MRzero –- Automated invention of MRI sequences using supervised learning

Alexander Loktyushin^{1,2}, Kai Herz^{1,3}, Nam Dang^{4}, Felix Glang^{1}, Anagha Deshmane^{1}, Simon Weinmüller^{4}, Arnd Doerfler^{4}, Bernhard Schölkopf^{2}, Klaus Scheffler^{1,3}, and Moritz Zaiss^{1,3}

^{1}Max Planck Institute for Biological Cybernetics, Tübingen, Germany, ^{2}Max Planck Institute for Intelligent Systems, Tübingen, Germany, ^{3}Eberhard Karls University Tübingen, Tübingen, Germany, ^{4}University Clinic Erlangen, Erlangen, Germany

We propose a framework — MRzero — that allows automatic invention of MR sequences. At the core of the framework is a differentiable forward process allowing to simulate image measurement process and reconstruction.

Figure 1: MRzero schematic. Figure a) shows the general MRI pipeline from spin system to reconstructed image. A differentiable MR scanner simulation implements Bloch equations for signal generation. (b): The output of forward process is compared to the target image, analytical derivatives w.r.t. sequence parameters are computed using auto-differentiation, and gradient descent is performed in parameter space to update sequence parameters. (c) Final or intermediate sequences can then be applied at the real scanner using the pulseq framework^{7}.

Figure 2: Learning RF and spatial encoding. Row a: k-space sampling at different iterations, Row b: flip angles over measurement repetitions. Row c: simulation-based reconstruction at different iterations 9, 99, 255, 355, and 1000. row d: phantom measurement, row e: in vivo brain scan. Row f: training error curve. An animated version can be found at: www.tinyurl.com/y4blmpe7. Target sequence: 2D transient gradient- and RF-spoiled GRE, matrix size 96, TR = 25 ms, TE = 3.2 ms, FA=5˚.