Design of Non-Cartesian k-space Trajectories for Reduced Scan Time in Magnetic Resonance Imaging Systems
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. To introduce VD in the four-shot setup, a linear chirp is used, instead of a sinusoid. For SFC-based trajectories, VD trajectories using Hilbert, Peano and Morton SFCs are designed under three schemas. These trajectories are compared with the commonly used echo-planar imaging (EPI) trajectory. It is observed that the sinusoids-based trajectories using linear chirps result in a 3 dB improvement in PSNR with 50 % reduction in read-out time and the SFC-based trajectories result in an improvement of 7 dB reconstruction quality with a similar read-out time as the EPI trajectory for a brain analytical phantom image. In the second part, the problem of making the trajectories feasible is considered such that the gradient constraints are satisfied. A generalized framework based on the projec- tion of infeasible trajectories onto the set of feasible trajectories is developed. The biggest advantage of the framework is that it provides a bouquet of methods with tunable param- eters, and the user can choose a trajectory that best suits their purpose of either reducing the read-out time or improving image quality. An existing method in the literature becomes a special case of this framework. Under the framework, traveling salesman prob- lem (TSP)-based and random-like stochastic trajectories are considered. The proposed methods result in shorter read-out times and/or better reconstruction performances as compared to the state-of-the-art methods. In particular, the proposed projection with permutation (PP) method results in a similar reconstruction quality with about 67% reduction in read-out time. In the third part, a greedy approach is discussed to learn a non-Cartesian trajectory for knee MRI images using distance-based rules. The trajectory is constructed such that it results in the highest average improvement in the reconstruction performance on the test images. A stochastic version of the algorithm is proposed to reduce the computational complexity of the greedy algorithm. The learned trajectory is observed to result in a visually better reconstruction with a 0.7 dB improvement than the learned Cartesian- based and TSP-based trajectories with similar read-out times. To summarize, in this thesis, non-Cartesian trajectories have been designed using deterministic, probabilistic and learning-based approaches. The proposed trajectories are observed to perform better than their state-of-the-art counterparts. For low-resolution images, the PP method outperforms the deterministic and other random-like trajectories both in terms of read-out time and reconstruction performance. Among the four-shot trajectories for high resolution brain imaging, the sinusoids-based deterministic trajectory performs better than the probabilistic trajectories with a shorter read-out time. For high resolution knee images, four-shot learned trajectory based on greedy method results in a better image quality for a similar read-out time.