Purpose: With the goal of producing a less computationally intensive alternative to fully iterative penalized-likelihood image reconstruction, our group has explored the use of penalized-likelihood sinogram restoration for transmission tomography. Previously, we have exclusively used a quadratic penalty in our restoration objective function. However, a quadratic penalty does not excel at preserving edges while reducing noise. Here, we derive a restoration update equation for nonquadratic penalties. Additionally, we perform a feasibility study to extend our sinogram restoration method to a helical cone-beam geometry and clinical data.
Methods: A restoration update equation for nonquadratic penalties is derived using separable parabolic surrogates (SPS). A method for calculating sinogram degradation coefficients for a helical cone-beam geometry is proposed. Using simulated data, sinogram restorations are performed using both a quadratic penalty and the edge-preserving Huber penalty. After sinogram restoration, Fourier-based analytical methods are used to obtain reconstructions, and resolution-noise trade-offs are investigated. For the fan-beam geometry, a comparison is made to image-domain SPS reconstruction using the Huber penalty. The effects of varying object size and contrast are also investigated. For the helical cone-beam geometry, we investigate the effect of helical pitch (axial movement/rotation). Huber-penalty sinogram restoration is performed on 3D clinical data, and the reconstructed images are compared to those generated with no restoration.
Results: We find that by applying the edge-preserving Huber penalty to our sinogram restoration methods, the reconstructed image has a better resolution-noise relationship than an image produced using a quadratic penalty in the sinogram restoration. However, we find that this relatively straightforward approach to edge preservation in the sinogram domain is affected by the physical size of imaged objects in addition to the contrast across the edge. This presents some disadvantages of this method relative to image-domain edge-preserving methods, although the computational burden of the sinogram-domain approach is much lower. For a helical cone-beam geometry, we found applying sinogram restoration in 3D was reasonable and that pitch did not make a significant difference in the general effect of sinogram restoration. The application of Huber-penalty sinogram restoration to clinical data resulted in a reconstruction with less noise while retaining resolution.
Conclusions: Sinogram restoration with the Huber penalty is able to provide better resolution-noise performance than restoration with a quadratic penalty. Additionally, sinogram restoration with the Huber penalty is feasible for helical cone-beam CT and can be applied to clinical data.