Magnetic resonance imaging (MRI) is uniquely well suited for studies of sedimentary rocks as it allows direct non-invasive detection of fluid content and fluid interactions in the pore space. Pure phase encoding MRI methods have proven to be robust in their ability to generate quantitative images in porous media. However, the sensitivity is low for pure phase encoding, especially with low magnetic field MRI systems that are common for porous media studies. Novel sampling strategies and data reconstruction methods, described in this thesis, improve measurement sensitivity with no hardware modifications required. Pure phase encode MRI methods acquire a single k-space data point with each radio frequency (RF) excitation. Reducing the number of acquired data points will significantly increase the measurement sensitivity. The goal is to look for data sampling and image reconstruction methods that ensure good image quality with reduced data. These methods are based on the inherent sparsity of MRI data, either in k-space or in transformed image spaces. Sample geometry based restricted sampling exploits k-space redundancy, with simple and reliable linear image reconstruction. The sampling patterns that collect regions of high intensity signal while neglecting low intensity regions can be naturally applied to a wide variety of pure phase encoding measurements. An important application is T 2 mapping spin-echo single point imaging (SES PI) that reveals different bedding plane structures within the rock core plug sample. In compressed sensing, spatial or spatiotemporal correlations of the static and dynamic MR images are exploited by transforming the images to sparse representations. Incoherent sampling and non-linear reconstruction are required. Imaging speed can also be improved by more efficient data collection. This can be achieved by combining phase and frequency encodings. A novel k-space trajectory, with rapid and accurate linear image reconstruction, is employed for high quality quantitative density images. In this thesis, new MRI data sampling and image reconstruction methods, for application to porous media, have been developed. These methods significantly improve the measurement sensitivity of quantitative MR imaging.
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