Penalty weighting for statistical iterative CT reconstruction

The core of common statistical iterative reconstruction methods is the maximization of the likelihood that the reconstructed image belongs to the measured data. Since the underlying inverse problem is ill-posed, the likelihood function is often extended by a penalty term to form an objective function, which contains assumptions about the content of the image, most often by favoring smooth images. As can be shown for common likelihood functions given in literature, the influence of a smoothing penalty term, and in consequence the smoothing effect within the image, varies spatially. This results in an inhomogeneous resolution of the reconstructed image, which can reduce the diagnostic value of the image. We present a method to calculate a spatially varying weighting function for the penalty term, which leads to a likelihood function with constant strength of the smoothing effect over the whole image. For verification, simulated data are reconstructed iteratively. While images reconstructed without weighting show varying sharpness of boundaries, images reconstructed with weighting are clearly advantageous with respect to this. The resolution homogeneity is bought by a different noise distribution: While the noise distribution without weighting is homogeneous, the noise distribution with weighting varies spatially.