Assessment of vectorial total variation penalties on realistic dual-energy CT data

Vectorial extensions of total variation have recently been developed for regularizing the reconstruction and denoising of multi-channel images, such as those arising in spectral computed tomography. Early studies have focused mainly on simulated, piecewise-constant images whose structure may favor total-variation penalties. In the current manuscript, we apply vectorial total variation to real dual-energy CT data of a whole turkey in order to determine if the same benefits can be observed in more complex images with anatomically realistic textures. We consider the total nuclear variation ($\text{T}{\text{V}}_{\text{N}}$) as well as another vectorial total variation based on the Frobenius norm ($\text{T}{\text{V}}_{\text{F}}$) and standard channel-by-channel total variation ($\text{T}{\text{V}}_{\text{S}}$). We performed a series of 3D TV denoising experiments comparing the three TV variants across a wide range of smoothness parameter settings, optimizing each regularizer according to a very-high-dose 'ground truth' image. Consistent with the simulation studies, we find that both vectorial TV variants achieve a lower error than the channel-by-channel TV and are better able to suppress noise while preserving actual image features. In this real data study, the advantages are subtler than in the previous simulation study, although the $\text{T}{\text{V}}_{\text{N}}$ penalty is found to have clear advantages over either $\text{T}{\text{V}}_{\text{S}}$ or $\text{T}{\text{V}}_{\text{F}}$ when comparing material images formed from linear combinations of the denoised energy images. (paper)