A Weighted Fidelity and Regularization-Based Method for Mixed or Unknown Noise Removal from Images on Graphs

Area of Science:

• Computer Vision
• Image Processing
• Graph Signal Processing

Background:

• Traditional image denoising is mature in Euclidean domains.
• Real-world applications increasingly involve irregular data on graphs.
• Existing methods struggle with mixed or unknown noise on graph-structured data.

Purpose of the Study:

• To develop a novel model for image denoising on graphs with mixed or unknown noise.
• To effectively remove noise while preserving essential image features.
• To address limitations of current denoising techniques in irregular domains.

Main Methods:

• A weighted fidelity term using L1 and L2 norms to analyze mixed noise distributions.
• A sparse regularization term incorporating wavelet frame transform on graphs.
• Optimization using augmented Lagrangian and accelerated proximal gradient methods.

Main Results:

• The proposed model effectively removes mixed and unknown noise (Poisson, Gaussian, impulse).
• Wavelet frame transform on graphs preserves image feature details.
• Comparative analyses show superior performance over existing algorithms on synthetic and real graph data.

Conclusions:

• The novel graph-based denoising model is effective and efficient for irregular domains.
• It provides a new approach for handling complex noise in computer vision and geometric modeling.
• The method successfully balances noise removal with feature preservation on graph data.