We introduce Neural Optimal Design of Experiments, a learning-based framework for optimal experimental design in inverse problems that avoids classical bilevel optimization and indirect sparsity regularization. NODE jointly trains a neural reconstruction model and a fixed-budget set of continuous design variables representing sensor locations, sampling times, or measurement angles, within a single optimization loop. By optimizing measurement locations directly rather than weighting a dense grid of candidates, the proposed approach enforces sparsity by design, eliminates the need for l1 tuning, and substantially reduces computational complexity. We validate NODE on an analytically tractable exponential growth benchmark, on MNIST image sampling, and illustrate its effectiveness on a real world sparse view X ray CT example. In all cases, NODE outperforms baseline approaches, demonstrating improved reconstruction accuracy and task-specific performance.

We propose Deep-Motion-Net: an end-to-end graph neural network (GNN) architecture that enables 3D (volumetric) organ shape reconstruction from a single in-treatment kV planar X-ray image acquired at any arbitrary projection angle. Estimating and compensating for true anatomical motion during radiotherapy is essential for improving the delivery of planned radiation dose to target volumes while sparing organs-at-risk, and thereby improving the therapeutic ratio. Achieving this using only limited imaging available during irradiation and without the use of surrogate signals or invasive fiducial markers is attractive. The proposed model learns the mesh regression from a patient-specific template and deep features extracted from kV images at arbitrary projection angles. A 2D-CNN encoder extracts image features, and four feature pooling networks fuse these features to the 3D template organ mesh. A ResNet-based graph attention network then deforms the feature-encoded mesh. The model is trained using synthetically generated organ motion instances and corresponding kV images. The latter is generated by deforming a reference CT volume aligned with the template mesh, creating digitally reconstructed radiographs (DRRs) at required projection angles, and DRR-to-kV style transferring with a conditional CycleGAN model. The overall framework was tested quantitatively on synthetic respiratory motion scenarios and qualitatively on in-treatment images acquired over full scan series for liver cancer patients. Overall mean prediction errors for synthetic motion test datasets were 0.16$\pm$0.13 mm, 0.18$\pm$0.19 mm, 0.22$\pm$0.34 mm, and 0.12$\pm$0.11 mm. Mean peak prediction errors were 1.39 mm, 1.99 mm, 3.29 mm, and 1.16 mm.

Deep learning is the current de facto state of the art in tomographic imaging. A common approach is to feed the result of a simple inversion, for example the backprojection, to a convolutional neural network (CNN) which then computes the reconstruction. Despite strong results on 'in-distribution' test data similar to the training data, backprojection from sparse-view data delocalizes singularities, so these approaches require a large receptive field to perform well. As a consequence, they overfit to certain global structures which leads to poor generalization on out-of-distribution (OOD) samples. Moreover, their memory complexity and training time scale unfavorably with image resolution, making them impractical for application at realistic clinical resolutions, especially in 3D: a standard U-Net requires a substantial 140GB of memory and 2600 seconds per epoch on a research-grade GPU when training on 1024x1024 images. In this paper, we introduce GLIMPSE, a local processing neural network for computed tomography which reconstructs a pixel value by feeding only the measurements associated with the neighborhood of the pixel to a simple MLP. While achieving comparable or better performance with successful CNNs like the U-Net on in-distribution test data, GLIMPSE significantly outperforms them on OOD samples while maintaining a memory footprint almost independent of image resolution; 5GB memory suffices to train on 1024x1024 images. Further, we built GLIMPSE to be fully differentiable, which enables feats such as recovery of accurate projection angles if they are out of calibration.

Recovering a high-quality image from noisy indirect measurement is an important problem with many applications. For such inverse problems, supervised deep convolutional neural network (CNN)-based denoising methods have shown strong results, but their success critically depends on the availability of a high-quality training dataset of similar measurements. For image denoising, methods are available that enable training without a separate training dataset by assuming that the noise in two different pixels is uncorrelated. However, this assumption does not hold for inverse problems, resulting in artifacts in the output of existing methods. Here, we propose Noise2Inverse, a deep CNN-based denoising method for linear inverse problems in imaging that does not require any additional clean or noisy data. Training a CNN-based denoiser is enabled by exploiting the noise model to compute multiple statistically independent reconstructions. We develop a theoretical framework which shows that such training indeed obtains a denoising CNN, assuming the measured noise is element-wise independent and zero-mean. On simulated CT datasets, Noise2Inverse demonstrates a substantial improvement in peak signal-to-noise ratio (> 2dB) and structural similarity index (> 30%) compared to image denoising methods and conventional reconstruction methods, such as Total-Variation Minimization. We also demonstrate that the method is able to significantly reduce noise in challenging real-world experimental datasets.