Robust partial Fourier reconstruction for diffusion-weighted imaging using a recurrent convolutional neural network

Purpose: To develop an algorithm for robust partial Fourier (PF) reconstruction applicable to diffusion-weighted (DW) images with non-smooth phase variations. Methods: Based on an unrolled proximal splitting algorithm, a neural network architecture is derived which alternates between data consistency operations and regularization implemented by recurrent convolutions. In order to exploit correlations, multiple repetitions of the same slice are jointly reconstructed under consideration of permutation-equivariance. The algorithm is trained on DW liver data of 60 volunteers and evaluated on retrospectively and prospectively sub-sampled data of different anatomies and resolutions. Results: The proposed method is able to significantly outperform conventional PF techniques on retrospectively sub-sampled data in terms of quantitative measures as well as perceptual image quality. In this context, joint reconstruction of repetitions as well as the particular type of recurrent network unrolling are found to be beneficial with respect to reconstruction quality. On prospectively PF-sampled data, the proposed method enables DW imaging with higher signal without sacrificing image resolution or introducing additional artifacts. Alternatively, it can be used to counter the TE increase in acquisitions with higher resolution. Further, generalizability can be shown to prospective brain data exhibiting anatomies and contrasts not present in the training set. Conclusion: This work demonstrates that robust PF reconstruction of DW data is feasible even at strong PF factors in anatomies prone to phase variations. Since the proposed method does not rely on smoothness priors of the phase but uses learned recurrent convolutions instead, artifacts of conventional PF methods can be avoided.