Perturbation-resilient block-iterative projection methods with application to image reconstruction from projections.

Area of Science:

• Applied Mathematics
• Image Processing
• Optimization

Background:

• Convex feasibility problems are fundamental in various scientific domains.
• Iterative algorithms often face challenges due to perturbations.
• Existing methods may lack robustness in practical applications.

Purpose of the Study:

• To propose a robust block-iterative projection algorithm for convex feasibility problems.
• To demonstrate the algorithm's resilience to bounded and summable perturbations.
• To showcase its utility in image reconstruction using specific functionals.

Main Methods:

• Development of a block-iterative projection algorithm.
• Analysis of convergence properties under perturbations.
• Application to image reconstruction using total variation and negative entropy functionals.

Main Results:

• The proposed algorithm guarantees convergence to a feasible point even with iterative errors.
• The resilience allows steering the solution towards points minimizing a chosen functional.
• Successful illustration in image reconstruction tasks.

Conclusions:

• The algorithm offers a robust solution for consistent convex feasibility problems.
• Its perturbation resilience is a key advantage for real-world applications.
• The approach is effective for image reconstruction, improving solution quality.