In this paper, a straightforward method of estimating the CT projections is applied to simplified pre-processing, simplified reconstruction filtering, and to low-dose and local CT image reconstruction. The method relies on the projection- to-projection data redundancy that is shown to exist in CT. In the pre-processing application, the output of a few, angularly sparse fully pre-processed projections, is utilized in a linearization model to estimate directly the output of pre- processing for all the other projections. In the reconstruction filtering application, and with projection i and k being fully filtered, intermediate projection j low frequency components are estimated by a linear combination of projections i and k. That estimate is then subtracted from projection j, and the resulting high-frequency components are then filtered without zeropadding. By linearity the same combination of fully filtered projections i and k is added back to projection j. A factor two simplification is obtained, that can be leveraged for reconstruction speed or cost reduction. The local reconstruction application builds on the filtering method, by showing that truncated data is sufficient for calculating a filtered projection high-frequencies, while a very simple projection completion model is shown to be effective in estimating the low frequencies. Image quality comparisons are described.