A comparison of linear interpolation models for iterative CT reconstruction.

Area of Science:

• Medical Imaging
• Computational Imaging
• Image Reconstruction

Background:

• Model-based iterative reconstruction (MBIR) methods can enhance computed tomography (CT) image quality.
• Selecting appropriate forward projection models and penalty terms is crucial but lacks clear guidance.
• Linear interpolation methods offer a balance between discretization errors and computational cost in CT.

Purpose of the Study:

• To investigate the performance of three linear interpolation forward projection models: distance-driven, Joseph's, and bilinear methods.
• To evaluate their impact on image quality metrics, including bias, noise, and computational cost.
• To assess the influence of statistical weights and penalty terms on model performance.

Main Methods:

• A two-stage methodology was employed to analyze the forward projection models.
• Stage one involved analyzing reconstructed images without statistical weights or penalty terms, incorporating singular value decomposition components.
• Stage two examined the impact of statistical weights and penalty terms on observed differences.

Main Results:

• Fundamental differences in bias and noise were observed among the models.
• Task-based assessment indicated that noise differences balanced out, yielding similar performance.
• The distance-driven method showed reduced bias but increased computational cost; strong penalties minimized model-induced differences.

Conclusions:

• Joseph's method provides a practical compromise between computational cost and effort.
• The distance-driven method can reduce bias at a higher computational cost.
• A key assumption in Joseph's and distance-driven methods was found to be robust with the bilinear method; strong penalties can compensate for model deficiencies.