Marco Barbieri^{1,2}, Philip K. Lee^{3}, Leonardo Brizi^{1}, Enrico Giampieri^{1}, Alexander R. Toews^{3}, Gastone Castellani^{4}, Daniel Remondini^{4}, Brian A. Hargreaves^{5,6,7}, and Claudia Testa^{8,9}

Dictionary size limits the number of parameters one can aim to estimate with Magnetic Resonance Fingerprinting (MRF) Deep Neural networks (NN) have been recently proposed for MRF applications, both with numerical simulationsand with phantoms and in-vivo acquisitions. With real-valued NNs only the magnitude of the MRF signal has been considered as input. This choice releases from the need of considering the phase of the signal during training but can affect noise robustness and signal differentiation due to loss of information. In this work we propose a strategy to train a real valued NN that takes the real and imaginary parts of an MRF-FISP signal as input. We also propose to use SVD as preprocessing step for noise reduction. The presented results may help the developing of deep learning approaches for MRF, pushing fingerprinting pulse sequences design to add more meaningful MR parameters, such as diffusion, with no more limitations due to the dictionary size.

**Methods**

**Results**

**Discussion**

**Conclusion**

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[3] E. Hoppe, G. K¨orzd¨orfer, T. W¨urfl, J. Wetzl, F. Lugauer, J. Pfeuffer, A. K. Maier, Deep learning for magnetic resonance fingerprinting: A new approach for predicting quantitative parameter values from time series, Studies in health technology and informatics 243 (2017) 202–206.

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[6] D. F. McGivney, E. Pierre, D. Ma, Y. Jiang, H. Saybasili, V. Gulani, M. A. Griswold, Svd compression for magnetic resonance fingerprinting in the time domain, IEEE Trans. Med. Imaging 33 (12) (Dec. 2014) 2311–2322.

[7] Y. Jiang, D. Ma, N. Seiberlich, V. Gulani, M. A. Griswold, Mr fingerprinting using fast imaging with steady state precession (fisp) with spiral readout, Magn. Reson. Med. 74 (6) (2014) 1621–1631. doi:10.1002/mrm.25559.

Pipeline used to train the NN. The simulated MRF signals have θ0 = -π. Phase augmentation and complex white gaussian noise adding can be used for data augmentation. The data augmentation step aims to make the NN robust to real world effect, such as noise and phase offsets in this case. The preprocessing step is thought to be applied also to real world data. It has a noise reduction step (SVD compression in time domain) and a normalization step.

Examples of phase evaluation for the fully (top box) and undersampled (bottom box) scans.
In the left box the phase of images for four TRs is presented and they were computed using the equation in the bottom. In right box the phase of the image considering the average signal over time (see equation in the bottom).

The left box shows examples of raw reconstructed images for four TRs. In the right box The Fourier spectrum of the signal evolution considering all the image is showed, which reveals that the undersampling creates noise peaked on specific frequencies instead of being white. Since white Gaussian noise is usually used to promote noise robustness the NN may not be properly trained for this type of noise.

Dictionary matching against NN prediction in case of fully sample IR-FISP acquisition. (a) and (b) show T1 and T2 dictionary matching reconstruction (T1 = [10:10:4000] ms, T2 = [5:5:1200, 1210:10:3000] ms). (c) and (d) shows T1 and T2 predictions of a NN using a 2 channels input trained with phase augmentation and without SVD preprocessing (e) and (f) show the T1 and T2 APE maps, where metrics follow the legend. (g), (h), (i), and (l) show the same quantities for a NN trained without the phase augmentation step. Accuracy decreases in regions where phase is different from the ideal case.

Dictionary matching against NN prediction in case of undersampled IR-FISP acquisition. (a) and (b) show T1 and T2 dictionary matching reconstruction (c) and (d) shows T1 and T2 predictions of a NN using a 2 channels input trained with phase augmentation and SVD preprocessing with (i) and (l) showing the T1 and T2 APE maps. (e) and (f) show the APE maps for NN trained with phase augmentation and without SVD. (g), and (h) show the APE maps for NN trained with phase augmentation, with SVD but the magnitude of the signal is given as input.