Magnetic resonance Imaging (MRI) has become the reference neuroimaging technique for probing brain structure and function non-invasively. In particular, anatomical MRI is a gold standard for clinical imaging diagnosis and research, with T1-weighted imaging being the most commonly used sequence. However, the use of this imaging modality is limited by long acquisition times, especially for high resolution anatomical imaging. In this regard, non-Cartesian sampling can accelerate acquisitions through flexible sampling trajectories like SPARKLING, which can efficiently sample k-space and allow efficient and optimal iterative reconstructions with minimal degradation in image quality. In this PhD thesis, the SPARKLING framework which was originally developed for T2*-w imaging will be extended to MPRAGE T1-w imaging, with a goal to accelerate the acquisitions by a factor of 10-15 times, thereby allowing us to reach 1-mm isotropic acquisitions within a minute. Additionally, for extensions of anatomical imaging schemes involving redundant sampling at different inversion times (TI) like MP2RAGE, we propose a novel interleaved under-sampling acquisition and corresponding reconstruction scheme, which minimizes redundancy across different readouts, allowing us to maximally accelerate the acquisition process. In practice, this is achieved through 3D+time extension of the SPARKLING algorithm, that can be combined through the proposed 4D reconstruction scheme. Finally, the thesis will also focus on characterizing the noise profile in k-space for non-Cartesian acquisitions and its effect on the observed resolution in the reconstructed MR images. This will help us build SNR-optimized sampling trajectories, which will be validated against state-of-the-art and clinically utilized protocols (like MP2RAGE) at varying field strengths from 3T to 11.7T. Benchmarking of all the acquisition schemes will be performed through quantitative metrics and also qualitative radiological evaluations, through collaboration of radiologists at NeuroSpin and AP-HP Henri Mondor hospital.