# Approximating the Ideal Observer and Hotelling Observer for binary signal detection tasks by use of supervised learning methods

arXiv: https://arxiv.org/abs/1905.06330 · HTML: https://mlsanity.com/paper/1905.06330/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 May 2019.

## Built on by (most cited first, 14 of 14)

- [Learning stochastic object models from medical imaging measurements by use of advanced ambient generative adversarial networks](https://mlsanity.com/paper/2106.14324/) (2021)
- [Impact of deep learning-based image super-resolution on binary signal detection](https://mlsanity.com/paper/2107.02338/) (2021)
- [Ideal Observer Computation by Use of Markov-Chain Monte Carlo with Generative Adversarial Networks](https://mlsanity.com/paper/2304.00433/) (2023)
- [Report on the AAPM Grand Challenge on deep generative modeling for learning medical image statistics](https://mlsanity.com/paper/2405.01822/) (2024)
- [Ambient-Pix2PixGAN for Translating Medical Images from Noisy Data](https://mlsanity.com/paper/2402.01186/) (2024)
- [Advancing the AmbientGAN for learning stochastic object models](https://mlsanity.com/paper/2102.00281/) (2021)
- [AmbientCycleGAN for Establishing Interpretable Stochastic Object Models Based on Mathematical Phantoms and Medical Imaging Measurements](https://mlsanity.com/paper/2402.01171/) (2024)
- [Enhancing signal detectability in learning-based CT reconstruction with a model observer inspired loss function](https://mlsanity.com/paper/2402.10010/) (2024)
- [Ambient Denoising Diffusion Generative Adversarial Networks for Establishing Stochastic Object Models from Noisy Image Data](https://mlsanity.com/paper/2501.19094/) (2025)
- [A deep Q-learning method for optimizing visual search strategies in backgrounds of dynamic noise](https://mlsanity.com/paper/2201.12385/) (2022)
- [Estimating Task-based Performance Bounds for Accelerated MRI Image Reconstruction Methods by Use of Learned-Ideal Observers](https://mlsanity.com/paper/2501.09224/) (2025)
- [Task-based Regularization in Penalized Least-Squares for Binary Signal Detection Tasks in Medical Image Denoising](https://mlsanity.com/paper/2501.18418/) (2025)
- [Using gradient of Lagrangian function to compute efficient channels for the ideal observer](https://mlsanity.com/paper/2501.19381/) (2025)
- [Score-Based Ideal Observer Approximation via Denoising Score Matching for Signal-Known-Exactly Detection Tasks](https://mlsanity.com/paper/2608.24768/) (2026)

## Abstract (arXiv)

It is widely accepted that optimization of medical imaging system performance should be guided by task-based measures of image quality (IQ). Task-based measures of IQ quantify the ability of an observer to perform a specific task such as detection or estimation of a signal (e.g., a tumor). For binary signal detection tasks, the Bayesian Ideal Observer (IO) sets an upper limit of observer performance and has been advocated for use in optimizing medical imaging systems and data-acquisition designs. Except in special cases, determination of the IO test statistic is analytically intractable. Markov-chain Monte Carlo (MCMC) techniques can be employed to approximate IO detection performance, but their reported applications have been limited to relatively simple object models. In cases where the IO test statistic is difficult to compute, the Hotelling Observer (HO) can be employed. To compute the HO test statistic, potentially large covariance matrices must be accurately estimated and subsequently inverted, which can present computational challenges. This work investigates supervised learning-based methodologies for approximating the IO and HO test statistics. Convolutional neural networks (CNNs) and single-layer neural networks (SLNNs) are employed to approximate the IO and HO test statistics, respectively. Numerical simulations were conducted for both signal-known-exactly (SKE) and signal-known-statistically (SKS) signal detection tasks. The performances of the supervised learning methods are assessed via receiver operating characteristic (ROC) analysis and the results are compared to those produced by use of traditional numerical methods or analytical calculations when feasible. The potential advantages of the proposed supervised learning approaches for approximating the IO and HO test statistics are discussed.