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

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.