A variable-density k-space sampling method is proposed to reduce aliasing artifacts in MR images. Because most of the energy of an image is concentrated around the k-space center, aliasing artifacts will contain mostly low-frequency components if the k-space is uniformly undersampled. On the other hand, because the outer k-space region contains little energy, undersampling that region will not contribute severe aliasing artifacts. Therefore, a variable-density trajectory may sufficiently sample the central k-space region to reduce low-frequency aliasing artifacts and may undersample the outer k-space region to reduce scan time and to increase resolution. In this paper, the variable-density sampling method was implemented for both spiral imaging and twodimensional Fourier transform (2DFT) imaging. Simulations, phantom images and in vivo cardiac images show that this method can significantly reduce the total energy of aliasing artifacts. In general, this method can be applied to all types of k-space sampling trajectories. Magn Reson Med 43: 452-458, 2000.

A new spiral imaging technique incorporates the acquisition of a field map into imaging interleaves. Variable density spiral trajectories are designed to oversample the central region of k‐space, and interleaves are acquired at two different echo times. A field map is extracted from this data and multifrequency reconstruction is used to form an off‐resonance corrected image using the entire dataset. Simulation, phantom, and in vivo results indicate that this technique can be used to achieve higher image and/or field map spatial resolution compared to conventional techniques. Magn Reson Med 45:521–524, 2001. © 2001 Wiley‐Liss, Inc.

Absfruct-Exact formulas to compute the switching activities of the invert line and each bus line for both even and odd bus widths are presented. This enables us to understand the finite and asymptotic behaviors of the bus-invert coding process. It is found that the previous published theoretical results form only a subset of our contributions.

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