Approximating the ideal observer for joint signal detection and estimation tasks by the use of Markov-Chain Monte Carlo with generative adversarial networks.

Purpose: The Bayesian ideal observer (IO) is a special model observer that achieves the best possible performance on tasks that involve signal detection or discrimination. Although IOs are desired for optimizing and assessing imaging technologies, they remain difficult to compute. Previously, a hybrid method that combines deep learning (DL) with a Markov-Chain Monte Carlo (MCMC) method was proposed for estimating the IO test statistic for joint signal detection-estimation tasks. That method will be referred to as the hybrid MCMC method. However, the hybrid MCMC method was restricted to use cases that involved relatively simple stochastic background and signal models. Approach: The previously developed hybrid MCMC method is generalized by utilizing a framework that integrates deep generative modeling into the MCMC sampling process. This method employs a generative adversarial network (GAN) that is trained on object or signal ensembles to establish data-driven stochastic object and signal models, respectively, and will be referred to as the hybrid MCMC-GAN method. This circumvents the limitation of traditional MCMC methods and enables the estimation of the IO test statistic with consideration of broader classes of clinically relevant object and signal models. Results: The hybrid MCMC-GAN method was evaluated on two binary detection-estimation tasks in which the observer must detect a signal and estimate its amplitude if the signal is detected. First, a stylized signal-known-statistically (SKS) and background-known-exactly task was considered. A GAN was employed to establish a stochastic signal model, enabling direct comparison of our GAN-based IO approximation with a closed-form expression for the IO decision strategy. The results confirmed that the proposed method could accurately approximate the performance of the true IO. Next, an SKS and background-known-statistically (BKS) task was considered. Here, a GAN was employed to establish a stochastic object model that described anatomical variability in an ensemble of magnetic resonance (MR) brain images. This represented a setting where traditional MCMC methods are inapplicable. In this study, although a reference estimate of the true IO performance was unavailable, the hybrid MCMC-GAN produced area under the estimation receiver operating characteristic curve (AEROC) estimates that exceeded those of a sub-ideal observer that represented a lower bound for the IO performance. Conclusion: By combining GAN-based generative modeling with MCMC, the hybrid MCMC-GAN method extends a previously proposed IO approximation method to more general detection-estimation tasks. This provides a new capability to benchmark and optimize imaging-system performance through virtual imaging studies.