Rank constrained denoising in magnetic resonance imaging

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.

Name thesis:degree_name

M.S.

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Electrical & Computer Engr

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Liu, Ding

Contributors dc:contributor

• Liang, Zhi-Pei

• Image Denoising
• Magnetic Resonance Imaging (MRI)

Statement dc:rights

• Copyright 2014 Ding Liu

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/72922

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/72922