Quantifying admissible undersampling for sparsity-exploiting iterative image reconstruction in X-ray CT.

Area of Science:

• Medical Imaging
• Image Reconstruction
• Computational Imaging

Background:

• Compressive sensing methods like total variation (TV) minimization promise reduced sampling in iterative image reconstruction.
• Quantifying sampling reduction in computed tomography (CT) is challenging due to ill-defined concepts of full sampling and admitted undersampling.
• Existing imaging models lack precise definitions for adequate data acquisition.

Purpose of the Study:

• To propose rigorous definitions of full sampling for CT imaging models.
• To establish sufficient-sampling conditions (SSCs) for quantifying undersampling in sparsity-exploiting reconstruction.
• To evaluate the impact of undersampling on breast CT reconstruction using TV minimization.

Main Methods:

• Introduced four novel sufficient-sampling conditions (SSCs) based on the system matrix condition number.
• Applied SSCs as benchmarks for full sampling in breast CT.
• Conducted numerical simulations to analyze factors influencing admissible undersampling in TV-minimization reconstruction.

Main Results:

• Defined quantifiable criteria for full sampling in CT, addressing invertibility and stability.
• Quantified the degree of undersampling permissible by TV-minimization in breast CT.
• Identified relationships between object sparsity, reconstruction method (few-view vs. few-detector), and admissible undersampling levels.

Conclusions:

• The proposed SSCs provide a framework for defining and quantifying full sampling in CT.
• This work enables a more precise understanding of sampling efficiency in compressive sensing CT.
• The findings are crucial for optimizing data acquisition and reconstruction in sparse-data CT applications.