Partial Least Squares: A Method to Estimate Efficient Channels for the Ideal Observers

We advocate a task-based approach to the assessment of image quality using the Bayesian ideal observer. The Bayesian ideal observer provides an absolute upper bound for performance estimates. However, using the full images as inputs to the observer is often infeasible due to their high dimensionality. A practical alternative is to reduce the dimensionality of the images by applying channels, while approximating the ideal observer by an observer constrained to the channels. Laguerre-Gauss (LG) channels and those derived from the singular value decomposition (SVD) of the system operator have previously been used with the Bayesian ideal observer. However, the channelized observer with LG and SVD channels was only applicable in situations with a rotationally symmetric signal or known system operator, respectively. We investigate a method using partial least squares (PLS) to compute efficient channels directly from the images, without prior knowledge of the background, signal, or system operator. Results show that the channelized ideal observer with PLS channels approximates the nonchannelized observer, and does so with fewer channels than the observer with either LG or SVD channels. The images are reduced from 4096 pixel values to 20 channel outputs, yet preserve the salient information. Furthermore, PLS reveals that the background image statistics provide important information necessary in signal-detection tasks. Overall, PLS is shown to be a viable channel generation method and may be applicable to real-life situations.