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

Abstract: It is widely accepted that the Bayesian ideal observer (IO) should be used to guide the objective assessment and optimization of medical imaging systems. The IO employs complete task-specific information to compute test statistics for making inference decisions and performs optimally in signal detection tasks. However, the IO test statistic typically depends non-linearly on the image data and cannot be analytically determined. The ideal linear observer, known as the Hotelling observer (HO), can sometimes be used as a surrogate for the IO. However, when image data are high dimensional, HO computation can be difficult. Efficient channels that can extract task-relevant features have been investigated to reduce the dimensionality of image data to approximate IO and HO performance. This work proposes a novel method for generating efficient channels by use of the gradient of a Lagrangian-based loss function that was designed to learn the HO. The generated channels are referred to as the Lagrangian-gradient (L-grad) channels. Numerical studies are conducted that consider binary signal detection tasks involving various backgrounds and signals. It is demonstrated that channelized HO (CHO) using L-grad channels can produce significantly better signal detection performance compared to the CHO using PLS channels. Moreover, it is shown that the proposed L-grad method can achieve significantly lower computation time compared to the PLS method.