Mingyan Li^{1}, Feng Liu^{1}, Jin Jin^{1}, Ewald Weber^{1}, and Stuart Crozier^{1}

We have previously developed a practical imaging scheme for the rotating RF coil (RRFC) in Cartesian trajectories. This scheme employs dynamic sensitivity averaging (DSA) of multiple k-spaces during coil rotation, which eliminates the need of time-consuming, position-dependent sensitivity estimation for image reconstruction of the RRFC. As demonstrated in previous work, two extra complementary profiles are required to achieve efficient DSA, thus the scan duration is potentially extended. To further improve the efficiency of DSA, compressed sensing (CS) is implemented to the image reconstruction of the RRFC.

The rotating loop coil has the same geometry as our previously developed RRFC prototype (Ø: 40 mm, 60° open angle, 26 mm in length) designed for a 9.4 T MRI pre-clinical system ^{1}. The electromagnetic simulation software FEKO (Hyperworks, USA) and Matlab (Massachusetts, USA) was used to generate designated rotation-dependent sensitivity profiles and corresponding k-space samples. As demonstrated in ^{6}, by adjusting rotation speed and imaging parameters, k-space lines are encoded with 120° angular increment and three successive k-spaces are able to generate an artefact-free image with DSA. In order to reduce the total scan duration, randomly undersampled (phase-encoding direction) k-space data will be reconstructed by solving constrained optimisation as:

$$\min\left(\lambda_{1}\parallel\psi m\parallel_{1}+\lambda_{2} TV\left(m\right)\right), s.t. \parallel b-Am\parallel_{2}<\epsilon$$

where *Ψ* is sparsity transform realised
by wavelet transform, *b *is the
acquired k-space data, *A* is the
encoding matrix combined with both Fourier and sensitivity encoding, λ_{1}
and λ_{2} are regularization factor for L_{1} and total
variation (TV), respectively. These two weighting factors were optimally chosen
according to the reconstruction quality measured by Peak-SNR (PSNR) and
root-mean-square-error (RMSE). In this work, the optimal weighting factors were
found as λ_{1} = λ_{2} = 0.001. The final images can be
reconstructed in two ways from three undersampled k-spaces: 1) use CS to recover
individual k-spaces which are encoded with different sensitivity profiles and
then apply DSA for the final image recovery; 2) use DSA to combine three
undersampled k-spaces into one k-space which are encoded with uniform
sensitivity and then apply CS reconstruction. These two reconstruction patterns
are referred to as CS - DSA and DSA - CS in Figure 1. The reconstruction is
performed by modifying sparse MRI toolbox ^{7} to incorporate DSA
scheme.

1. Li M, Weber E, Jin J, Hugger T, Tesiram Y, Ullmann P, Junge S, Liu F and Crozier S, Radial MRI using a rotating RF coil at 9.4 T, NMR in Biomedicine, 2017, Accepted

2. Trakic A, Wang H, Weber E, Li B, Poole M, Liu F and Crozier S, Image reconstructions with the rotating RF coil, Journal of Magnetic Resonance, 2009, V201, 186-198

3. Li M, Zuo Z, Jin J, Xue R, Trakic A, Weber E, Liu F and Crozier S, Highly Accelerated Acquisition and Homogeneous Image Reconstruction with Rotating RF Coil Array at 7 T — A Phantom Based Study, Journal of Magnetic Resonance, vol. 240, pp.102-112, 2014.

4. Li M, Jin J, Zuo Z, Liu F, Trakic A, Weber E, Zhuo Z, Xue R, Crozier S, In vivo Sensitivity Estimation and Imaging Acceleration with Rotating RF Coil Arrays at 7 Tesla, Journal of Magnetic Resonance, vol. 252c, 29-40, 2015.

5. Pruessmann K, Weiger M, Scheidegger M, Boesiger P, Peter SENSE: Sensitivity Encoding for Fast MRI, Magnetic Resonance in Medcine, 42:952–962, 1999

6. Li M, Jin J, Weber E, Tesiram Y, Hugger T, Stark S, Junge S, Liu F, and Crozier S, A Practical Imaging Scheme for a Rotating RF Coil (RRFC) at 9.4T by Applying Dynamic Sensitivity Averaging, in proceeding International Society for Magnetic Resonance in Medicine, 23th scientific meeting and exhibition, 2015, Honolulu, USA

7. Lustig M, Donoho D, Santos J, Pauly J, Compressed Sensing MRI, IEEE Signal Processing Magazine, V25, 72-82, 2008

Fig. 1 The reference image is reconstructed from three
k-spaces with DSA. The undersampling patterns (R=3, 4) are shown in the second
row. Reconstructed images of two strategies are shown in third and fourth rows.
The error images are shown in the last row.

Fig. 2 (a) Peak-SNR (PSNR) of reconstructed images with CS -
DSA (blue stars) and DSA - CS (red circles) when R = 3 and 4. (b) Root-mean-square-error (RMSE) of
reconstructed images with CS - DSA (blue stars) and DSA - CS (red circles) when
R = 3 and 4.