Regularization Designs for Uniform Spatial Resolution and Noise Properties in Statistical Image Reconstruction for 3-D X-ray CT

Statistical image reconstruction methods for X-ray computed tomography (CT) provide improved spatial resolution and noise properties over conventional filtered back-projection (FBP) reconstruction, along with other potential advantages such as reduced patient dose and artifacts. Conventional regularized image reconstruction leads to spatially variant spatial resolution and noise characteristics because of interactions between the system models and the regularization. Previous regularization design methods aiming to solve such issues mostly rely on circulant approximations of the Fisher information matrix that are very inaccurate for undersampled geometries like short-scan cone-beam CT. This paper extends the regularization method proposed in [1] to 3-D cone-beam CT by introducing a hypothetical scanning geometry that helps address the sampling properties. The proposed regularization designs were compared with the original method in [1] with both phantom simulation and clinical reconstruction in 3-D axial X-ray CT. The proposed regularization methods yield improved spatial resolution or noise uniformity in statistical image reconstruction for short-scan axial cone-beam CT.