Using Fisher information to approximate ideal-observer performance on detection tasks for lumpy-background images

When building an imaging system for detection tasks in medical imaging, we need to evaluate how well the system performs before we can optimize it. One way to do the evaluation is to calculate the performance of the Bayesian ideal observer. The ideal-observer performance is often computationally expensive, and it is very useful to have an approximation to it. We use a parameterized probability density function to represent the corresponding densities of data under the signal-absent and the signal-present hypotheses. We develop approximations to the ideal-observer detectability as a function of signal parameters involving the Fisher information matrix, which is normally used in parameter estimation problems. The accuracy of the approximation is illustrated in analytical examples and lumpy-background simulations. We are able to predict the slope of the detectability as a function of the signal parameter. This capability suggests that the Fisher information matrix itself evaluated at the null parameter value can be used as the figure of merit in imaging system evaluation. We are also able to provide a theoretical foundation for the connection between detection tasks and estimation tasks.