Speaker
Description
MRI mainly relies on linear gradients for spatial encoding. However, nonlinear spatial encoding functions – such as RF receivers’ sensitivities in parallel imaging, actively produced nonlinear gradient modulations in FRONSAC, or naturally occurred shot-to-shot phase variations in multi-shot EPI – can significantly impact acquisition speed and spatial resolution. Inspired by the reproducing kernel Hilbert space (RKHS) framework used to quantify signal sampling of parallel imaging directly in k-space, we proposed to manage diverse nonlinear spatial encoding functions in a unified mathematical perspective based on RKHS. Under such view, we presented several techniques across two distinct areas to achieve robust, fast, and high-resolution MRI. In one example, we generate nonlinear gradient modulations using an 8-channel local B0 coil array in a 9.4T human scanner. Applying sinusoidal modulations to 8 independent B0 channels during FLASH readout to accelerate sampling, we can now encode, auto-calibrate, compress, and reconstruct such sampled data entirely in k-space – analogous to handling multi-coil data in parallel imaging. Another example is to auto-calibrate the shot-to-shot instability in multi-shot EPI. Specifically, we introduce a small trajectory overlap between shots. By applying a GRAPPA/ESPIRiT type operation to these overlap regions, shot-to-shot phase variation kernels/maps can be extracted, enabling robust self-navigation for various multi-shot trajectories. Ultimately, under this RKHS view, nonlinear gradient modulations, multi-shot EPI, and parallel imaging can be mathematically bridged much more thoroughly. Unifying these physically distinct areas allows them to share the well-established efficiency and robustness of parallel imaging, offering new possibilities for fast and high-resolution MRI.