Visualization of the distortion induced by nonlinear noise reduction in computed tomography

Purpose: We developed a method to visualize the image distortion induced by nonlinear noise reduction algorithms in computed tomography (CT) systems.

Approach: Nonlinear distortion was defined as the induced residual when testing a reconstruction algorithm by the criteria for a linear system. Two types of images were developed: a nonlinear distortion of an object (${\mathrm{NLD}}_{\text{object}}$) image and a nonlinear distortion of noise (${\mathrm{NLD}}_{\text{noise}}$) image to visualize the nonlinear distortion induced by an algorithm. Calculation of the images requires access to the sinogram data, which is seldomly fully provided. Hence, an approximation of the ${\mathrm{NLD}}_{\text{object}}$ image was estimated. Using simulated CT acquisitions, four noise levels were added onto forward projected sinograms of a typical CT image; these were noise reduced using a median filter with the simultaneous iterative reconstruction technique or a total variation filter with the conjugate gradient least-squares algorithm. The linear reconstruction technique filtered back-projection was also analyzed for comparison.

Results: Structures in the ${\mathrm{NLD}}_{\text{object}}$ image indicated contrast and resolution reduction of the nonlinear denoising. Although the approximated ${\mathrm{NLD}}_{\text{object}}$ image represented the original ${\mathrm{NLD}}_{\text{object}}$ image well, it had a higher random uncertainty. The ${\mathrm{NLD}}_{\text{noise}}$ image for the median filter indicated both stochastic variations and structures reminding of the object while for the total variation filter only stochastic variations were indicated.

Conclusions: The developed images visualize nonlinear distortions of denoising algorithms. The object may be distorted by the noise and vice versa. Analyzing the distortion correlated to the object is more critical than analyzing a distortion of stochastic variations. The absence of nonlinear distortion may measure the robustness of the denoising algorithm.