Sinogram restoration in computed tomography with a non-quadratic, edge-preserving penalty

With the goal of producing a less computationally intensive alternative to fully-iterative penalized-likelihood image reconstruction, our group has been exploring the use of penalized-likelihood sinogram restoration for transmission tomography. Sinogram restoration allows for the correction of anode angle effects, off-focal radiation, detector afterglow, crosstalk, beam hardening, and noise effects without the backprojections and reprojections used in fully-iterative reconstruction methods. After sinogram restoration, reconstruction is performed using traditional filtered backprojection methods. Previously, we have exclusively used a quadratic penalty in our restoration objective function. Here, we derive a restoration update equation using separable parabolic surrogates (SPS) for non-quadratic penalties. Using the edge-preserving Huber penalty in our sinogram restoration, we show improvements in resolution-variance tradeoffs compared to using a quadratic penalty in the sinogram restoration. However, this simple approach to edge preservation in the sinogram domain is affected by the physical size of the edge and not just the increase in contrast across the edge. This is a disadvantage relative to image-domain edge-preserving methods.