Statistical methods for tomographic image reconstruction have shown considerable potential for improving image quality in X-ray CT. Penalized-likelihood (PL) image reconstruction methods require maximizing an objective function that is based on the log-likelihood of the sinogram measurements and on a roughness penalty function to control noise. In transmission tomography, PL methods (and MAP methods) based on conventional quadratic regularization functions lead to nonuniform and anisotropic spatial resolution, even for idealized shift-invariant imaging systems. We have previously addressed this problem for parallel-beam emission tomography by designing data-dependent, shift-variant regularizers that improve resolution uniformity. This paper extends those methods to the fan-beam geometry used in X-ray CT imaging. Simulation results demonstrate that the new method for regularization design requires very modest computation and leads to nearly uniform and isotropic spatial resolution in the fan-beam geometry when using quadratic regularization.

Statistical methods for tomographic image reconstruction lead to improved spatial resolution and noise properties in PET. Penalized-likelihood (PL) image reconstruction methods involve maximizing an objective function that is based on the log-likelihood of the sinogram measurements and on a roughness penalty function to control noise. In emission tomography, PL methods (and MAP methods) based on conventional quadratic regularization functions lead to nonuniform and anisotropic spatial resolution, even for idealized shift-invariant imaging systems. We have previously addressed this problem for parallel-beam 2D emission tomography [1], and for fan-beam 2D transmission tomography [2] by designing data-dependent, shift-variant regularizers that improve resolution uniformity and isotropy. even for idealized shift-invariant imaging systems. This paper extends those methods to 3D cylindrical PET, using an analytical design approach that is numerically efficient.

In X-ray CT, statistical methods for tomographic image reconstruction create images with better noise properties than conventional Filtered Back Projection (FBP) techniques. Penalized-likelihood (PL) image reconstruction methods maximize an objective function based on the log-likelihood of sinogram measurements and on a user defined roughness penalty which controls noise. Penalized-likelihood methods (as well as Penalized Weighted Least Squares methods) based on conventional quadratic regularizers result in nonuniform and anisotropic spatial resolution. We have previously addressed this problem for 2D emission tomography, 2D fan-beam transmission tomography, and 3D cylindrical emission tomography. This paper extends those methods to 3D multi-slice axial CT with small cone angles.