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Purpose Iterative algorithms introduce new challenges in the field of image quality assessment. The purpose of this study is to use a mathematical model to evaluate objectively the low contrast detectability in CT. Materials and methods A QRM 401 phantom containing 5 and 8 mm diameter spheres with a contrast level of 10 and 20 HU was used. The images were acquired at 120 kV with CTDIvol equal to 5, 10, 15, 20 mGy and reconstructed using the filtered back-projection (FBP), adaptive statistical iterative reconstruction 50% (ASIR 50%) and model-based iterative reconstruction (MBIR) algorithms. The model observer used is the Channelized Hotelling Observer (CHO). The channels are dense difference of Gaussian channels (D-DOG). The CHO performances were compared to the outcomes of six human observers having performed four alternative forced choice (4-AFC) tests. Results For the same CTDIvol level and according to CHO model, the MBIR algorithm gives the higher detectability index. The outcomes of human observers and results of CHO are highly correlated whatever the dose levels, the signals considered and the algorithms used when some noise is added to the CHO model. The Pearson coefficient between the human observers and the CHO is 0.93 for FBP and 0.98 for MBIR. Conclusion The human observers' performances can be predicted by the CHO model. This opens the way for proposing, in parallel to the standard dose report, the level of low contrast detectability expected. The introduction of iterative reconstruction requires such an approach to ensure that dose reduction does not impair diagnostics.