Domain independent post-processing with graph U-nets: applications to electrical impedance tomographic imaging⋆.

Objective.To extend the highly successful U-Net Convolutional Neural Network architecture, which is limited to rectangular pixel/voxel domains, to a graph-based equivalent that works flexibly on irregular meshes; and demonstrate the effectiveness on electrical impedance tomography (EIT).Approach.By interpreting the irregular mesh as a graph, we develop a graph U-Net with new cluster pooling and unpooling layers that mimic the classic neighborhood based max-pooling important for imaging applications.Mainresults.The proposed graph U-Net is shown to be flexible and effective for improving early iterate total variation (TV) reconstructions from EIT measurements, using as little as the first iteration. The performance is evaluated for simulated data, and on experimental data from three measurement devices with different measurement geometries and instrumentations. We successfully show that such networks can be trained with a simple two-dimensional simulated training set, and generalize to very different domains, including measurements from a three-dimensional device and subsequent 3D reconstructions.Significance.As many inverse problems are solved on irregular (e.g. finite element) meshes, the proposed graph U-Net and pooling layers provide the added flexibility to process directly on the computational mesh. Post-processing an early iterate reconstruction greatly reduces the computational cost which can become prohibitive in higher dimensions with dense meshes. As the graph structure is independent of 'dimension', the flexibility to extend networks trained on 2D domains to 3D domains offers a possibility to further reduce computational cost in training.

Graph Convolutional Networks for Model-Based Learning in Nonlinear Inverse Problems.

The majority of model-based learned image reconstruction methods in medical imaging have been limited to uniform domains, such as pixelated images. If the underlying model is solved on nonuniform meshes, arising from a finite element method typical for nonlinear inverse problems, interpolation and embeddings are needed. To overcome this, we present a flexible framework to extend model-based learning directly to nonuniform meshes, by interpreting the mesh as a graph and formulating our network architectures using graph convolutional neural networks. This gives rise to the proposed iterative Graph Convolutional Newton-type Method (GCNM), which includes the forward model in the solution of the inverse problem, while all updates are directly computed by the network on the problem specific mesh. We present results for Electrical Impedance Tomography, a severely ill-posed nonlinear inverse problem that is frequently solved via optimization-based methods, where the forward problem is solved by finite element methods. Results for absolute EIT imaging are compared to standard iterative methods as well as a graph residual network. We show that the GCNM has good generalizability to different domain shapes and meshes, out of distribution data as well as experimental data, from purely simulated training data and without transfer training.

Transient overexpression of striatal D2 receptors impairs operant motivation and interval timing.

The striatum receives prominent dopaminergic innervation that is integral to appetitive learning, performance, and motivation. Signaling through the dopamine D2 receptor is critical for all of these processes. For instance, drugs with high affinity for the D2 receptor potently alter timing of operant responses and modulate motivation. Recently, in an attempt to model a genetic abnormality encountered in schizophrenia, mice were generated that reversibly overexpress D2 receptors specifically in the striatum (Kellendonk et al., 2006). These mice have impairments in working memory and behavioral flexibility, components of the cognitive symptoms of schizophrenia, that are not rescued when D2 overexpression is reversed in the adult. Here we report that overexpression of striatal D2 receptors also profoundly affects operant performance, a potential index of negative symptoms. Mice overexpressing D2 exhibited impairments in the ability to time food rewards in an operant interval timing task and reduced motivation to lever press for food reward in both the operant timing task and a progressive ratio schedule of reinforcement. The motivational deficit, but not the timing deficit, was rescued in adult mice by reversing D2 overexpression with doxycycline. These results suggest that early D2 overexpression alters the organization of interval timing circuits and confirms that striatal D2 signaling in the adult regulates motivational process. Moreover, overexpression of D2 under pathological conditions such as schizophrenia and Parkinson's disease could give rise to motivational and timing deficits.