Transform-domain penalized-likelihood filtering of tomographic data

We present motivation for performing the filtering step of the widely used filtered back-projection algorithm in a non-Radon domain. For square-error optimal penalized-likelihood regularization, filtering in a domain for which the true projection data is sparse in the angle dimension yields coefficients that are more faithful to the ideal filtered data than directly filtering the observed Radon-domain data. In contrast to traditional regularization techniques that filter each projection independently, the proposed filtering technique delivers improved reconstructions by exploiting the correlation of the data in the angle dimension. This enables meaningful reconstructions to be created even from very noisy projection data. In addition, this approach allows for simple penalty matrices to be constructed, enables penalty coefficient to be calculated in a straightforward manner, and results in an easily computed, closed-form solution for the regularizing filters.