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This work aims to construct a method to objectively evaluate CT image quality when new clinical protocol performances must be compared with a standard reference. We compare iterative reconstruction in the image space with filtered back projection reconstruction and accurately quantify the dose reduction. The comparison strategy accounts for both physical and clinical image qualities that are evaluated using a standard metric. The quasi-ideal observer metric is also explored to verify its reportedly high correlation with perceived image quality. Water or spatial resolution phantom images are used to characterise the physical image quality using the classic metrics in the Fourier domain by calculating the modulation transfer functions and noise power spectra (NPS). The clinical-image quality is evaluated with a 4-alternative forced-choice test. The human observers are asked to detect a positive image that contains a simulated lesion in a background image. Then, the same positive images are characterised with the quasi-ideal observer metric, which calculates the non-prewhitening matched filter signal-to-noise ratio (SNRNPWMF). Iterative reconstruction strongly reduces the image noise, but the NPS are slightly shifted to lower frequencies, which gives the images a coarse graininess. Compared with the reference FBP protocol for abdomen exams, the highest dose reduction is 40% if the standard metric is used and 30% if the SNRNPWMF metric is used. The detectability test results achieve a better correlation with SNRNPWMF than with the standard metric. The identified Fourier metric is a useful descriptor of human quality perception and can be used for future protocol optimisation.