Fast, exact k‐space sample density compensation for trajectories composed of rotationally symmetric segments, and the SNR‐optimized image reconstruction from non‐Cartesian samples
Year: 2008
Type: article
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.
Source: Magnetic Resonance in Medicine
DOI: 10.1002/mrm.21597
Language: English
Subfield: Radiology, Nuclear Medicine and Imaging
Field: Medicine
Domain: Health Sciences
Open Access status: bronze
OpenAlex ID: W2012204000