A New Perspective on Scale: A Novel Transform for NMR Envelope Extraction

TL;DR

This paper introduces a novel transform for NMR envelope extraction that requires fewer sampling points and challenges traditional scale definitions by focusing on space-invariant state variations, validated through real Earth-field NMR data.

Contribution

The paper proposes a new transform for NMR envelope extraction based on a redefined scale, enabling accurate results with fewer samples and without relying on the Nyquist rate.

Findings

The proposed transform performs comparably to state-of-the-art methods.

It allows envelope extraction with significantly fewer sampling points.

Validation using real Earth-field NMR data confirms its effectiveness.

Abstract

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.