标题： 使用拉格朗日函数的梯度计算理想观察者的有效信道 显示英文标题

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

摘要： 广泛认为，贝叶斯理想观察者（IO）应被用于指导医学成像系统的客观评估和优化。 IO利用完整的任务特定信息来计算检验统计量以做出推断决策，并在信号检测任务中表现最优。 然而，IO检验统计量通常非线性依赖于图像数据，无法解析确定。 已知的理想线性观察者，即霍特林观察者（HO），有时可作为IO的替代。 然而，当图像数据是高维时，HO的计算可能很困难。 已经研究了能够提取任务相关特征的有效通道，以降低图像数据的维度，从而近似IO和HO的性能。 本工作提出了一种新方法，通过使用基于拉格朗日的损失函数的梯度来生成有效通道，该损失函数旨在学习HO。 生成的通道称为拉格朗日梯度（L-grad）通道。 进行了数值研究，考虑涉及各种背景和信号的二元信号检测任务。 证明了使用L-grad通道的通道化HO（CHO）相比使用PLS通道的CHO，在信号检测性能方面有显著提升。 此外，证明了所提出的L-grad方法相比PLS方法可以显著降低计算时间。 显示英文摘要

摘要： 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.