How little data is enough? Phase-diagram analysis of sparsity-regularized X-ray computed tomography

Area of Science:

• Medical Imaging
• Signal Processing
• Computational Science

Background:

• Compressed sensing (CS) utilizes phase diagrams to analyze sparsity and sampling relationships.
• X-ray computed tomography (CT) reconstruction accuracy depends on the number of projections.
• Existing CS theoretical results for phase diagrams do not directly apply to X-ray CT.

Purpose of the Study:

• To adapt phase-diagram analysis for empirical use in X-ray CT.
• To systematically determine the minimum number of projections for accurate sparsity-regularized CT reconstruction.
• To provide quantitative insights into undersampling effects in CT imaging.

Main Methods:

• Applied phase-diagram analysis, a CS tool, to X-ray CT.
• Conducted three case studies to evaluate phase-diagram analysis for undersampling scenarios.
• Investigated performance with Gaussian sensing matrices and randomized CT measurements versus standard sampling.

Main Results:

• Demonstrated cases where X-ray CT with phase-diagram analysis achieved performance comparable to optimal CS strategies (Gaussian sensing).
• Found that randomized CT measurements did not outperform standard structured sampling patterns.
• Showed preliminary evidence of phase-diagram analysis predicting sufficient projections for total-variation regularized reconstruction.

Conclusions:

• Phase-diagram analysis is a viable empirical tool for X-ray CT, offering quantitative answers on undersampling.
• The study provides a systematic approach to optimize projection acquisition in CT.
• Results guide the understanding of sparsity-regularized reconstruction and sampling strategies in medical imaging.