Design and Analysis of Field-of-View Independent k-Space Trajectories for Magnetic Resonance Imaging

Abstract

This manuscript describes a method of three-dimensional k-space sampling that is based on a generalised form of the previously introduced “Seiffert Spirals,” which exploits the equality between undersampling and the reconstruction of a field of view which is larger than what is represented by the primary sampling density, leading to an imaging approach that does not require any prior commitment to an imaging field of view. The concept of reconstructing arbitrary FOVs based on a low-coherently sampled k-space is demonstrated analytically by simulations of the corresponding point spread functions and by an analysis of the noise power spectrum of undersampled datasets. In-vivo images highlight the feasibility of the presented approach by reconstructing white noise governed images from an undersampled datasets with a smaller encoded FOV. Beneficial properties are especially given by an artefact behaviour, which is widely comparable to the introduction of white noise in the image domain. Furthermore, these aliasing properties provide a promising precondition for the combination with non-linear reconstruction techniques such as Compressed Sensing. All presented results show dominant low-coherent aliasing properties, leading to a noise-like aliasing behaviour, which enables parameterization of the imaging sequence according to a given resolution and scan-time, without the need for FOV considerations.