Image reconstruction from raw measurements is an inverse problem of fundamental importance in MRI. The basic formulation for such reconstructions involve a k-space sampled uniformly on a Cartesian grid at greater than the Nyquist rate, which is Fourier transformed to generate the desired image. However, this acquisition- reconstruction strategy is often difficult to perform in practical research and clinical settings, as it leads to long scan times, necessitating trade-offs in spatial and temporal resolutions. This observation has led to the development of multiple reconstruction strategies over the last few decades, including partial Fourier imaging, parallel imaging, non-Cartesian acquisitions and compressed sensing, where the reconstruction goes beyond a simple Fourier transform, and often involves careful mathematical modeling of the MR system and images. The aforementioned developments aim to address a continuous need for faster imaging, improved resolutions and robustness, both in clinical and research settings. However, as the existing methods reach the limits of resolution and acceleration achievable in the presence of system and physiological limitations, new reconstruction strategies are needed to improve image quality for various acquisition strategies. In this TRD, we seek to develop new image reconstruction techniques for enabling fast high-resolution acquisitions, improving noise resilience, allowing for different encoding strategies, while increasing robustness to underlying physiological and system variations. Our developments for fast high-resolution imaging include improved strategies for k-space interpolation reconstruction in Cartesian imaging, as well as new self- calibrated techniques for three-dimensional non-Cartesian imaging. For the former, we extend the liner shift- invariant convolutional interpolation approaches for reconstructing multi-coil data in two ways: i) Scan-specific deep learning without training databases for non-linear estimation of missing k-space data, in simultaneous multi-slice, parallel and partial Fourier imaging, ii) Region-specific shift-variant linear kernels for highly- accelerated volumetric parallel imaging. For non-Cartesian acquisitions, our self-calibration is used to estimate radius- and rotation-specific interpolation kernels, without additional ACS data. We also tackle the problem of improving non-Fourier encoded acquisitions, such as spatiotemporal encoding, and devise fast matrix sparsifying approaches to enable regularized reconstructions without high computational burden. To further improve reconstruction fidelity in multi-dimensional acquisitions, we propose the local use of high-order tensor models, along with an information theoretic approach for parameter-free regularization. Finally, we consider imaging in the presence of physiological and system variations, such as motion and B0 inhomogeneities, which are especially pronounced at ultrahigh field strengths, and develop a self-consistency based framework for nonlinear inversion, which utilizes improved initialization from external sensors or sequence elements.
