Two-Dimensional Tomography from Noisy Projections Taken at Unknown Random Directions

Area of Science:

• Medical Imaging
• Image Reconstruction
• Signal Processing

Background:

• Computerized tomography (CT) is essential for internal object imaging but requires known projection directions.
• Reconstructing CT images from projections with unknown directions and noise is challenging.
• Existing methods, including diffusion maps, are limited by low signal-to-noise ratios (SNRs).

Purpose of the Study:

• To develop a robust CT reconstruction method for unknown imaging directions and low SNRs.
• To enhance the performance of diffusion map-based CT reconstruction.
• To improve the accuracy and applicability of CT imaging in challenging scenarios.

Main Methods:

• Implemented a two-step denoising process combined with diffusion maps.
• Utilized principal component analysis (PCA) and Wiener filtering for initial projection denoising.
• Applied graph denoising using the Jaccard index to the similarity graph of filtered projections.

Main Results:

• Successfully reconstructed the 2-D Shepp-Logan phantom from noisy projections below established SNR thresholds.
• Demonstrated effective image reconstruction in a numerical experiment simulating abdominal CT.
• Achieved significantly improved reconstruction quality at lower SNRs compared to existing methods.

Conclusions:

• The combined PCA, Wiener filtering, graph denoising, and diffusion map approach enables robust CT reconstruction under challenging conditions.
• This method extends the applicability of CT imaging to scenarios with unknown directions and high noise levels.
• The developed techniques show potential for broader applications in signal processing and image analysis.