Exploitng sparse signal representations in capturing and recovery of nuclear magnetic resonance data

This thesis deals with the nuclear magnetic resonance field, especially spectroscopy and spectroscopy imaging, sparse signal representation and low-rank approximation approaches. Spectroscopy imaging methods are becoming very popular in clinical praxis, however, long measurement times and low resolution prevent them from their spreading. The goal of this thesis is to improve state of the art methods by using sparse signal representation and low-rank approximation approaches. The compressed sensing technique is demonstrated on the examples of magnetic resonance imaging speedup and hyperspectral imaging data saving. Then, a new spectroscopy imaging scheme based on compressed sensing is proposed. The thesis deals also with the in vivo spectrum quantitation problem by designing the MRSMP algorithm specifically for this purpose