Signal Detection and Parameter Estimation for Nuclear Magnetic Resonance Spectroscopy

Abstract

Nuclear Magnetic Resonance spectroscopy (NMR), as the prime technique for efficient and rapid screening of the compounds in chemical samples, represents the nuclei in molecules as resonance peaks in the spectrum. The peaks are regarded as the “fingerprints” of the chemical components in the molecules, providing necessary information for researchers to elucidate the structure of the chemicals.

The time domain signal obtained in the modern NMR experiment can ideally be modelled as the superposition of multiple damped complex exponentials in additive Gaussian noise. For obtaining key information of the chemical compound being analysed, all the useful components should be successfully detected and algorithms should be applied to estimate their parameters. However, practical features including large signal size, unknown number of components, the existence of weak and overlapped peaks, and signal distortions caused by experimental artefacts, make these tasks hard to achieve. In this thesis, we focus on finding effective methods for the signal detection and parameter estimation problems for NMR signals that are capable of handling the practical signal features.

To tackle the signal detection problem, we develop the Localised Capon spectral Estimator (LoCapE), which is a high resolution spectral estimator in selected regions of the spectrum. Without a priori knowledge on the number of components, LoCapE is capable of resolving extremely closely spaced components in experimental NMR signals that cannot be separated by the Discrete Fourier Transform (DFT).

In terms of the parameter estimation problem, we put forward several novel frequency domain interpolation algorithms for efficiently estimating parameters of signals related to the ideal NMR signal model. We first present the 2-D version of the parameter estimation algorithm proposed by Aboutanios and Mulgrew (the A&M algorithm), for estimating the frequencies/parameters of single 2-D exponentials in noise. This is followed by the presentation of the Iterative Windowed A&M (IWAM) algorithm for the estimation of the frequency and damping factor of a 1-D damped exponential in noise, that is robust when the signal has a long noisy tail. By combining with a leakage subtraction scheme, the A&M algorithm and the IWAM algorithm are then extended to the Multi-tone A&M (MAM) algorithms which address the parameter estimation of ideal 1-D NMR signals. Theoretical analysis and simulation results show that all the proposed parameter estimators are able to achieve performance that is extremely close to the Cramer-Rao Lower Bound (CRLB).

To achieve simultaneous signal detection and parameter estimation of actual NMR signals, the IWAM algorithm is finally incorporated with a generalised lineshape model and a least squares lineshape adaptation scheme. This results the Peak Extraction using Adaptive Lineshape (PEAL) algorithm which can obtain reliable component extraction and accurate parameter estimation on experimental proton NMR datasets with arbitrary lineshape distortion.