Simplification algorithms for CT reconstruction pre-processing and filtering

Several approaches have been proposed to speed-up the back-projection part of CT image reconstruction. In this paper, two methods of simplifying respectively the data pre-processing and filtering steps are introduced. Both methods rely on the projection data redundancy that is shown to exist from view-to-view in X-ray CT. For the pre-processing step, and for a given view, the input of pre-processing is divided into the output to form a linearization vector. Such linearization vectors for views i and k are applied (with regularization) to estimate intermediate pre-processed views j, i<j<k. For the filtering, considering view j, i<j<k, and with views i and k to be fully filtered, an estimate of the low frequency component of view j is calculated by linear combination of views i and k. That estimate is then subtracted from view j, and the resulting high-frequency component is then filtered using a much shorter kernel. By linearity of the filtering operation, the same combination of fully filtered views i and k is added back to view j. Simplifications greater than a factor two are obtained while maintaining full image quality. Simplification can then be leveraged for either increased reconstruction speed and/or cost take-out