A 3D study comparing filtered backprojection, weighted least squares, and penalized weighted least squares for CT reconstruction

We have extended 2D weighted least squares and penalized weighted least squares transmission reconstruction methods (WLSTR and PWLSTR respectively) to 3D to explore their impact on image noise and spatial resolution. 3D sinograms of circular and elliptical water cylinders were simulated using a conventional third generation CT system geometry. Data were generated using the realistic CT simulation software CATSIM. Resolution-Noise curves demonstrated that for high contrast wires the in-plane resolution can be improved using PWLS with a Huber-like prior compared to the resolution of the respective FBP image, maintaining the noise, or the noise can be reduced matching the resolution. The achieved noise reduction is greater for the elliptical cylinder than for the circular cylinder. For both phantoms we observed modest degradation in the xz-resolution compared to the in-plane resolution (for equal noise levels). Although in the case of the circular cylinder, improved resolution in the xz-plane is still achievable when compared to the respective resolution in the xz-plane observed in the FBP images (for equal noise levels), the resolution in the xz-plane for the elliptical cylinder is worse than the respective resolution of the FBP images. We present a method and results for resolution recovery in the latter case. Similarly to the previous 2D results, the Huber- like prior resulted in better resolution-noise curves than the quadratic. Furthermore, the use of priors reduces image noise significantly compared to the results generated without a prior.