Advanced time-domain methods for nuclear magnetic resonance spectroscopy data analysis

Over the past years magnetic resonance spectroscopy (MRS) has been of significant importance both as a fundamental research technique in different fields, as well as a diagnostic tool in medical environments. With MRS, for example, spectroscopic information, such as the concentrations of chemical substances, can be determined non-invasively. To that end, the signals are first modeled by an appropriate model function and mathematical techniques are subsequently applied to determine the model parameters. In this thesis, signal processing algorithms are developed to quantify in-vivo and ex-vivo MRS signals. These are usually characterized by a poor signal-to-noise ratio, overlapping peaks, deviations from the model function and in some cases the presence of disturbing components (e.g. the residual water in proton spectra). The work presented in this thesis addresses a part of the total effort to provide accurate, efficient and automatic data analysis of MRS signals. The various methods that exist to extract the parameters from a MRS signal are explained and connections between methods are pointed out. Typically, time-domain methods are divided into black-box and interactive methods. An often used interactive method is VARPRO. HSVD and HTLS are well-known examples of black-box methods. Interactive methods fit a model function to the data and minimize a cost function. Linear prediction and state-space methods are two variants of the black-box methods which do not involve the minimazation of a cost function. Algorithms which fall into this latter class of methods only approximately solve the linear prediction or state-space problem setting. It is shown here how the linear prediction and state-space problems can be solved without introducing approximations leading to maximum likelihood (ML) parameter estimates. However, then again the problems reduce to the solution of a minimization problem. The connection between time- and frequency-domain methods is also pointed out. In the class of interactive time-domain methods, AMARES (advanced method for accurate, robust and efficient spectral fitting) is developed and shown to outperform the popular VARPRO methods in terms of accuracy, robustness and flexibility. In biomedical studies MRS signals are in many cases acquired consecutively to monitor metabolic changes over time. Often information concerning the time evolution of some of the parameters in these time series is present. It is shown how the interactive and black-box time-domain methods can be extended to process multiple signals simultaneously. This leads to improved and more robust parameter estimates compared to the estimates obtained by processing the signals individually. Various techniques that have been used in the past to obtain estimates of parameters of selected peaks in the presence of unknown or uninteresting spectral features separated in frequency from the metabolites of interest are investigated and compared with each other. This problem is denoted by frequency-selective (FS) parameter estimation. In this context, a new technique based on the use of maximum-phase FIR filters in combination with AMARES is developed and compared with the existing methods. In terms of final parameter accuracy this new method outperforms the others. The method is also very easy to use and has a low computational complexity. The removal of residual water in proton spectra is treated as a special case of FS parameter estimation. A fast version of a singular value decompostion (SVD))based method is presented and found to be less performant than the filter-based approach in terms of efficiency, accuracy and ease of use.