title: Fast, exact k-space sample density compensation for trajectories composed of rotationally symmetric segments, and the SNR-optimized image reconstruction from non-Cartesian samples.
abstract: A recently developed method for exact density compensation of non uniformly arranged samples relies on the analytically known cross-correlations of Fourier basis functions corresponding to the traced k-space trajectory. This method produces a linear system whose solution represents compensated samples that normalize the contribution of each independent element of information that can be expressed by the underlying trajectory. Unfortunately, linear system-based density compensation approaches quickly become computationally demanding with increasing number of samples (i.e., image resolution). Here, it is shown that when a trajectory is composed of rotationally symmetric interleaves, such as spiral and PROPELLER trajectories, this cross-correlations method leads to a highly simplified system of equations. Specifically, it is shown that the system matrix is circulant block-Toeplitz so that the linear system is easily block-diagonalized. The method is described and demonstrated for 32-way interleaved spiral trajectories designed for 256 image matrices; samples are compensated non iteratively in a few seconds by solving the small independent block-diagonalized linear systems in parallel. Because the method is exact and considers all the interactions between all acquired samples, up to a 10% reduction in reconstruction error concurrently with an up to 30% increase in signal to noise ratio are achieved compared to standard density compensation methods.
authors.affiliation: Cardiovascular Imaging Section, Department of Radiology, Brigham and Women's Hospital, Boston, Massachusetts, USA. dmit-souras@alum.mit.edu
authors.forename: Dimitris
authors.initials: D
authors.lastname: Mitsouras
authors.forename: Robert V
authors.initials: RV
authors.lastname: Mulkern
authors.forename: Frank J
authors.initials: FJ
authors.lastname: Rybicki
mesh_terms: D000465:Algorithms; D016477:Artifacts; D001921:Brain / Q000033:anatomy & histology*; D016000:Cluster Analysis; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D008279:Magnetic Resonance Imaging / Q000379:methods*; D019047:Phantoms, Imaging; D015203:Reproducibility of Results; D012399:Rotation; D012680:Sensitivity and Specificity