Choosing Anisotropic Voxel Dimensions in Optimization-Based Image Reconstruction for Limited Angle CT

Resolution of reconstructions in limited angle X-ray computed tomography (CT) is inherently anisotropic due to the limited angular range of acquired projections. This justifies the use of anisotropic voxels in limited angle image reconstruction. For analytic reconstruction algorithms, this only changes the intervals at which the reconstruction is sampled, but for optimization-based image reconstruction, changing the voxel dimensions redefines the reconstruction optimization problem and can have pronounced effects on the reconstructed image. In this work we investigate the choice of anisotropic voxel dimensions in optimization-based image reconstruction for limited angle CT. In particular, a 2D simulation study is performed to assess the optimal choice of pixel dimension in the longitudinal direction the direction of lowest resolution. It is demonstrated that as this pixel dimension is decreased, deterioration of system matrix conditioning can lead to severe distortion in reconstructions performed with low regularization strength. This conditioning issue occurs at approximately the point where the number of pixels is equal to the number of measurements. While the distortion can be mitigated by increasing regularization, our results suggest that there are structures which are only resolvable by using even smaller voxel sizes.