Approximating the ideal observer via a variational information bottleneck

The Bayesian ideal observer (IO) defines an upper bound on task-based observer performance and is widely used as a theoretical benchmark for optimizing medical imaging systems and data-acquisition designs. However, except in special cases, the exact IO test statistic is analytically intractable. Recent deep neural network (DNN)-based approaches show promise for approximating IO performance while providing limited analytical insight and no guarantee that the learned test statistic corresponds to a likelihood ratio. In addition, their empirical performance can degrade in data-limited regimes, motivating methods that incorporate stronger statistical structure and regularization. To address this, we propose a data-driven framework based on the variational information bottleneck (VIB) to approximate the IO test statistic for binary signal-detection tasks.

The proposed method utilizes the variational bottleneck principle to encode high-dimensional image data into a low-dimensional latent space optimized to preserve task-relevant information while suppressing nuisance variability. An analytically motivated Gaussian IO loss encourages the class-conditional latent distributions to follow multivariate Gaussian models. Under the adopted Gaussian model for the class-conditional latent distributions, a closed-form Gaussian likelihood-ratio statistic can be evaluated. Unlike end-to-end convolutional neural network (CNN)-based IO approximation methods, this formulation yields an explicit likelihood-ratio test statistic and provides greater analytical interpretability.

Numerical studies demonstrate that the proposed VIB-based IO method achieves detection performance comparable to conventional CNN approaches on large datasets, and superior performance in data-limited regimes. Furthermore, the learned bottleneck representations exhibit stability under the domain shifts examined, supporting robust deployment across varying imaging conditions.

The proposed VIB-IO framework provides a theoretically grounded and relatively data-efficient alternative to conventional CNN-based IO approximations while retaining greater analytical transparency through an explicit latent-space Gaussian observer model. By combining the representational capacity of DNNs with an analytically tractable latent-space observer model, the proposed framework provides a principled approach for objective, task-based assessment of medical imaging systems.