A fast method based on NESTA to accurately reconstruct CT image from highly undersampled projection measurements

Area of Science:

• Medical Imaging
• Computational Science
• Optimization Algorithms

Background:

• Compressed sensing (CS) CT image reconstruction involves minimizing total-variation (TV) while maintaining data fidelity and nonnegativity.
• Existing algorithms struggle with computational efficiency and image quality.

Purpose of the Study:

• To develop a faster and more accurate algorithm for TV minimization in CT reconstruction.
• To address limitations in current CS-based CT reconstruction methods.

Main Methods:

• Implemented Nesterov's algorithm (NESTA), leveraging Nesterov's smoothing and sequence averaging for improved convergence.
• Compared NESTA against Simultaneous Algebraic Reconstruction Technique-TV (SART-TV) and Split-Bregman (SpBr) algorithms.
• Validated performance using digital and physical phantoms with undersampled projection data.

Main Results:

• NESTA achieved significant CT number error reduction across multiple phantoms (e.g., Shepp-Logan: 51.76HU to 9.98HU; Catphan 600: 50.13HU to 0.32HU).
• Substantial error reduction was observed on an anthropomorphic head phantom (84.21HU to 1.01HU).
• Demonstrated superior performance in computational efficiency and image quality compared to SART-TV and SpBr.

Conclusions:

• NESTA is a promising method for CS-based CT reconstruction, offering enhanced accuracy and efficiency.
• This study represents the first application of NESTA in this domain.
• Further research and optimization are recommended to fully realize NESTA's potential.