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Purpose  Using linear transformations of the acquired data can expand the study of detectability in an imaging system. From one image, an appropriate transformation will produce a set of signals with different contrast and different frequency contents. In this work this strategy is 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, statistical decision theory is applied to determine detectability of the different images or nodes resulting from the transformation. An ideal Bayesian observer (IBO) is applied to the data in the spatial domain to perform ROC analysis and to determine a detectability index for each of the nodes. In addition, image quality is characterized in terms of noise equivalent quanta (NEQ) and a 5 mm nodule detection task is performed.    Results  AUC maps resulting from the analysis show 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, allow comparing detectability of the different techniques as a function of the frequency in a single figure. The results obtained show differences between images acquired with different doses for each of the beam qualities analyzed. Classifying image quality by means of detectability indexes agrees with that of the AUC curves and the nodule detection task but differs from the NEQ for the low air KERMA images.    Conclusions  Combining a star–bar as test object, a wavelet packet as linear transformation and ROC analysis provides an appropriate task‐based test for detectability performance of an imaging system. The test presented in this work produces maps and curves quantifying system detectability as a function of the frequency characterizing the signal to detect and allows calculating detectability differences between different acquisition techniques.

Detectability assessment of an x‐ray imaging system using the nodes in a wavelet packet decomposition of a star–bar object