Penalized-likelihood sinogram restoration for computed tomography

We formulate computed tomography (CT) sinogram preprocessing as a statistical restoration problem in which the goal is to obtain the best estimate of the line integrals needed for reconstruction from the set of noisy, degraded measurements. CT measurement data are degraded by a number of factors-including beam hardening and off-focal radiation-that produce artifacts in reconstructed images unless properly corrected. Currently, such effects are addressed by a sequence of sinogram-preprocessing steps, including deconvolution corrections for off-focal radiation, that have the potential to amplify noise. Noise itself is generally mitigated through apodization of the reconstruction kernel, which effectively ignores the measurement statistics, Although in high-noise situations adaptive filtering methods that loosely model data statistics are sometimes applied. As an alternative, we present a general imaging model relating the degraded measurements to the sinogram of ideal line integrals and propose to estimate these line integrals by iteratively optimizing a statistically based objective function. We consider three different strategies for estimating the set of ideal line integrals, one based on direct estimation of ideal "monochromatic" line integrals that have been corrected for single-material beam hardening, one based on estimation of ideal "polychromatic" line integrals that can be readily mapped to monochromatic line integrals, and one based on estimation of ideal transmitted intensities, from which ideal, monochromatic line integrals can be readily estimated. The first two approaches involve maximization of a penalized Poisson-likelihood objective function while the third involves minimization of a quadratic penalized weighted least squares (PWLS) objective applied in the transmitted intensity domain. We find that at low exposure levels typical of those being considered for screening CT, the Poisson-likelihood based approaches outperform the PWLS objective as well as a standard approach based on adaptive filtering followed by deconvolution. At higher exposure levels, the approaches all perform similarly.