Bayesian Activity Estimation and Uncertainty Quantification of Spent Nuclear Fuel Using Passive Gamma Emission Tomography

In this paper, we address the problem of activity estimation in passive gamma emission tomography (PGET) of spent nuclear fuel. Two different noise models are considered and compared, namely, the isotropic Gaussian and the Poisson noise models. The problem is formulated within a Bayesian framework as a linear inverse problem and prior distributions are assigned to the unknown model parameters. In particular, a Bernoulli-truncated Gaussian prior model is considered to promote sparse pin configurations. A Markov chain Monte Carlo (MCMC) method, based on a split and augmented Gibbs sampler, is then used to sample the posterior distribution of the unknown parameters. The proposed algorithm is first validated by simulations conducted using synthetic data, generated using the nominal models. We then consider more realistic data simulated using a bespoke simulator, whose forward model is non-linear and not available analytically. In that case, the linear models used are mis-specified and we analyse their robustness for activity estimation. The results demonstrate superior performance of the proposed approach in estimating the pin activities in different assembly patterns, in addition to being able to quantify their uncertainty measures, in comparison with existing methods

Bayesian inference and uncertainty quantification for image reconstruction with Poisson data

We provide a complete framework for performing infinite-dimensional Bayesian inference and uncertainty quantification for image reconstruction with Poisson data. In particular, we address the following issues to make the Bayesian framework applicable in practice. We first introduce a positivity-preserving reparametrization, and we prove that under the reparametrization and a hybrid prior, the posterior distribution is well-posed in the infinite dimensional setting. Second we provide a dimension-independent MCMC algorithm, based on the preconditioned Crank-Nicolson Langevin method, in which we use a primal-dual scheme to compute the offset direction. Third we give a method combining the model discrepancy method and maximum likelihood estimation to determine the regularization parameter in the hybrid prior. Finally we propose to use the obtained posterior distribution to detect artifacts in a recovered image. We provide an example to demonstrate the effectiveness of the proposed method

Learned, Uncertainty-driven Adaptive Acquisition for Photon-Efficient Multiphoton Microscopy

Multiphoton microscopy (MPM) is a powerful imaging tool that has been a critical enabler for live tissue imaging. However, since most multiphoton microscopy platforms rely on point scanning, there is an inherent trade-off between acquisition time, field of view (FOV), phototoxicity, and image quality, often resulting in noisy measurements when fast, large FOV, and/or gentle imaging is needed. Deep learning could be used to denoise multiphoton microscopy measurements, but these algorithms can be prone to hallucination, which can be disastrous for medical and scientific applications. We propose a method to simultaneously denoise and predict pixel-wise uncertainty for multiphoton imaging measurements, improving algorithm trustworthiness and providing statistical guarantees for the deep learning predictions. Furthermore, we propose to leverage this learned, pixel-wise uncertainty to drive an adaptive acquisition technique that rescans only the most uncertain regions of a sample. We demonstrate our method on experimental noisy MPM measurements of human endometrium tissues, showing that we can maintain fine features and outperform other denoising methods while predicting uncertainty at each pixel. Finally, with our adaptive acquisition technique, we demonstrate a 120X reduction in acquisition time and total light dose while successfully recovering fine features in the sample. We are the first to demonstrate distribution-free uncertainty quantification for a denoising task with real experimental data and the first to propose adaptive acquisition based on reconstruction uncertaint