Evaluation of noise and resolution properties of penalized-likelihood CT sinogram smoothing and restoration algorithms

Abstract

In this work we study the resolution and noise properties of penalized-likelihood sinogram smoothing and restoration algorithms that we have been developing for preprocessing of computed tomography (CT) data. We have formulated 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. The degradations that afflict raw CT data include beam hardening, off-focal radiation, detector afterglow, and electronic crosstalk, among others. We estimate the line integrals by maximizing a roughness-penalized Poisson likelihood-based objective function. The maximization algorithm is based on the separable paraboloidal surrogates strategy and image reconstruction can then proceed by use of existing, non-iterative approaches. In the case of sinogram smoothing, the only degradation modeled directly is noise; the other effects can then be corrected for by standard means. In the case of sinogram restoration, a number of different degradations are included directly in the objective function. We demonstrate that the approaches can correct for sinogram degradations, eliminating the image artifacts caused by beam hardening and off-focal radiation. We also evaluate the local modulation transfer function, local noise power spectrum, and local noise equivalent quanta in a numerical test phantom and find that the proposed approaches outperform standard approaches based on deconvolution and shift-invariant filtration.