Graph-cut based discrete-valued image reconstruction.

Area of Science:

• Computer Vision
• Image Processing
• Optimization

Background:

• Graph-cut methods are effective for image labeling and denoising.
• Linear image mappings hinder graph-cut application in discrete-amplitude reconstruction.
• Discrete linear inverse problems pose challenges due to variable mixing from sensing operators.

Purpose of the Study:

• Develop a graph-cut framework for direct solution of discrete amplitude linear image reconstruction problems.
• Address limitations imposed by linear sensing operators in inverse problems.
• Propose a surrogate energy functional for efficient graph-cut application.

Main Methods:

• Analyzed cost functions of discrete linear inverse problems.
• Developed a surrogate energy functional to overcome sensing operator challenges.
• Devised a monotonic iterative algorithm using the surrogate functional.
• Conducted experiments with local convolutional and nonlocal tomographic operators.

Main Results:

• Demonstrated robustness to noise and stability to regularization parameter changes.
• Showcased superior performance in limited-angle tomographic reconstruction.
• Outperformed state-of-the-art discrete and continuous reconstruction techniques in challenging scenarios.

Conclusions:

• The proposed graph-cut framework effectively solves discrete amplitude linear image reconstruction problems.
• The surrogate energy functional enables efficient application of graph-cuts to these problems.
• The method shows significant advantages in complex, discrete-valued image reconstruction tasks.