Score-Based Ideal Observer Approximation via Denoising Score Matching for Signal-Known-Exactly Detection Tasks

The Bayesian Ideal Observer (IO) establishes the theoretical upper bound on task performance for binary detection tasks. However, analytical computation of the IO test statistic is generally intractable. Numerical approaches based on Markov-chain Monte Carlo (MCMC) methods, including their recent deep generative model-based extensions, typically require extensive posterior sampling for each test image. Supervised learning has also been investigated to approximate the IO performance. However, such methods are typically trained for a specific detection task and signal and may require retraining when the task or signal changes. The score function, defined as the gradient of the log probability density, encodes the local geometry of the data distribution and is a fundamental quantity in modern score-based generative modeling. This work reformulates the IO test statistic in terms of the score function and introduces a score-based ideal observer (SIO). The proposed SIO uses a denoising convolutional neural network trained exclusively on signal-absent images to estimate the signal-absent score function. Once trained, the resulting score model can be used to approximate the IO test statistic for detection tasks involving arbitrary additive signals, without per-image posterior sampling or signal-specific retraining. Numerical studies consider a signal-known-exactly (SKE) detection task with a stochastic lumpy-background model. The results demonstrate that the proposed SIO can closely approximate the IO performance.