Bayesian Scattering: A Principled Baseline for Uncertainty on Image Data

Optical scattering has conventionally been regarded as an impediment in imaging research due to the degradation of image quality during reconstruction. Nevertheless, this study explores two cases in which optical scattering may serve a beneficial role in image reconstruction tasks. We compared the No Scattering MNIST dataset with three Scattering MNIST datasets, each generated under distinct scattering conditions. To assess the information content of the resulting speckle patterns, we employed a Variational Autoencoder (VAE) approach which achieves accuracy comparable to state-of-the-art deep learning approaches, but has an interpretable latent space. We find that scattering can enhance data robustness against spatial pixel loss by effectively distributing information. We also demonstrate that scattering can enable distinctions of focal depth information. We anticipate that these findings will contribute to more efficient imaging techniques, particularly in the presence of obstacles and three-dimensional signals.

We propose a novel Bayesian framework for joint image reconstruction and uncertainty quantification from compressed sensing magnetic resonance imaging data. The problem is formulated as a linear inverse problem, where prior distributions are assigned to the unknown image parameters. Specifically, the image is assumed to be sparse in a given transform domain. We develop a general framework applicable to any sparsifying transform and demonstrate its performance using (1) a total variation transform based on image spatial gradients and (2) a wavelet-domain transform. Bayesian inference is performed using a split-and-augmented Gibbs sampler, while the resulting non-differentiable conditional distributions are efficiently sampled using a proximal Markov chain Monte Carlo method. The proposed algorithms are validated on both single-coil and multi-coil datasets using various k-space sampling patterns and acceleration factors. The results demonstrate that the proposed Bayesian methods consistently outperform their optimisation-based counterparts in image reconstruction while providing uncertainty estimates for the reconstructed images. Furthermore, the estimated uncertainty maps show a strong correlation with the true reconstruction errors and substantially outperformed deep learning-based uncertainty estimation methods.

Uncertainty quantification complements model predictions by characterizing their reliability, which is essential for high-stakes decision making such as medical image segmentation. However, most existing methods reduce uncertainty to a scalar confidence estimate, leaving its spatial distribution semantically underconstrained. In this work, we focus on uncertainty interpretability, namely, whether estimated uncertainty behaves in a human-understandable manner with respect to sources of ambiguity. We identify three perception-aligned principles requiring the spatial distribution of uncertainty to reflect: (1) image contrast between structures, (2) severity of image corruption, and (3) geometric complexity in anatomical structures. Accordingly, we develop a principle-guided uncertainty supervision framework (PriUS) based on evidential learning, in which the corresponding supervision objectives are explicitly enforced during training. We further introduce quantitative metrics to measure the consistency between predicted uncertainty and image attributes that induce ambiguity. Experiments on ACDC, ISIC, and WHS datasets showed that, compared with state-of-the-art methods, PriUS produced more consistent uncertainty estimates while maintaining competitive segmentation performance.