Kalina P Slavkova^{1}, Julie C DiCarlo^{2,3}, Viraj Wadhwa^{4}, Jingfei Ma^{5}, Gaiane M Rauch^{6}, Zijian Zhou^{5}, Thomas E Yankeelov^{2,3,7,8,9}, and Jonathan I Tamir^{2,4,8}

^{1}Department of Physics, The University of Texas at Austin, Austin, TX, United States, ^{2}Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX, United States, ^{3}Livestrong Cancer Institutes, The University of Texas at Austin, Austin, TX, United States, ^{4}Department of Electrical and Computer Engineering, The University of Texas at Austin, Austin, TX, United States, ^{5}Department of Imaging Physics, MD Anderson Cancer Center, Houston, TX, United States, ^{6}Department of Abdominal Imaging, MD Anderson Cancer Center, Houston, TX, United States, ^{7}Department of Biomedical Engineering, The University of Texas at Austin, Austin, TX, United States, ^{8}Department of Diagnostic Medicine, The University of Texas at Austin, Austin, TX, United States, ^{9}Department of Oncology, The University of Texas at Austin, Austin, TX, United States

We evaluate the ability of the ConvDecoder architecture regularized using a physical model to reconstruct under-sampled dynamic MRI data, namely variable-flip angle data as a proof-of-principle. The performance of the reconstruction is evaluated by comparing the normalized error with results returned by compressed sensing and the non-regularized ConvDecoder. We hypothesize that ConvDecoder with physics-based regularization will enable significantly fewer *k*-space measurements, thereby allowing for expedited scan time while maintaining spatial resolution.

$$L=\min_{w}||y-AG(w)||+\lambda ||G(w)-\hat{x}||$$

$$\hat{x}(T_1,\theta)=\max_{T_1}||G(w) ^{\top} D(T_1,\theta)||$$

Here, $$$\hat{x}$$$ is the FSPGR model computed by the inner product of

[1] Wang HZ, Riederer SJ, & Lee JN. Optimizing the precision in T1 relaxation estimation using limited flip angles. *Magn Reson Med*. 1987;5(5):399-416. PMID: 3431401.

[2] Yankeelov TE & Gore JC. Dynamic Contrast Enhanced Magnetic Resonance Imaging in Oncology: Theory, Data Acquisition, Analysis, and Examples. *Curr Med Imaging Review*. 2009;3(2): 91-107.

[3] Sorace AG, Partridge SC, Li X, Virostko J, Barnes SL, Hippe DS, Huang W, & Yankeelov TE. Distinguishing benign and malignant breast tumors: preliminary comparison of kinetic modeling approaches using multi-institutional dynamic contrast-enhanced MRI data from the International Breast MR Consortium 6883 trial. *Journal of Medical Imaging*. 2018;5(1):011019.

[4] Darestani M, & Heckel R. (2020). Can Un-trained Neural Networks Compete with Trained Neural Networks at Image Reconstruction?. *arXiv preprint*. 2020. arXiv:2007.02471.

[5] Van Veen D, Jalal A, Soltanolkotabi M, Price E, Vishwanath S, & Dimakis AG. Compressed sensing with deep image prior and learned regularization. *arXiv preprint*. 2018; arXiv:1806.06438.

[6] Ulyanov D, Vedaldi A, & Lempiitsky V. Deep Image Prior. *arXiv preprint*. 2017; arXiv:1711.10925.

[7] Heckel R & Hand P. Deep Decoder: Concise Image Representations from Untrained Non-convolutional Networks.* arXiv preprint*. 2018; arXiv:1810.03982.

[8] Guo S, Noll DC, Fessler JA. Dictionary-Based Oscillating Steady State fMRI Reconstruction. In: Proc. Intl. Soc. Mag. Reson. Med. 27 (2019); Montreal, CA; Abstract 1253.

[9] BART Toolbox for Computational Magnetic Resonance Imaging, doh: 10.5281/zenodo.592960

[10] Uecker M, Lai P, Murphy MJ, Virtue P, Elad M, Pauly JM, Vasanawala SS, & Lustig M. ESPIRiT--an eigenvalue approach to autocalibrating parallel MRI: where SENSE meets GRAPPA. *Magn Reson Med*. 2014;71(3):990-1001.

[11] Tamir JI, Yu SX, & Lustig M. DeepInPy: Deep Inverse Problems in Python. In: ISMRM Workshop on Data Sampling and Image Reconstruction (2020); Sedona, AZ, USA.

[12] Ma D, Gulani V, Seiberlich N, Liu K, Sunshine JL, Duerk JL, Griswold MA. Magnetic Resonance Fingerprinting. *Nature* 495, no. 7440 (2013). doi:10.1038/nature11971.