辨率和信噪比的相同有利特征被编码的 MRS 时间信号所支持。此外，事实证明，即使对于阶数低至 4 的导数，dFPT 也大大优于导数快速傅立叶变换。讨论了临床意义。目前发现改进分辨率和信噪比的相同有利特征被编码的 MRS 时间信号所支持。此外，事实证明，即使对于阶数低至 4 的导数，dFPT 也大大优于导数快速傅立叶变换。讨论了临床意义。目前发现改进分辨率和信噪比的相同有利特征被编码的 MRS 时间信号所支持。此外，事实证明，即使对于阶数低至 4 的导数，dFPT 也大大优于导数快速傅立叶变换。讨论了临床意义。