Multiplicative Noise and Blur Removal by Framelet Decomposition and -Based L-Curve Method

Area of Science:

• Image processing
• Applied mathematics
• Computer vision

Background:

• Multiplicative noise and blur significantly degrade image quality.
• Existing image restoration methods often struggle with complex noise models.
• Framelet-based approaches offer powerful tools for image representation and analysis.

Purpose of the Study:

• To develop a robust framelet-based convex optimization model for multiplicative noise and blur removal.
• To introduce a variable decomposition strategy for separating image and noise components.
• To enhance image restoration performance compared to current methods.

Main Methods:

• Image representation using framelet expansion.
• Variable decomposition to model multiplicative noise.
• Optimization using L1-norm for framelet coefficients and statistical measures for noise.
• Convex optimization solved via alternating direction of multiplier method.
• Regularization parameter selection using L1-based L-curve method.

Main Results:

• The proposed framelet-based model effectively removes multiplicative noise and blur.
• Variable decomposition successfully separates image and noise variables.
• Convexity ensures efficient and stable solutions.
• Numerical examples demonstrate superior performance over existing methods.
• The L1-based L-curve method provides effective regularization parameter selection.

Conclusions:

• The framelet-based convex optimization model is highly effective for multiplicative noise and blur removal.
• The variable decomposition approach is crucial for handling multiplicative noise.
• The method offers significant improvements in image restoration quality and efficiency.