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.
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