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MR image reconstruction using the Chambolle-Pock algorithm
Jing Cheng1, Sen Jia1, Haifeng Wang1, and Dong Liang1

1Shenzhen Institutes of Advanced Technology,Chinese Academy of Sciences, Shenzhen, China

### Synopsis

The combination of Parallel imaging (PI) and compressed sensing (CS) allow high quality MR image reconstruction from partial k-space data. However, most CS-PI MRI methods suffer from detail loss with large acceleration and complicated parameter selection. In this work, we describe and evaluate an efficient and robust algorithm to overcome these limitations. The experimental results on in vivo data show that, the proposed method using a first-order primal-dual algorithm can successfully remove undersampling artifacts while keeping the details with little parameter tuning compared with the existing advanced method.

### INTRODUCTION

CS-based MR image reconstruction is usually considered as an optimization problem which consists of the data consistency and the sparsity constraint1. Thus the final reconstructed image is highly related to the parameters in the optimization problem. In practice, the reconstruction algorithm need to tune many free parameters to have the best diagnostic image quality with the available data. For clinical applications, it is necessary to have a robust algorithm that have no or little parameters to tune. In this work, we describe and evaluate one general algorithm which is insensitive to the sole free parameter to CS-pMRI reconstruction in the TV-minimization framework. The use of this method is illustrated by applying it to in vivo brain data.

### CONCLUSION

In this work, we have described a new method– CP algorithm for TV-based CS-pMRI reconstruction. The CP-based method presented here shows highly efficient reconstruction in terms of both image quality and parameter selection. Using the CP algorithm, other applications could be investigated such as other optimization-based reconstruction formulations with different image representations, objective and constraint designs, or projection models.

### Acknowledgements

This work is supported in part by the National Natural Science Foundation of China under grant nos. 61401449, 61471350 and 61771463.

### References

1. Liang D, Liu B, Wang J, Ying L. Accelerating SENSE using compressed sensing. Magn Reson Med 2009; 62: 1574-1584.

2. Chambolle A, Pock T. A first-order primal-dual algorithm for convex problems with applications to imaging. J. Math. Imag. Vis. 2011; vol. 40:1–26.

3. Rockafellar, RT. Convex analysis. Princeton Univ. Press; 1970.

4. Huang F, Yin W, Lin W, Ye X, Guo W, Reykowski A. A rapid and robust numerical algorithm for sensitivity encoding with sparsity constraints: Self-feeding sparse SENSE. Magn Reson Med 2010; 6(4):1078-1088.

### Figures

Figure 1. Comparison of reconstruction methods for R=4. Both SFSS and CP can reduce the level of aliasing artifacts, whereas the SFSS method shows noiser than CP.

Figure 2. Comparison of reconstruction methods for R=6. The second row are the respective zoom-in images indicated by the red rectangular in the reference image. The CP method contains more features than SFSS, especially at the location indicated by the red arrows.

Figure 3. Reconstructions with different values of λ . The number on the left top of each subfigure is the value of λ. The brain image on the last row is the reference form full data and the plots are the root mean square error (RMSE) and the mean structural similarity index (mSSIM) of the reconstruction versus the values of λ. The CP method has wider range of proper parameter.

Proc. Intl. Soc. Mag. Reson. Med. 26 (2018)
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