提出新变换，用更少采样点实现高精度核磁共振包络提取
A New Perspective on Scale: A Novel Transform for NMR Envelope Extraction
- 基于空间不变状态变化定义新尺度，替代传统物理参照
- 在远低于奈奎斯特采样率下仍能准确提取包络
- 适合低采样成本的核磁共振信号处理场景
核磁共振（NMR）中的包络提取是数据处理的关键步骤。传统方法依赖增加采样点数以提高检测精度，但本文提出一种新型变换，可在显著减少采样点数的情况下实现可接受的包络提取，甚至无需满足奈奎斯特采样率。论文挑战了传统的尺度定义，指出经典尺度在所有情境下均缺乏物理参照。为此，作者提出基于空间不变状态变化的新尺度，并区分出尺度变异型与尺度不变型观测者。研究证明，将尺度变异型观测者转换为尺度不变型，等价于包络提取。为验证理论，设计并实现了地磁场核磁共振实验装置，利用真实数据评估所提变换在参数恢复上的性能，并与经典及先进方法对比。
原文摘要 · Abstract (English)
Envelope extraction in nuclear magnetic resonance (NMR) is a fundamental step for processing the data space generated by this technique. Envelope detection accuracy improves with increasing the number of sampling points; however, we propose a novel transform that enables acceptable envelope extraction with significantly fewer sampling points, even without meeting the Nyquist rate. In this paper, we challenge the traditional scale definition and demonstrate that classic scaling lacks a physical referent in all situations. To achieve this aim, we introduce a scale based on the variations of space-invariant states, rather than the observable characteristics of matter and energy. According to this definition of the scale, we distinguished two kinds of observers: scale-variant and scale-invariant. We demonstrated that converting a scale-variant observer to a scale-invariant observer is equivalent to envelop extraction. To analyse and study the theories presented in the paper, we have designed and implemented an Earth-field NMR setup and used real data generated by it to evaluate the performance of the proposed envelope-detection transform. We compared the output of the proposed transform with that of classic and state-of-the-art methods for parameter recovery of NMR signals.
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