A New Non-Linear Hyperbolic-Parabolic Coupled PDE Model for Image Despeckling

Area of Science:

• Computational Mathematics
• Image Processing
• Partial Differential Equations

Background:

• Image noise, particularly speckle noise, degrades image quality and hinders analysis.
• Existing Partial Differential Equation (PDE)-based methods often struggle with preserving fine details and edges.
• Nonlocal methods offer improved performance but can be computationally intensive.

Purpose of the Study:

• To propose a novel non-linear hyperbolic-parabolic coupled PDE model for image despeckling.
• To enhance the preservation of edge information in despeckled images.
• To demonstrate the effectiveness and competitiveness of the proposed model against existing methods.

Main Methods:

• Development of a non-linear hyperbolic-parabolic coupled PDE system.
• Inclusion of a separate equation for edge variable calculation.
• Application of a generalized weighted average finite-difference scheme and Gauss-Seidel iteration for solving the system.
• Mathematical proof of the existence of a weak solution using Schauder fixed point theorem.

Main Results:

• The proposed model effectively removes speckle noise from gray-level images.
• Improved preservation of edge information compared to standard PDE-based models.
• Demonstrated effectiveness on artificial speckle noise and real Synthetic Aperture Radar (SAR) and Ultrasound images.
• Competitive performance against nonlocal techniques.

Conclusions:

• The proposed non-linear coupled PDE model offers a significant advancement in image despeckling.
• The method excels in preserving image details, particularly edges.
• This work represents the first utilization of non-linear coupled hyperbolic-parabolic PDEs for image despeckling, offering a promising new direction.