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.

翻译：普遍认为，贝叶斯理想观测者（IO）应用于指导医学成像系统的客观评估与优化。IO 利用完整的任务特定信息计算检验统计量以进行推断决策，并在信号检测任务中实现最优性能。然而，IO 检验统计量通常非线性依赖于图像数据，且无法解析确定。理想线性观测者，即霍特林观测者（HO），有时可作为 IO 的替代。然而，当图像数据为高维时，HO 的计算可能较为困难。为降低图像数据维度以逼近 IO 和 HO 的性能，已研究了能够提取任务相关特征的高效通道。本文提出一种通过使用基于拉格朗日的损失函数梯度来生成高效通道的新方法，该损失函数旨在学习 HO。所生成的通道称为拉格朗日梯度（L-grad）通道。数值研究考虑了涉及不同背景与信号的二元信号检测任务。结果表明，使用 L-grad 通道的通道化 HO（CHO）相较于使用 PLS 通道的 CHO，能产生显著更优的信号检测性能。此外，研究显示所提出的 L-grad 方法相比 PLS 方法能实现显著更低的计算时间。