Eibert, "A diagonalized multilevel fast multipole method with spherical harmonics expansion of the

k-space integrals," IEEE Transactions on Antennas and Propagation, vol.

The term [[gamma].sup.[mu]][[phi].sub.(n,k,x)][[gamma].sup.v][[phi].sub.(n,k,x)] refers to the normalized information flux density passing through an elementary surface d[k.sup.[mu]]d[k.sup.v] in

K-space. The gradient of the flux density yields the baseband bandwidth [k.sub.(n)[mu]].

In the first step, free breathing cardiac phases without motion estimation are recovered from undersampled

k-space data.

This condition not only enforces restrictions on the choice of

k-space trajectories sampling the entire IR but also renders imagespace methods unlikely to fully exploit the inherent redundancy in the data (i.e., about 1000 radial spokes for a 4s acquisition).

The effects of time varying intravascular signal intensity and

k-space acquisition order on three-dimensional MR angiography image quality.

As this work is supposed to be a proof of concept, we favored simulating motion artefacts in

k-space rather than simulating a motion-corrupted raw MRI signal using tools such as the Physics-Oriented Simulated Scanner for Understanding MRI (POSSUM) [8].

GRAPPA is a widely used

k-space based pMRI technique [7].

However, the MRI data sampled in the spatial Fourier transform or

K-space of an object are acquired sequentially in time.

A sequence space X with a linear topology is called a

K-space if each of the projection maps [P.sub.i]: X [right arrow] C defined by [P.sub.i](x) = x(i) for x = [(x(i)).sup.[infinity].sub.i=1] [member of] X is continuous for each natural i.

Integrations over the bands in

k-space are quite challenging.

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The acquired data corresponds to the Fourier transform of the image, A([k.sub.x], [k.sub.y]), also called the

k-space data.