Undersampled reconstruction in resting functional magnetic resonance imaging (R-fMRI) holds the potential to enable higher spatial resolution in brain R-fMRI without increasing scan duration. We propose a novel framework to reconstruct k-t undersampled R-fMRI relying on a deep convolutional neural network (CNN) framework that leverages the insight that R-fMRI measurements are in k-space (frequency domain) and explicitly models the Fourier transformation from the frequency domain to the spatial domain. The architecture of our CNN framework comprises a multi-stage scheme that jointly learns two multilayer CNN components for (i)~filling in missing k-space data using acquired data in frequency-temporal neighborhoods and (ii)~image quality enhancement in the spatiotemporal domain. We propose four methods within our framework, including a Bayesian CNN that produces uncertainty maps indicating the per-voxel (and per-timepoint) confidence in the blood oxygenation level dependent (BOLD) time-series reconstruction. Results on brain R-fMRI show that our CNN framework improves over the state of the art, quantitatively and qualitatively, in terms of the connectivity maps for three cerebral functional networks.

Deep neural networks (DNNs) for generative mixture modeling typically rely on unsupervised learning that employs hard clustering schemes, or variational learning with loose / approximate bounds, or under-regularized modeling. We propose a novel statistical framework for a DNN mixture model using a single generative adversarial network. Our learning formulation proposes a novel data-likelihood term relying on a well-regularized / constrained Gaussian mixture model in the latent space along with a prior term on the DNN weights. Our min-max learning increases the data likelihood using a tight variational lower bound using expectation maximization (EM). We leverage our min-max EM learning scheme for semi-supervised learning. Results on three real-world datasets demonstrate the benefits of our compact modeling and learning formulation over the state of the art for mixture modeling and clustering.

Current approaches for semantic image inpainting rely on deep neural networks (DNNs) that learn under full supervision, i.e., using a training set comprising pairs of (i)corrupted images with holes and (ii)corresponding uncorrupted images. However, for several real-world applications, obtaining large sets of uncorrupted images is challenging or infeasible. Current methods also rely on adversarial training involving min-max optimization that is prone to instability during learning. We propose a novel image-inpainting DNN framework that can learn in both completely unsupervised and semi-supervised modes. Moreover, our DNN learning formulation bypasses adversarial training and, thereby, lends itself to more stable training. Results on the publicly available CelebA dataset show that our method, even when learning unsupervisedly, outperforms the state of the art that learns with full supervision.