Application of linear prediction and rapid acquisition to nuclear magnetic resonance - Chainani, Edward Torres (2001)
In pulsed nuclear magnetic resonance (NMR) spectroscopy, information is obtained by perturbing the nucleus from its equilibrium position and acquiring the transient response. Fourier transformation is then used in data processing of the signals due to its rapid computation of the NMR spectrum. To obtain good signal-to-noise ratio, it is common practice to average many transients. To obtain good resolution, lengthier acquisition times are favored. For insensitive nuclei where thousands of collected transients are necessary, this is a time-consuming procedure, especially if the nuclear relaxation time constant is in the order of seconds or minutes. A faster acquisition method is proposed in this thesis, The proposed method acquires signals more rapidly than by conventional acquisition methods; however, the signals are truncated. This method is based on Driven-Equilibrium Fourier Transform (DEFT) in which the nuclei, once perturbed, are immediately returned to equilibrium. In processing truncated data, the shortcomings of the Fourier transform must be overcome by alternative spectral estimation methods. An alternative processing method - linear prediction (LP) - is sought to reconstruct the spectrum from the incomplete time-domain magnetic resonance data. The LP method fits the NMR model function consisting of exponentially damped sinusoids with arbitrary frequency, amplitude, damping factors and phases to the data. The fitting can be carried out by a linear least-squares (LS) procedure, and thus does not require starting values, unlike some methods. By using singular value decomposition (SVD) as the basis of the LS procedure, it is possible to distinguish between probable signal components and noise. By using backward linear prediction, the method is insensitive to truncation at the end of the signal, and renders the missing portion unnecessary. Unlike Fourier transformation (FT), truncated data in LP does not necessarily lead to loss of frequency resolution. The LP method's application to truncated, fast acquisition of data based on the DEFT pulse sequence is discussed in detail. This combination of methods is a novel way of acquiring and processing NMR spectroscopic data.
Thesis (M.S. Electrical Engineering)--University of the Philippines, Diliman.
Keywords: Nuclear magnetic resonance spectroscopy -- Linear programming; Prediction theory; Fourier transformations