Non-negative Matrix Factorisation Techniques: Advances in Theory and Applications

Nowadays, Magnetic Resonance Spectroscopy (MRS) represents a powerful nuclear magnetic resonance (NMR) technique in oncology since it provides information on the biochemical profile of tissues, thereby allowing clinicians and radiologists to identify in a non-invasive way the different tissue types characterising the sample under investigation. The main purpose of the pre-sent chapter is to provide a review of the most recent and significant applica-tions of non-negative matrix factorization (NMF) to MRS data in the field of tissue typing methods for tumour diagnosis. Specifically, NMF-based methods for the recovery of constituent spectra in ex vivo and in vivo brain MRS data, for brain tissue pattern differentiation using Magnetic Resonance Spectro-scopic Imaging (MRSI) data, and for automatic detection and visualisation of prostate tumours will be described. Furthermore, since several NMF imple-mentations are available in the literature, a comparison in terms of pattern de-tection accuracy of some NMF algorithms will be reported and discussed, and the NMF performance for MRS data analysis will be compared with that of other blind source separation (BSS) techniques.