Abstract：Imaging velocity is a major factor affecting clinical applications of magnetic resonance(MR) imaging. And an effective solution of reducing scanning time is to under-sample in k-space and reconstruct the image from under-sampled MR signals. In this paper, the impact of under-sampling pattern on reconstruction quality is analyzed and a joint optimization strategy is proposed to update the under-sampling pattern with image reconstruction model in the context of deep-learning. To optimize the non-continuous under-sampling pattern, it is firstly initialized with full-sampling pattern. Then, relatively less important phase-encodings are gradually pruned until the sparsity requirement in k-space is satisfied. And the optimization of k-space under-sampling pattern is conducted alternatively with that of the reconstruction model. Moreover, the relative importance is estimated with the weight by assigning weight to each phase-coding. Experiments demonstrate that the proposed method improves the quality of the reconstructed MR image compared with the proposed method.
[1] JACKSON J I, MEYER C H, NISHIMURA D G, et al. Selection of a Convolution Function for Fourier Inversion Using Gridding(Computerised Tomography Application). IEEE Transactions on Medical Imaging, 1991, 10(3): 473-478. [2] FEINBERG D A, HALE J D, WATTS J C, et al. Halving MR Imaging Time by Conjugation: Demonstration at 3.5 kG. Radiology, 1986, 161(2): 527-531. [3] MARSEILLE G J, DE BEER R, FUDERER M, et al. Nonuniform Phase-Encode Distributions for MRI Scan Time Reduction. Journal of Magnetic Resonance(Series B), 1996, 111(1): 70-75. [4] MCGIBNEY G, SMITH M R, NICHOLS S T, et al. Quantitative Evaluation of Several Partial Fourier Reconstruction Algorithms Used in MRI. Magnetic Resonance in Medicine, 1993, 30(1): 51-59. [5] LUSTIG M, DONOHO D L, SANTOS J M, et al. Compressed Sen-sing MRI. IEEE Signal Processing Magazine, 2008, 25(2): 72-82. [6] DONOHO D L. Compressed Sensing. IEEE Transactions on Information Theory, 2006, 52(4): 1289-1306. [7] RAVISHANKAR S, BRESLER Y. MR Image Reconstruction from Highly Undersampled k-Space Data by Dictionary Learning. IEEE Transactions on Medical Imaging, 2011, 30(5): 1028-1041. [8] WANG S S, SU Z H, YING L, et al. Accelerating Magnetic Resonance Imaging via Deep Learning // Proc of the 13th IEEE International Symposium on Biomedical Imaging. Washington, USA: IEEE, 2016: 514-517. [9] LUSTIG M, DONOHO D, PAULY J M. Sparse MRI: The Application of Compressed Sensing for Rapid MR Imaging. Magnetic Resonance in Medicine, 2007, 58(6): 1182-1195. [10] TSAI C M, NISHIMURA D G. Reduced Aliasing Artifacts Using Variable-Density k-Space Sampling Trajectories. Magnetic Resonance in Medicine, 2000, 43(3): 452-458. [11] ZIJLSTRA F, VIERGEVER M A, SEEVINCK P R. Evaluation of Variable Density and Data-Driven k-Space Under-Sampling for Compressed Sensing Magnetic Resonance Imaging. Investigative Radiology, 2016, 51(6): 410-419. [12] LIU D D, LIANG D, LIU X, et al. Under-Sampling Trajectory Design for Compressed Sensing MRI // Proc of the 34th Annual International Conference of the IEEE Engineering in Medicine and Biology Society. Washington, USA: IEEE, 2012: 73-76. [13] LEVINE E, HARGREAVES B. On-the-Fly Adaptive k-Space Sam-pling for Linear MRI Reconstruction Using Moment-Based Spectral Analysis. IEEE Transactions on Medical Imaging, 2018, 37(2): 557-567. [14] HALDAR J P, KIM D. OEDIPUS: An Experiment Design Framework for Sparsity-Constrained MRI. IEEE Transactions on Medical Imaging, 2019, 38(7): 1545-1558. [15] BAHADIR C D, DALCA A V, SABUNCU M R. Learning-Based Optimization of the Under-Sampling Pattern in MRI // Proc of the Conference on Information Processing in Medical Imaging. Berlin, Germany: Springer, 2019: 780-792. [16] ZHANG Z Z, ROMERO A, MUCKLEY M J, et al. Reducing Uncertainty in Undersampled MRI Reconstruction with Active Acquisition // Proc of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. Washington, USA: IEEE, 2019: 2049-2058. [17] JIN K H, UNSER M, YI K M. Self-supervised Deep Active Acce-lerated MRI[J/OL]. [2020-07-25]. https://arxiv.org/pdf/1901.04547.pdf. [18] LIU Z, LI J G, SHEN Z Q, et al. Learning Efficient Convolutional Networks through Network Slimming // Proc of the IEEE International Conference on Computer Vision. Washington, USA: IEEE, 2017: 2755-2763. [19] HU H Y, PENG R, TAI Y W, et al. Network Trimming: A Data-Driven Neuron Pruning Approach towards Efficient Deep Architectures[J/OL]. [2020-07-25]. https://arxiv.org/pdf/1607.03250.pdf. [20] MOLCHANOV P, MALLYA A, TYREE S, et al. Importance Estimation for Neural Network Pruning // Proc of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. Washington, USA: IEEE, 2019: 11264-11272. [21] ZBONTAR J, KNOLL F, SRIRAM A, et al. fastMRI: An Open Dataset and Benchmarks for Accelerated MRI[J/OL]. [2020-07-25]. https://arxiv.org/pdf/1811.08839.pdf. [22] PASZKE A, GROSS S, MASSA F, et al. PyTorch: An Imperative Style, High-Performance Deep Learning Library // WALLACH H, LAROCHELLE H, BEYGELZIMER A, et al., eds. Advances in Neural Information Processing Systems 32. Cambridge, USA: The MIT Press, 2019: 8024-8035. [23] VIRTANEN P, GOMMERS R, OLIPHANT T E, et al. SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods, 2020, 17(3): 261-272.
2021, Vol. 34 
