Guanxiong Luo^{1}, Moritz Blumenthal^{1}, and Martin Uecker^{1,2}

^{1}Institute for Diagnostic and Interventional Radiology, University Medical Center Göttingen, Germany, Göttingen, Germany, ^{2}Campus Institute Data Science (CIDAS), University of Göttingen, Germany, Göttingen, Germany

The application of deep learning has is a new paradigm for MR image reconstruction. Here, we demonstrate how to incorporate trained neural networks into pipelines using reconstruction operators already provided by the BART toolbox. As a proof of concept, we demonstrate how to incorporate a deep image prior trained via TensorFlow into reconstruction within BART's framework.

The initialization of an exported TensorFlow graph, the restoration of a saved model, and the inference are implemented with TensorFlow's C API whose libraries were downloaded from TensorFlow's official page [6]. The dependencies on CUDA and cuDNN for TensorFlow are satisfied with Conda [7]. The system matrix $$$\mathcal{A}$$$ already existed in BART. FISTA [8] was used to solve Eq (1). The proximal operation on $$$R_{logp}(\boldsymbol{x})$$$ was approximated with gradient update. The learned log-likelihood prior was presented to the user as a regularization option for the reconstruction command. The usage is as follow:

$$\texttt{bart pics -R LP:\{model_path\}:$\lambda$:pct:n <kspace> <sensitivities> <output>}, $$where $$$\texttt{pct}$$$ is the update percentage and the $$$\texttt{n}$$$ specifies how many times the gradient inference runs for every FISTA iteration.

To test the trained prior, we reconstructed the image from simulated radial k-space data and tracked peak signal-to-noise ratio, residual norm, and bits/pixel over iterations following the approach proposed in [5] (cf, Figure 2). At last, the developed pipeline was used to reconstruct an image of a human brain from prospectively sampled radial k-space data (Figure 3).

[1] Uecker M et al., BART Toolbox for Computational Magnetic Resonance Imaging, DOI:10.5281/zenodo.592960

[2] Abadi M et al., TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems

[3] Block KT et al. ”Undersampled radial MRI with multiple coils. Iterative image reconstruction using a total variation constraint.” Magnetic Resonance in Medicine: An Official Journal of the International Society for Magnetic Resonance in Medicine 57.6 (2007):1086-1098.

[4] Michael L et al. ”Compressed sensing MRI.” IEEE signal processing magazine 25.2(2008): 72-82.

[5] Luo G et al., ”MRI reconstruction using deep Bayesian estimation.” Magnetic Resonance in Medicine 84.4 (2020): 2246-2261.

[6] https://www.TensorFlow.org/install/lang_c

[7] Anaconda Software Distribution. (2020). Anaconda Documentation. Anaconda Inc. Retrieved from https://docs.anaconda.com/

[8] Beck A and Teboulle M. ”A fast iterative shrinkage-thresholding algorithm for linear inverse problems.” SIAM journal on imaging sciences 2.1 (2009): 183-202.

[9] Rosenzweig S, Holme HCM, Uecker M. ”Simple auto‐calibrated gradient delay estimation from few spokes using Radial Intersections (RING).” Magnetic resonance in medicine 81.3 (2019): 1898-1906.

[10] Salimans, Tim, et al. "Pixelcnn++: Improving the pixelcnn with discretized logistic mixture likelihood and other modifications." arXiv preprint arXiv:1701.05517 (2017).