Using fisher information to compute ideal-observer performance on detection tasks

In medical imaging, signal detection is one of the most important tasks. A common way to evaluate the performance of an imaging system for a signal-detection task is to calculate the detectability of the ideal observer. Since the detectability of an ideal observer is not always easy to calculate, it is useful to have approximations for it. These approximations can also be used to check the bias of numerical computations of the ideal-observer detectability. For signal detection tasks, we usually have two probability densities for the data vector, the signal-absent density and the signal-present density. In this work, we use a single probability density with a variable scalar or vector parameter to represent the corresponding densities under the two hypotheses. The ideal-observer detectability is derived from the area under the receiver operating characteristic curve of the ideal observer for the given detection task. We have found that we can develop expansions for the square of this detectability as a function of the signal parameter, and that the lowest order expansions involve the Fisher information matrix for the problem of estimating the signal parameter. There are four basic methods we have considered for deriving such expansions. We compute these approximations to ideal-observer detectability for several cases. We compare these to the exact detectability values for these same cases, derived from results in previous work, to examine the usefulness of these approaches. The idea of using one parameterized probability density function is introduced in order to relate detection performance to estimation performance. Even without an analytical expression for ideal-observer detectability we are able to compute analytical forms for its derivatives in terms of the Fisher information matrix and similarly defined statistical moments. The results suggest that there is a connection between the performance of a system on signal-detection tasks and signal-estimation tasks.