Signal processing in diffusion MRI : high quality signal reconstruction - Neuman, Bartosz P. (2014)
Magnetic Resonance Imaging (MRI) is a medical imaging technique which is especially sensitive to different soft tissues, producing a good contrast between them. It allows for in vivo visualisation of internal structures in detail and became an indispensable tool in diagnosing and monitoring the brain related diseases and pathologies. Amongst others, MRI can be used to measure random incoherent motion of water molecules, which in turn allows to infer structural information. One of the main challenges in processing and analysing four dimensional diffusion MRI images is low signal quality. To improve the signal quality, either denoising algorithm or angular and spatial regularisations are utilised. Regularisation method based on Laplace--Beltrami smoothing operator was successfully applied to diffusion signal. In this thesis, a new regularisation strength selection scheme for diffusion signal regularisation is introduced. A mathematical model of diffusion signal is used in Monte--Carlo simulations, and a regularisation strength that optimally reconstructs the diffusion signal is sought. The regularisation values found in this research show a different trend than the currently used L-curve analysis, and further improve reconstruction accuracy. Additionally, as an alternative to regularisation methods a backward elimination regression for spherical harmonics is proposed. Instead of using the regularisation term as a low-pass filter, the statistical t-test is classifying regression terms into reliable and corrupted. Four algorithms that use this information are further introduced. As the result, a selective filtering is constructed that retains the angular sharpness of the signal, while at the same time reducing corruptive effect of measurement noise. Finally, a statistical approach for estimating diffusion signal is investigated. Based on the physical properties of water diffusion a prior knowledge for the diffusion signal is constructed. The spherical harmonic transform is then formulated as a Bayesian regression problem. Diffusion signal reconstructed with the addition of such prior knowledge is accurate, noise resilient, and of high quality.