Hongyi Gu^{1,2}, Burhaneddin Yaman^{1,2}, Steen Moeller^{2}, Il Yong Chun^{3}, and Mehmet Akçakaya^{1,2}

^{1}Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN, United States, ^{2}Center for Magnetic Resonance Research, University of Minnesota, Minneapolis, MN, United States, ^{3}Electrical and Computer Engineering, University of Hawai’i at Mānoa, Honolulu, HI, United States

Research shows that deep learning (DL) based MRI reconstruction outperform conventional methods, such as parallel imaging and compressed sensing (CS). Unlike CS with pre-determined linear representations for regularization, DL uses nonlinear representations learned from a large database. Transform learning (TL) is another line of work bridging the gap between these two approaches. In this work, we combine ideas from CS, TL and DL to learn deep linear convolutional transforms, which has comparable performance to DL and supports uniform under-sampling unlike CS, while enabling sparse convex optimization at inference time.

$$\arg \min _{\mathbf{x}} \frac{1}{2}\|\mathbf{y}-\mathbf{E x}\|_{2}^{2}+\mathcal{R}(\mathbf{x})\tag{1}$$

where $$$\mathbf{y}$$$ is multi-coil k-space, $$$\mathbf{E}$$$ is forward multi-coil encoding operator

For the proposed DLC-TL, we used $$$N$$$ = 6 linear transforms and $$$T$$$ = 10 unrolls.

1.Pruessmann K P, Weiger M, Bornert P, Boesiger P. Advances in sensitivity encoding with arbitrary k-space trajectories. Magn Reson Med. 2001;46(4):638-651.

2.Lustig M, Donoho D, Pauly J. Sparse MRI: The application of compressed sensing for rapid MR imaging. Magn Reson Med. 2007;58(6):1182-1195.

3.Knoll F, Hammernik K, Zhang C, et al. Deep-learning methods for parallel magnetic resonance imaging reconstruction. IEEE Sig Proc Mag. 2020;37(1):128-140.

4.Liang D, Cheng J, Ke Z, Ying L. Deep magnetic resonance image reconstruction: inverse problems meet neural networks. IEEE Sig Proc Mag. 2020;37(1):141-151.

5.Wen B, Ravishankar S, Pfister L, Bresler Y. Transform learning for magnetic resonance image reconstruction: From model-based learning to building neural networks. IEEE Sig Proc Mag. 2020;37(1):41-53.

6.Ye J C. Compressed sensing MRI: a review from signal processing perspective. BMC Biomed Eng. 2019;1:8.

7.Ramzi Z, Starck J, Moreau T, Ciuciu P. Wavelets in the deep learning era. in Proc. IEEE EUSIPCO. 2021;1417-1421.

8.Gu H, Yaman B, Uğurbil K, et al. Compressed sensing MRI with $$$\ell_1$$$-wavelet reconstruction revisited using modern data science tools. in Proc. IEEE EMBC. 2021.

9.Chun I Y, Fessler J A. Convolutional analysis operator learning: Acceleration and convergence. IEEE Trans Image Process. 2020;29:2108-2122.

10.Saxe A M, McClelland J L, Ganguli S. Exact solutions to the nonlinear dynamics of learning in deep linear neural networks. arXiv preprint. 2014;arXiv:1312.6120.

11.Choromanska A, Henaff M, Mathieu M, et al. The loss surfaces of multilayer networks. J Magn Reason. 2015;38:192-204.

12.Bell-Kligler S, Shocher A, Irani M. Blind super-resolution kernel estimation using an internal-GAN. in Proc. NeurIPS. 2019.

13.Aggarwal H K, Mani M P, Jacob M. MoDL: Model-based deep learning architecture for inverse problems. IEEE Trans Med Imaging. 2019;38(2):394-405.

14.Knoll F, Zbontar J, Sriram A, et al. fastMRI: A publicly avail-able raw k-space and DICOM dataset of knee images for accelerated MR image reconstruction using machine learning. Radiol AI. 2020;2(1):e190007.

15.Hosseini S A H, Yaman B, Moeller S, et al. Dense recurrent neural networks for accelerated MRI: History-cognizant unrolling of optimization algorithms. IEEE J Sel Top Signal Process. 2020;14(6):1280-1291.

16.Yaman B, Hosseini S A H, Moeller S, Ellermann J, Uğurbil K, Akçakaya M. Self-supervised learning of physics-guided reconstruction neural networks without fully sampled reference data. Magn Reson Med. 2020;84:3172-3191.

DOI: https://doi.org/10.58530/2022/3452