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Compressed Sensing MRI Revisited: Optimizing $$$\ell_{1}$$$-Wavelet Reconstruction with Modern Data Science Tools
Hongyi Gu1,2, Burhaneddin Yaman2,3, Kamil Ugurbil2, Steen Moeller2, and Mehmet Akcakaya2,3
1Electrical Engineering, University of Minnesota, Minneapolis, MN, United States, 2Center for magnetic resonance research, Minneapolis, MN, United States, 3University of Minnesota, Minneapolis, MN, United States
An optimized l1-wavelet compressed sensing method achieves comparable reconstruction quality to physics-guided deep learning, while using much fewer parameters and a linear representation amenable to interpretation. 
Figure 1. Schematic of the unrolled ADMM for $$$\ell_{1}$$$-wavelet compressed sensing (CS). One unrolled iteration of ADMM with $$$\ell_{1}$$$-wavelet regularizers consists of regularizer (R), data consistency (DC) and dual update (DWT: Discrete wavelet transform). For T = 10 iterations, this leads to a total of 116 trainable parameters, as dual update is not needed for the last iteration.
Figure 3. Two representative slices from coronal PD–FS knee MRI, reconstructed using CG-SENSE, PG-DL, and the optimized -wavelet CS. CG-SENSE is visibly outperformed by PG-DL and -wavelet CS. Both PG-DL and the optimized -wavelet CS show comparable image quality and quantitative metrics.