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UBC Theses and Dissertations

A sparsity based approach towards fast MRI acquisition Angshul, Majumdar


Magnetic Resonance Imaging (MRI) is a safe medical imaging modality that can acquire high quality scans. However, MRI has a relatively long acquisition time compared to other medical imaging modalities like X-Ray Computer Tomography and Ultrasonography. Reducing the MRI data acquisition time had been a challenge to researchers for the last two decades. Broadly there are two approaches to reduce the scan time – i) the hardware based approach by which the design of the scanner is changed to accommodate faster scans and ii) the software based approach where the sampling and reconstruction methods are changed to make faster scans. In this thesis, we propose techniques to reduce MRI acquisition time from the software based approach. The MRI scanner acquires the data in the Fourier frequency domain (more commonly referred to as the k-space in MRI). Traditionally, the k-space is sampled on a uniform Cartesian grid, and the image is therefore reconstructed using the inverse Fast Fourier Transform. Full sampling of the k-space is time consuming and forms the main source of delay in MRI acquisition. We show that it is possible to reduce the scan time by using non-uniform under-sampling of the k-space along with smart reconstruction algorithms to produce good quality MR images. The main contributions of this thesis are the following: 1. A novel MR image model that assumes the image to be a super-position of sparse and low-rank component is proposed; this yields more accurate reconstruction than previously known techniques in single channel static MR image reconstruction. 2. Algorithms for multi-echo MR imaging that jointly exploits the inter-echo correlation are proposed, resulting in a more accurate image reconstruction than existing techniques. 3. For the first time, a robust technique for multi-channel parallel MRI that does not require estimation of coil sensitivity maps is proposed. This technique produces images whose quality is at par or even better than state-of-the-art techniques. 4. Novel techniques for near real-time dynamic MRI reconstruction that are faster and more accurate than existing ones proposed 5. Efficient algorithms to solve a variety of problems in sparse/group-sparse/row-sparse signal recovery and low-rank matrix recovery are derived.

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