Recent medical image reconstruction techniques focus on generating high-quality medical images suitable for clinical use at the lowest possible cost and with the fewest possible adverse effects on patients. Recent works have shown significant promise for reconstructing MR images from sparsely sampled k-space data using deep learning. In this work, we propose a technique that rapidly estimates deep neural networks directly at reconstruction time by fitting them on small adaptively estimated neighborhoods of a training set. In brief, our algorithm alternates between searching for neighbors in a data set that are similar to the test reconstruction, and training a local network on these neighbors followed by updating the test reconstruction. Because our reconstruction model is learned on a dataset that is in some sense similar to the image being reconstructed rather than being fit on a large, diverse training set, it is more adaptive to new scans. It can also handle changes in training sets and flexible scan settings, while being relatively fast. Our approach, dubbed LONDN-MRI, was validated on multiple data sets using deep unrolled reconstruction networks. Reconstructions were performed at four fold and eight fold undersampling of k-space with 1D variable-density random phase-encode undersampling masks. Our results demonstrate that our proposed locally-trained method produces higher-quality reconstructions compared to models trained globally on larger datasets as well as other scan-adaptive methods.

We introduce a novel energy formulation for Plug- and-Play (PnP) image recovery. Traditional PnP methods that use a convolutional neural network (CNN) do not have an energy based formulation. The primary focus of this work is to introduce an energy-based PnP formulation, which relies on a CNN that learns the log of the image prior from training data. The score function is evaluated as the gradient of the energy model, which resembles a UNET with shared encoder and decoder weights. The proposed score function is thus constrained to a conservative vector field, which is the key difference with classical PnP models. The energy-based formulation offers algorithms with convergence guarantees, even when the learned score model is not a contraction. The relaxation of the contraction constraint allows the proposed model to learn more complex priors, thus offering improved performance over traditional PnP schemes. Our experiments in magnetic resonance image reconstruction demonstrates the improved performance offered by the proposed energy model over traditional PnP methods.

Although there have been significant advances in the field of image restoration recently, the system complexity of the state-of-the-art (SOTA) methods is increasing as well, which may hinder the convenient analysis and comparison of methods. In this paper, we propose a simple baseline that exceeds the SOTA methods and is computationally efficient. To further simplify the baseline, we reveal that the nonlinear activation functions, e.g. Sigmoid, ReLU, GELU, Softmax, etc. are not necessary: they could be replaced by multiplication or removed. Thus, we derive a Nonlinear Activation Free Network, namely NAFNet, from the baseline.