2026-09-20T11:44:37Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/72922 2023-07-11 col_2142_5131 col_2142_8888 com_2142_5130 com_2142_8887 com_2142_234

Liang, Zhi-Pei Liu, Ding 2015-01-21T19:49:31Z 2015-01-21T19:49:31Z 2014-12 2015-01-21 2014-12 Noise is an important issue in magnetic resonance imaging (MRI), since the signal-to-noise ratio (SNR) is a major limiting factor for imaging speed and the achievable spatial resolution. This thesis investigates the utility of low-rank property in the denoising problem for the following two MRI modalities: diffusion magnetic resonance imaging and magnetic resonance spectroscopic imaging (MRSI). For denoising magnitude diffusion weighted image series, we utilize both low-rank and edge constraints within a maximum a posteriori (MAP) framework. We propose a fast novel majorize-minimize (MM) algorithm to solve the resulting optimization problem by majorizing the log-likelihood from the noncentral distribution, leading to a new optimization problem that can be solved eff ciently. Simulations based on numerical phantoms and real ex vivo data demonstrate that our new denoising algorithm obtains similar or even better qualitative improvement in image quality and quantitative improvement in diff usion parameter estimation compared with a conventional Quasi-Newton based algorithm, but with much less computation time. For denoising MRSI data, we consider the denoising algorithm utilizing two low-rank structures in MRSI data, which are due to the spatiotemporal partial separability in the k-t domain and the linear predictability (LP) along the temporal dimension, respectively. We conduct a comprehensive investigation of how to optimally segment the 1-D temporal single-voxel MRSI signals to improve the denoising performance of the LP-based low-rank filtering, by studying the relation between the singular value distribution of the Hankel matrices, which are formed by these temporal signals, and the corresponding reconstructed spectra. The investigation results are demonstrated using simulated data. Item withdrawn by Laura Spradlin (lspradl2@illinois.edu) on 2014-11-19T14:41:48Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Liu_Ding.pdf: 1486331 bytes, checksum: 2dc506e7624ee7714978db761a91be2f (MD5) Made available in DSpace on 2015-01-21T19:49:31Z (GMT). No. of bitstreams: 1 Ding_Liu.pdf: 1486331 bytes, checksum: 2dc506e7624ee7714978db761a91be2f (MD5) http://hdl.handle.net/2142/72922 en Copyright 2014 Ding Liu Image Denoising Magnetic Resonance Imaging (MRI) Rank constrained denoising in magnetic resonance imaging text Electrical & Computer Eng 1933 Electrical & Computer Engr 1200 University of Illinois at Urbana-Champaign Thesis M.S. MS:Electr & Computer Eng-UIUC 10KS1200MS