Application of the sparse regularization in NMR Diffusometry measurements

This work's main focus is on the application of sparse regularization in to NMR diffusometry experiments. The thesis is divided into three main parts: 1. Methodology overview , where the basic theory of methods is described on which the methodology introduced in further parts is built. This part contains the discussion on the basic NMR phenomena, the idea of multidimensional NMR, NMR diffusometry and relaxometry. Additionally the part is focused on the process of diffusion and available methods allowing to study this phenomenon. 2. Sparsity-based toolbox for NMR, where the discussion on the sparsity constraint in NMR is presented. The part starts from discussing the current state of the art sparsity constraint in NMR - the Compressed Sensing methods. It is followed by the discussion on the use of this constraint in NMR diffusometry where the new methods and algorithms, utilizing such constraint, are presented. Finally the work goes beyond the sparsity constraint by introducing mixed constraint that optimizes the balance between sparseness and smoothness. 3. Applications , where the application of the methodology introduced in previous part are shown. The part starts by showing the examples of using both sparsity and mixed constraint in the measurements of polymer mixtures. Then, the application of diffusion NMR to metabolomic studies and reaction monitoring are introduced. Finally, there are presented the applications of sparse-sampled 3D experiments, where one dimension is either encoding diffusion coefficient, or relaxation constant.