Streaking artifact suppression of quantitative susceptibility mapping reconstructions via L1-norm data fidelity optimization (L1-QSM)

Purpose: The presence of dipole-inconsistent data due to substantial noise or artifacts causes streaking artifacts in quantitative susceptibility mapping (QSM) reconstructions. Often used Bayesian approaches rely on regularizers, which in turn yield reduced sharpness. To overcome this problem, we present a novel L1-norm data fidelity approach that is robust with respect to outliers, and therefore prevents streaking artifacts. Methods: QSM functionals are solved with linear and nonlinear L1-norm data fidelity terms using functional augmentation, and are compared with equivalent L2-norm methods. Algorithms were tested on synthetic data, with phase inconsistencies added to mimic lesions, QSM Challenge 2.0 data, and in vivo brain images with hemorrhages. Results: The nonlinear L1-norm-based approach achieved the best overall error metric scores and better streaking artifact suppression. Notably, L1-norm methods could reconstruct QSM images without using a brain mask, with similar regularization weights for different data fidelity weighting or masking setups. Conclusion: The proposed L1-approach provides a robust method to prevent streaking artifacts generated by dipole-inconsistent data, renders brain mask calculation unessential, and opens novel challenging clinical applications such asassessing brain hemorrhages and cortical layers

Structured low-rank methods for robust 3D multi-shot EPI

Magnetic resonance imaging (MRI) has inherently slow acquisition speed, and Echo-Planar Imaging (EPI), as an efficient acquisition scheme, has been widely used in functional magnetic resonance imaging (fMRI) where an image series with high temporal resolution is needed to measure neuronal activity. Recently, 3D multi-shot EPI which samples data from an entire 3D volume with repeated shots has been drawing growing interest for fMRI with its high isotropic spatial resolution, particularly at ultra-high fields. However, compared to single-shot EPI, multi-shot EPI is sensitive to any inter-shot instabilities, e.g., subject movement and even physiologically induced field fluctuations. These inter-shot inconsistencies can greatly negate the theoretical benefits of 3D multi-shot EPI over conventional 2D multi-slice acquisitions. Structured low-rank image reconstruction which regularises under-sampled image reconstruction by exploiting the linear dependencies in MRI data has been successfully demonstrated in a variety of applications. In this thesis, a structured low-rank reconstruction method is optimised for 3D multi-shot EPI imaging together with a dedicated sampling pattern termed seg-CAIPI, in order to enhance the robustness to physiological fluctuations and improve the temporal stability of 3D multi-shot EPI for fMRI at 7T. Moreover, a motion compensated structured low-rank reconstruction framework is also presented for robust 3D multi-shot EPI which further takes into account inter-shot instabilities due to bulk motion. Lastly, this thesis also investigates into the improvement of structured low-rank reconstruction from an algorithmic perspective and presents the locally structured low-rank reconstruction scheme