Transform-Domain Penalized-Likelihood Filtering of Projection Data

We present motivation for performing the filtering step of FBP in a non-Radon domain. Specifically, we show that for penalized-likelihood regularization, with a shift-invariant penalty function, filtering noisy projection data in a domain for which the true projection data is sparse yields filtered data that is more faithful to the ideal filtered data than directly filtering the Radon-domain data. In contrast to simply penalizing across angles, the proposed method exploits correlation in the angle dimension. This allows for simple penalty matrices to be constructed, enables penalty coefficient to be calculated in a straightforward manner, and results in easily an computed, closed-form solution for the regularizing filters. Reconstructions employing this transform-domain filtering are superior to their Radon-domain filtered counterparts.