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

TL;DR

The paper addresses the computational challenge of approximating the Bayesian ideal observer (IO) in high-dimensional medical imaging by introducing Lagrangian-gradient (L-grad) channels. These channels are derived from the gradient of a Lagrangian-based HO-learning loss and are used within a channelized observer framework to closely approximate IO/HO performance while reducing dimensionality. In two SKE task studies (MVNLumpy Gaussian background and VICTRE mammography ROIs with a spiculated mass), L-grad and especially L-grad-CMD channels outperform traditional PLS channels in AUC and offer substantial reductions in channel-generation time, including up to about seven-fold speedups at larger training sizes. The results support the practical viability of IO-guided channel design, enabling efficient, accurate HO approximation in complex, high-dimensional imaging systems.

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.

Figures (6)

• Figure 1: The five images from left to right are examples of signal-present images associated with the considered MVNLumpy. Gaussian noise was added to simulate the measured image data. The rightmost image shows the Gaussian signal to be detected.
• Figure 2: (a) CHO performance with 50 L-grad, L-grad-CMD, and PLS channels computed on training dataset with different sizes. (b) CHO performance as a function of the number of channels when 2000 training images were considered.
• Figure 3: The first nine channels produced by PLS (a), L-grad (b), and L-grad-CMD (c).
• Figure 4: From left to right: Five examples of signal-present images generated by use of VICTRE mammography ROIs and the spiculated mass signal to be detected.
• Figure 5: (a) CHO performance with L-grad and PLS channels computed with varying numbers of training images for the VICTRE ROIs. (b) CHO performance as a function of the number of channels when the channels were trained on 2000 ROIs.