Hao Li^{1}, Andrew Nicholas Priest^{1}, Martin John Graves^{1}, and David John Lomas^{1}

In this study, we developed an acceleration technique combining compressed sensing (CS), parallel imaging (PI) and partial Fourier (PF) for the fresh blood imaging (FBI) sequence. Then, we evaluated the influence of the pattern design parameters and explored the optimal values for these parameters. By using the optimised sampling patterns, the FBI acquisition can be accelerated up to 10 times while the image quality is maintained.

**Introduction**

**Method**

Fig. 1 shows a typical acceleration sampling pattern in the phase-encoding dimension for 3D acquisition. The pattern design parameters that were optimised in this study included auto-calibration signal (ACS) region shape/size, PI sampling region shape/size, PI acceleration factor in y and z directions, sigma variance value in the Gaussian probability distribution for CS sampling and the CS acceleration factor.

Fig. 2
shows the image reconstruction process. The Berkeley Advanced Reconstruction
Toolbox (BART)^{3} with ESPIRiT^{4} for PI calibration and l1-wavelet for CS reconstruction
was used to reconstruct the undersampled data. Because angiography images require more
image details to visualise small branch vessels, we chose a small value of
0.005 for the l1 penalty parameter λ in this study.

Images of the lower limb arteries were acquired at 1.5 T (GE Healthcare, Waukesha, WI) using 25 channels of a peripheral vascular coil. The FBI sequence parameters were: TE 60ms, TR 3 RR interval, ETL 90, acquired matrix 224×224×80, FOV 40 cm, slice thickness 2 mm. The optimisation experiments were performed by simulation using the fully sampled data set acquired from a healthy volunteer. The total number of sampling points every pattern was kept constant for each experiment, except in optimisation of the CS acceleration factor. Only one or two parameters were varied in each study to test their influence on the reconstruction quality. Then, the optimised sampling patterns were tested on the FBI lower limb datasets from three healthy volunteers.

The
fully sampled image was used as the reference image. Image quality was assessed
using correlation coefficients (CC) and the normalized mean square error (NMSE)^{5} calculated between the reference image and the
reconstructed image. A semi-automatic method^{6} was also implemented to assess the sharpness of the vessel
edges.

**Results and discussion**

Fig. 3 shows two examples of the parameter optimisation process. The sigma optimisation (Fig.3(A, B)) demonstrates that NMSE, CC and sharpness all achieved the optimal values when sigma equals 0.18, indicating this is the optimal value for the CS sampling density in this study. The PF sampling ratio optimisation (Fig.3(C, D)) demonstrates that sharpness can generally be improved by using a larger PF sampling ratio. However, NMSE increases and CC decreases dramatically with increasing PF sampling ratio, especially for ratios larger than 0.4. One reason for this conflict may be that (for constant sample number) a larger PF sampling ratio allows more high-frequency components, increasing the sharpness but the corresponding reduction of central k-space sampling reduces the reconstruction accuracy. Taking both factors into account, the range from 0.35-0.42 was considered the optimal PF sampling ratio. Table 1 summarises all the optimal value ranges and suggested values for the parameters in sampling pattern design in this study.

Sampling patterns with different overall acceleration factors can be designed using the optimal value ranges. We evaluated the performance of different sampling patterns with overall acceleration factors from 5 to 20 (Fig. 4(A)) on the data from three healthy volunteers. Fig. 4(B) shows a local region of right femoral arteries selected from the MIPs of one reconstructed image set with different overall acceleration factors. It can be observed that the image quality is similar to that of the fully sampled image when the acceleration factor is less than 10. When the factor is larger than 10, the MIP image demonstrates some edge blurring and loss of detail. This conclusion is consistent with the quantitative results shown in Fig. 4(C). The NMSE begins to increase and CC and sharpness begin to decrease rapidly when the overall acceleration factor is larger than 10. Therefore, it is suggested to choose an overall acceleration factor of less than 10.

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Fig. 1 A typical acceleration sampling
pattern combining PI, CS and PF.

Fig. 2 Flow chart of the entire image reconstruction process in 3D PF-PICS. The centre of k-space is used for computing the eigenvalue map in the PI reconstruction based on ESPIRiT. CS reconstruction with l1-norm in the wavelet domain is applied to restore the missing samples. The symmetric part of k-space is used for the phase correction in PF reconstruction.

Fig 3. Two examples of the parameter optimisation process A: Sampling patterns with varying sigma values. B: NMSE, CC and sharpness measured in patterns with different sigma values. C: Sampling patterns with varying PF sampling ratios. D: NMSE, CC and sharpness measured in images using the patterns with different PF sampling ratios. The red regions in B and D refer to the suggested value range. All of the patterns have the same number of sampling points.

Table 1. The optimal value ranges and
suggested values for the sampling pattern design (matrix size: 224×224×80).

Fig. 4 Performance of sampling
patterns with different overall acceleration factors. A: The sampling patterns with
overall acceleration factors from 5 to 20. B: Selected regions from the MIPs of the corresponding
reconstructed images. C: Quantitative results on three healthy volunteers. The red regions refer to the suggested acceleration factor range.