Comparison of three undersampling approaches in computed tomography reconstruction.

Area of Science:

• Medical Imaging
• Computational Imaging
• Radiology

Background:

• Computed tomography (CT) utilizes projection data undersampling to reduce X-ray radiation dose and data size for faster imaging.
• Optimizing undersampling strategies is crucial for maintaining image quality despite reduced data acquisition.
• This study investigates three distinct undersampling approaches to determine the most effective method for CT image reconstruction.

Purpose of the Study:

• To compare the efficacy of three different undersampling strategies in computed tomography (CT).
• To identify the optimal undersampling approach for achieving the best CT image reconstruction quality at a given undersampling ratio.
• To provide insights into the mathematical properties of undersampling operators.

Main Methods:

• Three undersampling methods were analyzed: regular view, regular ray, and random ray undersampling.
• Undersampling operators were represented using singular value decomposition (SVD) based on the singular vectors of the full projection operator.
• Singular value spectra and vectors were compared across the different undersampling strategies.

Main Results:

• Random ray undersampling demonstrated superior preservation of the full projection operator's properties compared to regular view and regular ray methods.
• Numerical experiments confirmed that random ray undersampling results in lower CT image reconstruction errors.
• The effectiveness of random undersampling was particularly evident at higher undersampling ratios.

Conclusions:

• Random ray undersampling is the most effective strategy for preserving information in CT projection data.
• This method significantly outperforms regular view and regular ray undersampling in terms of CT image reconstruction quality.
• The findings suggest random undersampling as a preferred approach for dose reduction and rapid imaging in CT.