Optimization model for multiplicative noise and blur removal based on Gaussian curvature regularization

Area of Science:

• Image processing
• Computer vision
• Applied mathematics

Background:

• Image restoration is challenging due to simultaneous blur and multiplicative noise.
• Existing methods may struggle with preserving fine details or introducing artifacts.

Purpose of the Study:

• To develop a novel variational restoration model for images corrupted by multiplicative noise and blur.
• To preserve image sharpness, textures, and fine structures during restoration.

Main Methods:

• Introduced a variational restoration model with a convex data-fitting term.
• Utilized Gaussian curvature as a regularizer to handle multiplicative Gamma noise.
• Employed the augmented Lagrange multiplier method with splitting techniques for optimization.

Main Results:

• The proposed model effectively removes multiplicative Gamma noise.
• The method eliminates staircase effects while preserving edges, textures, and fine structures.
• Numerical results indicate superior performance in simultaneous deblurring and noise removal.

Conclusions:

• The developed variational model offers a robust solution for restoring degraded images.
• The approach shows significant potential for outperforming existing methods in complex image restoration tasks.