Efficient channels for the ideal observer

For a signal-detection task, the Bayesian ideal observer is optimal among all observers because it incorporates all the statistical information of the raw data from an imaging system. The ideal observer test statistic, the likelihood ratio, is difficult to compute when uncertainties are present in backgrounds and signals. In this work, we propose a new approximation technique to estimate the likelihood ratio. This technique is a dimensionality-reduction scheme we will call the channelized-ideal observer (CIO). We can reduce the high-dimensional integrals of the ideal observer to the low-dimensional integrals of the CIO by applying a set of channels to the data. Lumpy backgrounds and circularly symmetric Gaussian signals are used for simulations studies. Laguerre-Gaussian (LG) channels have been shown to be useful for approximating ideal linear observers with these backgrounds and signals. For this reason, we choose to use LG channels for our data. The concept of efficient channels is introduced to closely approximate ideal-observer performance with the CIO for signal-known-exactly (SKE) detection tasks. Preliminary results using one to three LG channels show that the performance of the CIO is better than the channelized-Hotelling observer for the SKE detection tasks.