Using gradient of Lagrangian function to compute efficient channels for the ideal observer

The Bayesian ideal observer (IO) performs optimally in signal detection tasks and is a powerful tool for objective assessment of medical imaging systems. However, the IO test statistic typically depends nonlinearly on the image data and cannot be analytically determined. The Hotelling observer (HO) can sometimes be used as a surrogate for the IO. However, when image data have high dimensionality, the HO computation can be difficult. To reduce dimensionality of image data for approximating the HO performance, this work proposes a novel method for generating efficient channels, referred to as the Lagrangian-gradient (L-grad) channels, by using the gradient of the Lagrangian-based loss function that was designed to learn the HO. It is demonstrated that the L-grad channels can lead to significantly improved signal detection performance in comparison with the PLS channels. Moreover, the L-grad channels can achieve much faster computation time than the PLS channels.