Madison Kretzler^{1}, Jesse Hamilton^{2}, Mark Griswold^{2,3}, and Nicole Seiberlich^{2,3}

^{1}Electrical Engineering, Case Western Reserve University, Cleveland, OH, United States, ^{2}Biomedical Engineering, Case Western Reserve University, Cleveland, OH, United States, ^{3}Radiology, University Hospitals, Cleveland, OH, United States

### Synopsis

**This abstract presents a-f
BLAST, a non-iterative approach to non-Cartesian k-t BLAST for radial
trajectories, and demonstrates its use for accelerated cardiac imaging.**### Purpose

k-t
BLAST

^{1} is a technique that works in the spatiotemporal
frequency domain (x-f space) to resolve aliasing caused by lattice undersampling of the k-t
space. Due to the strategic k-t sampling
pattern, aliasing patterns in the in the x-f space are predictable and can be
resolved using additional information from a training dataset. Previous methods
for extending the concepts of k-t BLAST to non-Cartesian trajectories focused
on solving the general inversion problem using an iterative conjugate gradient
(CG) method

^{2}, but this approach can be time-consuming and
does not take advantage of the symmetry inherent in some commonly-used
trajectories. This method presents a
non-iterative extension of Cartesian k-t BLAST to dynamic radial imaging by
using the radial symmetry of the data to simplify the reconstruction problem.

### Methods

In Cartesian k-t BLAST the k-space is undersampled in an
interleaved fashion, which produces an offset aliasing pattern in the x-f space. Unlike Cartesian data, radially sampled data
does not produce an aliased image with the clear aliasing artifacts required
for k-t BLAST. However, the Radon
transform of the underlying image can be generated by performing a Fourier
transform only along the read-out direction; a subsequent Fourier transform
along the projection direction will result in aliasing artifacts that are
similar to those seen in Cartesian k-t BLAST. We refer to this domain as the
“aliased space,” as shown in Figure 1. This space can then be Fourier
transformed through time to obtain a type of x-f space, which we call the a-f
space, where the necessary offset aliasing is present to perform the k-t BLAST
reconstruction. Low-resolution training data can be obtained from the center of
k-space of the undersampled radial data. After the k-t BLAST reconstruction in
a-f space, the reconstructed data are transformed back into radial k-space, and
then gridded using the NUFFT

^{3}. This technique was first applied
to in-vivo cardiac breathheld cine scans
downsampled to mimic different acceleration factors. These data
were collected along an interleaved radial trajectory on a Siemens Skyra 3T
whole-body scanner with a bSSFP sequence using TR = 29 ms, TE = 1.5ms, BW = 1
kHz, FoV = 300mm, spatial resolution = 2.3x2.3x8.0 mm

^{3}, flip-angle =
57 degrees. Matrix dimensions were 128x128 with 144 fully sampled projections
for the cine and 144/R for the accelerated scans. The fully-sampled cine images
were used to calculate RMSE values for the reconstructed image series. Additionally, a-f BLAST was applied to
prospectively accelerated real-time radial scans with R=4 and the same scan
parameters as the cine dataset with the following exceptions: TR=2.94ms, flip angle=37 degrees.

### Results

Figure 2 shows that a-f BLAST reduces the radial artifacts
from a retrospectively undersampled cine dataset with R=4 without compromising
the temporal resolution in the x-t images. Figure 3 shows the RMSE values for reconstructions
of varying acceleration factors. It can be seen for increasing accelerations RMSE
values steadily increase and image quality deteriorates. Figure 4 shows the
performance of a-f BLAST for prospectively accelerated R=4 radial data. Figure 5 is a gif showing the same dataset as
Figure 4 in an animated form.

### Discussion/Conclusion

a-f BLAST, or non-iterative non-Cartesian k-t BLAST
performed in Radon space, may enable a significantly faster reconstruction of
radially undersampled images by removing the gridding/degridding steps required
in non-Cartesian k-t BLAST.

^{2} The a-f BLAST approach does not require a
separate training dataset, as the center of k-space can be used as the
low-resolution training data. However, the two techniques have not been
compared for speed or performance, which depends on the relative sparsity of
the data in each of the domains (a-f vs. x-f). a-f BLAST also presents a new
space which can be used to rapidly reconstruct undersampled radial data, which
may be advantageous for other reconstruction techniques, including non-Cartesian parallel imaging and
compressed sensing.

### Acknowledgements

No acknowledgement found.### References

1. Tsao, J., Boesiger, P. &
Pruessmann, K. P. k-t BLAST and k-t SENSE: Dynamic MRI With High Frame Rate
Exploiting Spatiotemporal Correlations. Magn. Reson. Med. 50,
1031–1042 (2003).

2. Hansen, M. S. et al. k-t BLAST
reconstruction from non-Cartesian k-t space sampling. Magn. Reson. Med. 55,
85–91 (2006).

3. Fessler, J. A. & Sutton, B. P.
Nonuniform fast fourier transforms using min-max interpolation. IEEE Trans.
Signal Process. 51, 560–574 (2003).