Low Dimensional Methods for High Dimensional Magnetic Resonance Imaging

Magnetic Resonance Imaging (MRI) is an amazing imaging modality in many aspects. It offers one of the best imaging contrast for visualizing soft issues. It has no ionizing radiation at all. Its flexibility has also enabled many applications, including assessing blood flow, imaging brain activity via oxygenation contrast, and measuring tissue stiffness. Since MRI was invented, this imaging technology has saved numerous lives, and has been the frontier of biomedical and engineering research./nOn the other hand, imaging speed remains a main limitation of MRI. Inherently, MRI takes time to collect measurements, and often requires minutes to complete a scan. In this regard, MRI is quite similar to early cameras: Subjects have to be motionless for minutes to obtain an image, which is uncomfortable to patients. This often leads to motion and motion artifacts. When severe motion artifacts occur, scans have to be repeated./nThis dissertation aims to change that by developing techniques to reconstruct three-dimensional (3D) dynamic MRI from continuous acquisitions. An ideal 3D dynamic scan would be able to resolve all dynamics at a high spatiotemporal resolution. Subjects would not have to be motionless. The comprehensive information in the single scan would also greatly simplify clinical workflow. While this dissertation has not achieved this ideal scan yet, it proposes several innovations toward this goal. In particular, www.doi.org/10.6084/m9.figshare.7464485 shows a 3D rendering of a reconstruction result from this dissertation. Arbitrary slices at different orientation can be selected over time. Respiratory motion, contrast enhancements, and even slight bulk motion can be seen./nThe main challenge in high resolution 3D dynamic MRI is that the reconstruction problem is inherently underdetermined and demanding of computation and memory. To overcome these challenges, this dissertation builds on top of many fundamental methods, including non-Cartesian imaging, parallel imaging and compressed sensing. In particular, this dissertation heavily relies on the compressed sensing framework, which has three components: 1) the image of interest has a compressed signal representation. 2) MRI can acquire (pseudo)-randomized samples in k-space, which provides incoherent encoding of the underlying image. 3) sparsity/compressibility can be efficiently enforced in reconstruction to recover the compressed representation from the undersampled measurements./nIn this dissertation, I propose a multiscale low rank model that can compactly represent dynamic image sequences. The resulting representation can be applied beyond MRI, and is useful for other applications, such as motion separation in surveillance video. With the multiscale low rank representation, I propose a technique incorporating stochastic optimization to efficiently reconstruct 3D dynamic MRI. This makes it feasible to run such large-scale reconstructions on local workstations. To further speed up the reconstruction time, I propose accelerating the convergence of non-Cartesian reconstruction using a specially designed preconditioner. Finally, I leverage external undersampled datasets to further improve reconstruction quality using convolutional sparse coding.

Advisor: Lustig, Michael