Evan Bell

Evan Bell, Shijun Liang, Ismail Alkhouri et al.

Deep Image Prior (DIP) has recently emerged as a promising one-shot neural-network based image reconstruction method. However, DIP has seen limited application to 3D image reconstruction problems. In this work, we introduce Tada-DIP, a highly effective and fully 3D DIP method for solving 3D inverse problems. By combining input-adaptation and denoising regularization, Tada-DIP produces high-quality 3D reconstructions while avoiding the overfitting phenomenon that is common in DIP. Experiments on sparse-view X-ray computed tomography reconstruction validate the effectiveness of the proposed method, demonstrating that Tada-DIP produces much better reconstructions than training-data-free baselines and achieves reconstruction performance on par with a supervised network trained using a large dataset with fully-sampled volumes.

Shijun Liang, Evan Bell, Qing Qu et al.

The ability of deep image prior (DIP) to recover high-quality images from incomplete or corrupted measurements has made it popular in inverse problems in image restoration and medical imaging including magnetic resonance imaging (MRI). However, conventional DIP suffers from severe overfitting and spectral bias effects. In this work, we first provide an analysis of how DIP recovers information from undersampled imaging measurements by analyzing the training dynamics of the underlying networks in the kernel regime for different architectures. This study sheds light on important underlying properties for DIP-based recovery. Current research suggests that incorporating a reference image as network input can enhance DIP's performance in image reconstruction compared to using random inputs. However, obtaining suitable reference images requires supervision, and raises practical difficulties. In an attempt to overcome this obstacle, we further introduce a self-driven reconstruction process that concurrently optimizes both the network weights and the input while eliminating the need for training data. Our method incorporates a novel denoiser regularization term which enables robust and stable joint estimation of both the network input and reconstructed image. We demonstrate that our self-guided method surpasses both the original DIP and modern supervised methods in terms of MR image reconstruction performance and outperforms previous DIP-based schemes for image inpainting.

Daniel A. Serino, Evan Bell, Marc Klasky et al.

In high energy density physics (HEDP) and inertial confinement fusion (ICF), predictive modeling is complicated by uncertainty in parameters that characterize various aspects of the modeled system, such as those characterizing material properties, equation of state (EOS), opacities, and initial conditions. Typically, however, these parameters are not directly observable. What is observed instead is a time sequence of radiographic projections using X-rays. In this work, we define a set of sparse hydrodynamic features derived from the outgoing shock profile and outer material edge, which can be obtained from radiographic measurements, to directly infer such parameters. Our machine learning (ML)-based methodology involves a pipeline of two architectures, a radiograph-to-features network (R2FNet) and a features-to-parameters network (F2PNet), that are trained independently and later combined to approximate a posterior distribution for the parameters from radiographs. We show that the estimated parameters can be used in a hydrodynamics code to obtain density fields and hydrodynamic shock and outer edge features that are consistent with the data. Finally, we demonstrate that features resulting from an unknown EOS model can be successfully mapped onto parameters of a chosen analytical EOS model, implying that network predictions are learning physics, with a degree of invariance to the underlying choice of EOS model.

Evan Bell, Daniel A. Serino, Ben S. Southworth et al.

Estimating physical parameters or material properties from experimental observations is a common objective in many areas of physics and material science. In many experiments, especially in shock physics, radiography is the primary means of observing the system of interest. However, radiography does not provide direct access to key state variables, such as density, which prevents the application of traditional parameter estimation approaches. Here we focus on flyer plate impact experiments on porous materials, and resolving the underlying parameterized equation of state (EoS) and crush porosity model parameters given radiographic observation(s). We use machine learning as a tool to demonstrate with high confidence that using only high impact velocity data does not provide sufficient information to accurately infer both EoS and crush model parameters, even with fully resolved density fields or a dynamic sequence of images. We thus propose an observable data set consisting of low and high impact velocity experiments/simulations that capture different regimes of compaction and shock propagation, and proceed to introduce a generative machine learning approach which produces a posterior distribution of physical parameters directly from radiographs. We demonstrate the effectiveness of the approach in estimating parameters from simulated flyer plate impact experiments, and show that the obtained estimates of EoS and crush model parameters can then be used in hydrodynamic simulations to obtain accurate and physically admissible density reconstructions. Finally, we examine the robustness of the approach to model mismatches, and find that the learned approach can provide useful parameter estimates in the presence of out-of-distribution radiographic noise and previously unseen physics, thereby promoting a potential breakthrough in estimating material properties from experimental radiographic images.

Yuanyun Hu, Evan Bell, Guijin Wang et al.

Diffusion models are now commonly used to solve inverse problems in computational imaging. However, most diffusion-based inverse solvers require complete knowledge of the forward operator to be used. In this work, we introduce a novel probabilistic and robust inverse solver with measurement-conditioned diffusion prior (PRISM) to effectively address blind inverse problems. PRISM offers a technical advancement over current methods by incorporating a powerful measurement-conditioned diffusion model into a theoretically principled posterior sampling scheme. Experiments on blind image deblurring validate the effectiveness of the proposed method, demonstrating the superior performance of PRISM over state-of-the-art baselines in both image and blur kernel recovery.

Shijun Liang, Evan Bell, Avrajit Ghosh et al.

Deep learning methods are highly effective for many image reconstruction tasks. However, the performance of supervised learned models can degrade when applied to distinct experimental settings at test time or in the presence of distribution shifts. In this study, we demonstrate that pruning deep image reconstruction networks at training time can improve their robustness to distribution shifts. In particular, we consider unrolled reconstruction architectures for accelerated magnetic resonance imaging and introduce a method for pruning unrolled networks (PUN) at initialization. Our experiments demonstrate that when compared to traditional dense networks, PUN offers improved generalization across a variety of experimental settings and even slight performance gains on in-distribution data.

Evan Bell, Michael T. McCann, Marc Klasky

In this paper, we introduce silhouette tomography, a novel formulation of X-ray computed tomography that relies only on the geometry of the imaging system. We formulate silhouette tomography mathematically and provide a simple method for obtaining a particular solution to the problem, assuming that any solution exists. We then propose a supervised reconstruction approach that uses a deep neural network to solve the silhouette tomography problem. We present experimental results on a synthetic dataset that demonstrate the effectiveness of the proposed method.