Unsupervised deep learning with convolutional neural networks for static parallel transmit design: A retrospective study

Abstract

Purpose: To mitigate $B_1^{+}$ inhomogeneity at 7T for multi-channel transmit arrays using unsupervised deep learning with convolutional neural networks (CNNs).

Methods: Deep learning parallel transmit (pTx) pulse design has received attention, but such methods have relied on supervised training and did not use CNNs for multi-channel $B_1^{+}$ maps. In this work, we introduce an alternative approach that facilitates the use of CNNs with multi-channel $B_1^{+}$ maps while performing unsupervised training. The multi-channel $B_1^{+}$ maps are concatenated along the spatial dimension to enable shift-equivariant processing amenable to CNNs. Training is performed in an unsupervised manner using a physics-driven loss function that minimizes the discrepancy of the Bloch simulation with the target magnetization, which eliminates the calculation of reference transmit RF weights. The training database comprises 3824 2D sagittal, multi-channel $B_1^{+}$ maps of the healthy human brain from 143 subjects. $B_1^{+}$ data were acquired at 7T using an 8Tx/32Rx head coil. The proposed method is compared to the unregularized magnitude least-squares (MLS) solution for the target magnetization in static pTx design.

Results: The proposed method outperformed the unregularized MLS solution for RMS error and coefficient-of-variation and had comparable energy consumption. Additionally, the proposed method did not show local phase singularities leading to distinct holes in the resulting magnetization unlike the unregularized MLS solution.

Conclusion: Proposed unsupervised deep learning with CNNs performs better than unregularized MLS in static pTx for speed and robustness.

Keywords: 7 T; RF inhomogeneity mitigation; convolutional neural networks; deep learning; parallel excitation; unsupervised learning.