Approximating the Hotelling observer with autoencoder-learned efficient channels for binary signal detection tasks

Purpose: The objective assessment of image quality (IQ) has been advocated for the analysis and optimization of medical imaging systems. One method of computing such IQ metrics is through a numerical observer. The Hotelling observer (HO) is the optimal linear observer, but conventional methods for obtaining the HO can become intractable due to large image sizes or insufficient data. Channelized methods are sometimes employed in such circumstances to approximate the HO. The performance of such channelized methods varies, with different methods obtaining superior performance to others depending on the imaging conditions and detection task. A channelized HO method using an AE is presented and implemented across several tasks to characterize its performance. Approach: The process for training an AE is demonstrated to be equivalent to developing a set of channels for approximating the HO. The efficiency of the learned AE-channels is increased by modifying the conventional AE loss function to incorporate task-relevant information. Multiple binary detection tasks involving lumpy and breast phantom backgrounds across varying dataset sizes are considered to evaluate the performance of the proposed method and compare to current stateof- the-art channelized methods. Additionally, the ability of the channelized methods to generalize to images outside of the training dataset is investigated. Results: AE-learned channels are demonstrated to have comparable performance with other state-of-the-art channel methods in the detection studies and superior performance in the generalization studies. Incorporating a cleaner estimate of the signal for the detection task is also demonstrated to significantly improve the performance of the proposed method, particularly in datasets with fewer images. Conclusions: AEs are demonstrated to be capable of learning efficient channels for the HO. The resulting significant increase in detection performance for small dataset sizes when incorporating a signal prior holds promising implications for future assessments of imaging technologies.