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Magnetic Resonance in Medicine 57:338–352 (2007) Basis Function Cross-Correlations for Robust k-Space Sample Density Compensation, with Application to the Design of Radiofrequency Excitations
BibTeX
@MISC{Mitsouras_magneticresonance,
author = {Dimitris Mitsouras and Robert V. Mulkern and Onur Afacan and Dana H. Brooks and Frank J. Rybicki},
title = {Magnetic Resonance in Medicine 57:338–352 (2007) Basis Function Cross-Correlations for Robust k-Space Sample Density Compensation, with Application to the Design of Radiofrequency Excitations},
year = {}
}
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Abstract
The problem of k-space sample density compensation is restated as the normalization of the independent information that can be expressed by the ensemble of Fourier basis functions corresponding to the trajectory. Specifically, multiple samples (complex exponential functions) may be contributing to each independent information element (independent basis function). Normalization can be accomplished by solving a linear system based on the cross-correlation matrix of the underlying Fourier basis functions. The solution to this system is straightforward and can be obtained without resorting to discretization since the cross-correlations of Fourier basis functions are analytically known. Furthermore, no restrictions are placed on the k-space trajectory and its point-spread function. Additionally, the linear system can be used to elucidate key trade-offs involved in k-space trajectory design. The approach can be used
Keyphrases
robust k-space sample density compensation fourier basis function basis function cross-correlations magnetic resonance radiofrequency excitation linear system independent information independent information element k-space trajectory key trade-off complex exponential function k-space trajectory design k-space sample density compensation independent basis function point-spread function multiple sample cross-correlation matrix
