Efficient backward selection ofk-space samples in MRI on a hexagonal grid

Abstract

Certain types of magnetic resonance imaging (MRI) such as magnetic resonance spectroscopic imaging and three-dimensional (3D) MRI require a great deal of time to acquire the image data. The acquisition time can be reduced if the image has a limited region of support, such as when imaging the brain or a cross section of the chest. Hexagonal sampling of the spatial frequency-domain (k-space) yields a 13.4% sampling density reduction compared to rectangular sampling of thek-space for images with a circular region of support (ROS) without incurring spatial aliasing in the reconstructed image. However, certain nonuniform sampling patterns are more efficient than hexagonal sampling for the same ROS. Sequential backward selection (SBS) has been used in previous work to optimize a nonuniform set ofk-space samples selected from a rectangular grid. To reduce the selection time, we present SBS of samples from a hexagonal grid. A Smith normal decomposition is used to transform the nonrectangular 2D discrete Fourier transform to a standard rectangular 2D fast Fourier transform so that the spatial-domain samples are represented directly on a rectangular grid without interpolation. The hexagonal grid allows the SBS algorithm to begin with a smaller set of candidate samples so that fewer samples have to be eliminated. Simulation results show that a significantly reduced selection time can be achieved with the proposed method in comparison with SBS on a rectangular grid.