In this paper, we propose a novel deep convolutional neural network (CNN)-based algorithm for solving ill-posed inverse problems. Regularized iterative algorithms have emerged as the standard approach to ill-posed inverse problems in the past few decades. These methods produce excellent results, but can be challenging to deploy in practice due to factors including the high computational cost of the forward and adjoint operators and the difficulty of hyperparameter selection. The starting point of this paper is the observation that unrolled iterative methods have the form of a CNN (filtering followed by pointwise nonlinearity) when the normal operator (H*H, where H* is the adjoint of the forward imaging operator, H) of the forward model is a convolution. Based on this observation, we propose using direct inversion followed by a CNN to solve normal-convolutional inverse problems. The direct inversion encapsulates the physical model of the system, but leads to artifacts when the problem is ill posed; the CNN combines multiresolution decomposition and residual learning in order to learn to remove these artifacts while preserving image structure. We demonstrate the performance of the proposed network in sparse-view reconstruction (down to 50 views) on parallel beam X-ray computed tomography in synthetic phantoms as well as in real experimental sinograms. The proposed network outperforms total variation-regularized iterative reconstruction for the more realistic phantoms and requires less than a second to reconstruct a 512 × 512 image on the GPU.

In this survey paper, we review recent uses of convolution neural networks (CNNs) to solve inverse problems in imaging. It has recently become feasible to train deep CNNs on large databases of images, and they have shown outstanding performance on object classification and segmentation tasks. Motivated by these successes, researchers have begun to apply CNNs to the resolution of inverse problems such as denoising, deconvolution, super-resolution, and medical image reconstruction, and they have started to report improvements over state-of-the-art methods, including sparsity-based techniques such as compressed sensing. Here, we review the recent experimental work in these areas, with a focus on the critical design decisions: Where does the training data come from? What is the architecture of the CNN? and How is the learning problem formulated and solved? We also bring together a few key theoretical papers that offer perspective on why CNNs are appropriate for inverse problems and point to some next steps in the field.

We present a new image reconstruction method that replaces the projector in a projected gradient descent (PGD) with a convolutional neural network (CNN). Recently, CNNs trained as image-to-image regressors have been successfully used to solve inverse problems in imaging. However, unlike existing iterative image reconstruction algorithms, these CNN-based approaches usually lack a feedback mechanism to enforce that the reconstructed image is consistent with the measurements. We propose a relaxed version of PGD wherein gradient descent enforces measurement consistency, while a CNN recursively projects the solution closer to the space of desired reconstruction images. We show that this algorithm is guaranteed to converge and, under certain conditions, converges to a local minimum of a non-convex inverse problem. Finally, we propose a simple scheme to train the CNN to act like a projector. Our experiments on sparse-view computed-tomography reconstruction show an improvement over total variation-based regularization, dictionary learning, and a state-of-the-art deep learning-based direct reconstruction technique.

Administration of cholecystokinin (CCK) to rats caused a dose-dependent increase in plasma levels of the neurohypophyseal hormone oxytocin (OT). The OT secretion was comparable to that found in response to nausea-producing chemical agents that cause learned taste aversions. The effect of CCK on OT secretion was blunted after gastric vagotomy, as was the inhibition of food intake induced by CCK. Food ingestion also led to elevated plasma OT in rats, but CCK and aversive agents caused even greater OT stimulation. Thus, after administration of large doses of CCK, vagally mediated activation of central nausea pathways seems to be predominantly responsible for the subsequent decrease in food intake. Despite their dissimilar affective states, both nausea and satiety may activate a common hypothalamic oxytocinergic pathway that controls the inhibition of ingestion.