  Purpose: Using linear transformation of the data allows studying
detectability of an imaging system on a large number of signals. An appropriate
transformation will produce a set of signals with different contrast and
different frequency contents. In this work both strategies are explored to
present a task-based test for the detectability of an x-ray imaging system.
Methods: Images of a new star-bar phantom are acquired with different entrance
air KERMA and with different beam qualities. Then, after a wavelet packet is
applied to both input and output of the system, conventional statistical
decision theory is applied to determine detectability on the different images
or nodes resulting from the transformation. A non-prewhitening matching filter
is applied to the data in the spatial domain, and ROC analysis is carried out
in each of the nodes. Results: AUC maps resulting from the analysis present the
area under the ROC curve over the whole 2D frequency space for the different
doses and beam qualities. Also, AUC curves, obtained by radially averaging the
AUC maps allows comparing detectability of the different techniques as a
function of the frequency in one only figure. The results obtained show
differences between images acquired with different doses for each of the beam
qualities analyzed. Conclusions: Combining a star-bar as test object, a wavelet
packet as linear transformation, and ROC analysis results in an appropriate
task-based test for detectability performance of an imaging system. The test
presented in this work allows quantification of system detectability as a
function of the 2D frequency interval of the signal to detect. It also allows
calculation of detectability differences between different acquisition
techniques and beam qualities.
