MR image reconstruction using deep density priors

Purpose: MR image reconstruction exploits regularization to compensate for missing k-space data. In this work, we propose to learn the probability distribution of MR image patches with neural networks and use this distribution as prior information constraining images during reconstruction, effectively employing it as regularization. Methods: We use variational autoencoders (VAE) to learn the distribution of MR image patches, which models the high-dimensional distribution by a latent parameter model of lower dimensions in a non-linear fashion. The proposed algorithm uses the learned prior in a Maximum-A-Posteriori estimation formulation. We evaluate the proposed reconstruction method with T1 weighted images and also apply our method on images with white matter lesions. Results: Visual evaluation of the samples showed that the VAE algorithm can approximate the distribution of MR patches well. The proposed reconstruction algorithm using the VAE prior produced high quality reconstructions. The algorithm achieved normalized RMSE, CNR and CN values of 2.77\%, 0.43, 0.11; 4.29\%, 0.43, 0.11, 6.36\%, 0.47, 0.11 and 10.00\%, 0.42, 0.10 for undersampling ratios of 2, 3, 4 and 5, respectively, where it outperformed most of the alternative methods. In the experiments on images with white matter lesions, the method faithfully reconstructed the lesions. Conclusion: We introduced a novel method for MR reconstruction, which takes a new perspective on regularization by using priors learned by neural networks. Results suggest the method compares favorably against the other evaluated methods and can reconstruct lesions as well. Keywords: Reconstruction, MRI, prior probability, MAP estimation, machine learning, variational inference, deep learning