CIF:Small:Low-rank matrix and tensor methods for higher-dimensional MR image reconstruction

Magnetic resonance imaging (MRI) is an important medical imaging modality widely used clinically to visualize soft-tissue structure and function in the human body. However, acquiring diagnostic quality MR images is a relatively slow process, and shortening MRI scan times is an important goal for reducing motion artifacts, improving clinical efficiency and patient comfort, and reducing cost. The long duration of MRI also forces a tradeoff between image spatial, temporal, and contrast resolution, and there are many potential applications where clinical requirements cannot be met by current protocols. Sparsity-driven reconstruction techniques are being increasingly employed to try and address these needs. However, MRI data commonly has auxiliary non-spatial dimensions (e.g., time, receiver channel), and sparse methods only efficiently exploit intra-dimensional redundancies. Calibration or training procedures are consequently used to identify and incorporate inter-dimensional redundancies into the reconstruction model. This comes at the expense of prolonged scan duration, error propagation, and limited experimental freedom.

This project focuses on the development of a robust, efficient, flexible, and totally calibration- and training-free framework for higher-dimensional MR image reconstruction. It is hypothesized that totally training-free MRI can be achieved by structuring image reconstruction as a low-rank matrix or tensor estimation problem that: 1) actively exploits inter-dimensional redundancies; 2) works complementarily with existing sparsity-based strategies; and 3) naturally generalizes for advanced imaging scenarios like non-Cartesian imaging. The first stage of the research focuses on building the mathematical foundation for this framework. The second stage focuses on practical realization, through development of efficient optimization strategies, high-performance code implementations, and automated parameter selection methodologies. These developments may lead to improved diagnoses, faster scanning, cost reduction, and the enablement of novel clinical MRI applications.