a-f BLAST: A Non-Iterative Radial k-t BLAST Reconstruction in Radon Space
Madison Kretzler1, Jesse Hamilton2, Mark Griswold2,3, and Nicole Seiberlich2,3

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


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.


k-t BLAST1 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) method2, 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.


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 mm3, 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.


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.


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.


No acknowledgement found.


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).


Figure 1: Undersampled interleaved radial data (far left) can be transformed into a space that has an appearance similar to undersampled Cartesian data in x-f space (far right) by performing Fourier transforms along each dimension without gridding. The aliasing in this a-f space can be resolved with a k-t BLAST reconstruction, followed by gridding of the radial data to generate an image.

Figure 2: An example of a-f BLAST, showing (top) the fully-sampled in-vivo cardiac cine, R=4 Nyquist-sampled, R=4 zero-filled, and R=4 reconstructed images, and x-t images of single heartbeat for each (bottom).

Figure 3: a-f BLAST reconstructions of the same retrospectively undersampled radial cine data as Figure 2 and their RMSE values with varying acceleration factors.

Figure 4: a-f BLAST performed on prospectively accelerated cardiac images with a temporal resolution of 105.84ms and R = 4 for frames in diastole (top), systole (center), and the x-t space (bottom).

Figure 5: Gif of the R=4 a-f BLAST reconstructions from Figure 4 showing zero-filled, Nyquist-sampled, and a-f BLAST images (from left to right).

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)