Inverse problem involves estimating parameters or data from inadequate observations. Bayesian estimation introduces regularization to provide mild assumptions on the solution and prevent overfitting for ill-posed inverse problems. The forward model describes the explicit relationship between observations and the parameters or data that we want to estimate. Therefore, the forward projection operator is a key modeling choice in inverse problems. In this proposal, we introduce some new choices of forward models in Bayesian image estimation to improve the image quality. We present the adaptive blob basis function that can describe the forward process in X-ray CT more accurately by including models of the source, voxel and detector. Our preliminary experimental results show potential liability of such low-frequency operators as the blob when high frequency boosting is desired. We also propose a new type of detector model which is aimed at reducing aliasing artifacts in CT images as well as saving computation time compared with sinogram interpolation methods. Markov random fields (MRFs) are a broadly useful and relatively economical stochastic model for imagery in Bayesian estimation. The simplicity of their most common examples allows local computation in iterative optimization. This simplicity may be a liability, however, when the inherent bias of minimum mean-squared error or maximum a posteriori probability (MAP) estimators attenuate all but the lowest spatial frequencies. For applications where more flexibility in spectral response is desired, potential benefit exists in models which accord higher a priori probabilities to content in higher frequencies. We explore the potential of larger neighborhoods in MRFs considered from the point of view of probabilistic modeling of spatial frequency content. We consider particularly the preservation of detail in bone structure in CT images. Our experimental results show emphasis of the typical inner bone frequencies similar to that of bone-enhanced conventional X-ray CT reconstruction.