Design of Non Cartesian k space Trajectories for Reduced Scan Time in Magnetic Resonance Imaging Systems

Abstract

Magnetic resonance imaging (MRI) is a non-invasive and safe medical imaging technique. This imaging modality collects samples in the Fourier domain, called as the k-space. The k-space is traversed along continuous trajectories using varying magnetic gradients. Scan times in MRI are generally limited by either signal-to-noise ratio (SNR) or the gradient amplitude and slew rate. SNR limitations are met by advances in higher-field systems as well as improved design for receive coils. Further hardware improvements in gradient sys- tem switching times enable rapid imaging with higher resolution. The k-space is usually traversed in multiple shots, especially for higher resolution images. Scan time reduction in MRI is important to improve patient comfort, reduce image artifacts related to motion, improve dynamic imaging. With the development of the theory of compressed sensing and recent advances in deep learning-based image reconstruction methods, it is possible to reconstruct MRI images with an undersampled k-space data. For practical implemen- tation of compressed sensing in MRI, a variable density (VD) sampling is utilized. In the recent years, many methods have been proposed to undersample Cartesian trajectory to reduce scan time, however, the non-Cartesian trajectories have been observed to be more advantageous in terms of better utilization of gradients and benign artifacts. In this the- sis, we focus on the design non-Cartesian k-space trajectories that result in a good image reconstruction with shorter read-out times. PSNR and SSIM are used as metrics to com- pare image reconstruction quality and the sensitivity of the trajectories to system-related effects such as off-resonance and gradient imperfection are also studied. In the first part of the thesis, two types of deterministic trajectories based on sinusoids and space-filling curves (SFCs) are designed. For sinusoids-based trajectories, sinusoidal curves are used to traverse the k-space...