Fast and High-Resolution MRI with Nonlinear Spatial Encoding Functions

Abstract

This thesis presents recent advances in image acceleration and high-resolution methods for Magnetic Resonance Imaging (MRI), driven by a deepened understanding of how to characterize and utilize nonlinear spatial encoding functions. Conventionally, MRI spatial encoding relies on linear gradients and RF receivers (i.e., in high field) – a process well understood by k-space theory. However, despite decades of progress, MRI remains fundamentally constrained by sequential sampling in the Fourier-domain, which limits both speed and spatial resolution. To further boost performance, this work develops two separate categories of techniques for fast and high-resolution MRI, respectively, which are ultimately found to be unified under a novel mathematical perspective.

The first category accelerates MRI sampling by exploiting a local B0 coil array, as a novel gradient hardware system that can generate a wide range of linear and nonlinear magnetic field modulations. This disrupts the traditional k-space framework, and pushes acquisition into a largely unexplored regime. Consequently, k-space is sampled by time-varying local neighborhoods (i.e., patches), rather than point-by-point trajectory (due to linear gradients) or time-invariant kernels (due to RF receivers), allowing more information to be captured per unit time. Despite significant theoretical and practical challenges, this thesis establishes a comprehensive pipeline for this approach, encompassing hardware design, signal encoding, magnetic field calibration, data compression, and image reconstruction.

The second category achieves high-resolution MRI through a novel self-navigation approach for multi-shot Echo-Planar-Imaging (EPI). By treating the notorious shot-to-shot phase fluctuations as a specialized form of nonlinear spatial encoding functions, this thesis enables robust self-navigation across a wide range of multi-shot trajectories. Our technique provides strong resilience to inter-shot physiological signal instability in flexibly designed multi-shot trajectories, shortens total scan time, and fundamentally expands the theoretical scope of self-navigation in MRI.

Behind these technical progresses, one of the key insights is that, signal encoding with nonlinear B0 gradient modulations can follow similar mathematical rules as RF receiver coils in well-established parallel imaging. By formulating linear and nonlinear spatial encoding functions within a reproducing kernel Hilbert space (RKHS) framework – originally developed for parallel imaging – we can treat continuous B0 field modulations and shot-to-shot phase fluctuations similar to the way people treat RF receivers. This perspective inspired several practical techniques: group-kernel auto-calibration, group-patch joint compression and RKHS reconstruction for MRI accelerated by B0 gradient modulations, and overlap-kernel EPI for multi-shot self-navigation. While substantially boosting speed and spatial resolution, these methods achieve unprecedented field calibration robustness and reconstruction speed, inheriting the beauty from parallel imaging methods such as GRAPPA and SENSE-ESPIRiT. Ultimately, nonlinear gradient modulation and multi-shot EPI become mathematically bridged to parallel imaging, where different forms of nonlinear spatial encoding functions provide independent, complementary encoding dimensions.