Combining Computational Techniques With Physics for Applications in Accelerated MRI

Abstract

Magnetic Resonance Imaging (MRI) non-invasively measures high-resolution images of soft tissue contrast in human anatomy without any ionizing radiation or injection of contrast agent. However, MRI incurs large costs to patients and researchers due to expensive equipment and slow imaging times. Significant research effort in the MRI field aims to reduce costs by developing techniques that increase information per unit time acquired by the scanner. This thesis presents methods that combine our knowledge of MRI physics with modern computational techniques to design algorithms that improve acquisition efficiency.

We first propose SPARK, a machine learning method for reconstructing images from accelerated structural MRI acquisitions trained from just a single scan. Spark exploits calibration regions to train neural networks that correct a physics based input reconstruction, improving performance at smaller calibration sizes and synergizing with a wide range of techniques. We next introduce Latent Signal Models for time-resolved MRI reconstruction. Latent Signal Models trains neural-networks to approximate the Bloch equations, and inserts the models directly into the MRI reconstruction problem. This enables fast optimization through a proxy for the Bloch equations and yields fewer degrees of freedom than linear models. Third, we explore cramer-rao-bound optimization of sequences for quantitative MR parameter mapping. Auto-differentiation through simulations computes necessary gradients for optimization. Finally, we propose an optimization scheme that designs radio-frequency pulse amplitudes for reduced heating in Fetal MRI, while maintaining signal-to-noise and contrast-to-noise ratios.