Finally, we investigate the response of Algorithm 1 to inconsistent projection data. Two forms of inconsistency are introduced in the data model. First, there is mismatch between the discrete phantom grid, $1024\xd71024$, and reconstructed image grid, $512\xd7512$. Second, noise is introduced with a Poisson-like Gaussian distribution, i.e., the variance of the Gaussian is set equal to the mean, where the mean is the average transmission at each detector bin assuming $7.5\xd7104$ photons are incident to each bin prior to passing through the subject. Thus, we are modeling a low-dose CT scan as what is typically proposed for breast CT. Images corresponding to the accurate solution of Eq. (12) with the TV constraint parameter selected to be that of the phantom, $\gamma =\gamma 0$, and various values of the parameters $\omega $ and $c$, are displayed in Fig. 10. The parameter $\omega $ clearly impacts noise texture, and here, we only aim to show how image quality changes with this parameter. Optimal setting of $\omega $ can only be determined based on the particular image task of the CT scan. Although $c$ has little impact on the reconstructed images for these simulations with untruncated projections and full image representation, this parameter helps to control gray level for ROI imaging.