Rapid 3D whole-heart cine imaging using golden ratio stack of spirals

The sparsity which is implicit in MR images is exploited to significantly undersample k-space. Some MR images such as angiograms are already sparse in the pixel representation; other, more complicated images have a sparse representation in some transform domain-for example, in terms of spatial finite-differences or their wavelet coefficients. According to the recently developed mathematical theory of compressed-sensing, images with a sparse representation can be recovered from randomly undersampled k-space data, provided an appropriate nonlinear recovery scheme is used. Intuitively, artifacts due to random undersampling add as noise-like interference. In the sparse transform domain the significant coefficients stand out above the interference. A nonlinear thresholding scheme can recover the sparse coefficients, effectively recovering the image itself. In this article, practical incoherent undersampling schemes are developed and analyzed by means of their aliasing interference. Incoherence is introduced by pseudo-random variable-density undersampling of phase-encodes. The reconstruction is performed by minimizing the l(1) norm of a transformed image, subject to data fidelity constraints. Examples demonstrate improved spatial resolution and accelerated acquisition for multislice fast spin-echo brain imaging and 3D contrast enhanced angiography. (c) 2007 Wiley-Liss, Inc.

Parallel imaging allows the reconstruction of images from undersampled multicoil data. The two main approaches are: SENSE, which explicitly uses coil sensitivities, and GRAPPA, which makes use of learned correlations in k-space. The purpose of this work is to clarify their relationship and to develop and evaluate an improved algorithm.

In dynamic magnetic resonance imaging (MRI) studies, the motion kinetics or the contrast variability are often hard to predict, hampering an appropriate choice of the image update rate or the temporal resolution. A constant azimuthal profile spacing (111.246 degrees), based on the Golden Ratio, is investigated as optimal for image reconstruction from an arbitrary number of profiles in radial MRI. The profile order is evaluated and compared with a uniform profile distribution in terms of signal-to-noise ratio (SNR) and artifact level. The favorable characteristics of such a profile order are exemplified in two applications on healthy volunteers. First, an advanced sliding window reconstruction scheme is applied to dynamic cardiac imaging, with a reconstruction window that can be flexibly adjusted according to the extent of cardiac motion that is acceptable. Second, a contrast-enhancing k-space filter is presented that permits reconstructing an arbitrary number of images at arbitrary time points from one raw data set. The filter was utilized to depict the T1-relaxation in the brain after a single inversion prepulse. While a uniform profile distribution with a constant angle increment is optimal for a fixed and predetermined number of profiles, a profile distribution based on the Golden Ratio proved to be an appropriate solution for an arbitrary number of profiles.