Subspace-based quantification of magnetic resonance spectroscopy data using biochemical prior knowledge

Nowadays, Nuclear Magnetic Resonance (NMR) is widely used in oncology as a non-invasive diagnostic tool in order to detect the presence of tumor regions in the human body. An application of NMR is Magnetic Resonance Imaging, which is applied in routine clinical practice to localize tumors and determine their size. Magnetic Resonance Imaging is able to provide an initial diagnosis, but its ability to delineate anatomical and pathological information is significantly improved by its combination with another NMR application, namely Magnetic Resonance Spectroscopy. The latter reveals information on the biochemical profile tissues, thereby allowing clinicians and radiologists to identify in a non{invasive way the different tissue types characterizing the sample under investigation, and to study the biochemical changes underlying a pathological situation. In particular, an NMR application exists which provides spatial as well as biochemical information. This application is called Magnetic Resonance Spectroscopic Imaging (MRSI) and involves the simultaneous acquisition of signals from many volume elements. The success of MRSI as a diagnostic tool depends on the accurate estimation of the concentrations of the chemical compounds that are present in the suspicious region. Such quantities can be obtained by computing the physical parameters that characterize the MRSI signals located in that region. The first part of the thesis concerns the development of accurate, robust and efficient algorithms for the quantification of time domain MRSI signals. A variety of methods are available in the literature. They are generally divided into two classes: optimization-based methods and subspace-based methods. The former are iterative, require user involvement and allow inclusion of biochemical prior knowledge. The subspace{based methods are easier to use, since minimal user interaction is required, but they allow limited incorporation of biochemical prior knowledge. In this thesis, we focus on the latter class. In particular, we develop an improved version of the popular HLSVD method. This method is very frequently used in NMR for solvent suppression and is freely available in the MRUI software package. Our studies show that sometimes HLSVD fails in the estimation of the parameters of interest because some numerical problems occur in its implementation, which is based on the Lanczos algorithm for the computation of the truncated SVD of the Hankel data matrix. We propose two alternative variants of HLSVD, namely HLSVD{PRO (based on the Lanczos algorithm with partial reorthogonalization) and HLSVD{IRL (based on the implicitly restarted Lanczos algorithm which are able to outperform HLSVD in terms of accuracy and efficiency. In the literature, it has extensively been proved that the performance of parameter estimation methods significantly improves if biochemical prior knowledge is used. In this thesis we propose a new subspace{based method called KNOB-TLS, which allows the use of more prior knowledge about the signal parameters than previously published subspace-based methods. Extensive simulation and in vivo studies show that the proposed algorithm performs best in terms of robustness and accuracy and provides results that are comparable to those of the optimization-based methods. The final topic is the development of a fast and accurate tissue segmentation and classification technique. This is based on a statistical method, called Canonical Correlation Analysis, able to simultaneously exploit the spectral and spatial information characterizing the MRSI data. The potential and limitations of the new technique to retrieve the possible tissue types characterizing the considered sample, are investigated. Moreover, its performance is compared to that of ordinary correlation analysis, which does not exploit any spatial information. Extensive simulation and in vivo studies are carried out by using prostate MRSI data as well as two{dimensional Turbo Spectroscopic Imaging brain data. Test results show that the proposed tissue typing technique is fast and accurate, even when the region under investigation presents a high degree of heterogeneity. Furthermore, it outperforms ordinary correlation analysis in robustness and accuracy.