δ-Norm-Based Robust Regression With Applications to Image Analysis.

Area of Science:

• Computer Vision
• Machine Learning
• Image Processing

Background:

• Traditional regression models use matrix norms (e.g., l1, l2) sensitive to outliers.
• This sensitivity leads to poor performance on heavily corrupted images, misdirecting the regression process.
• Existing norms struggle to suppress the negative influence of noisy data.

Purpose of the Study:

• To propose a novel delta-norm (δ-norm) for robust regression that is less sensitive to outliers.
• To develop a delta-norm-based robust regression (DRR) model that accounts for data structure.
• To extend DRR to a multiscale version for handling mixed noise.

Main Methods:

• Introduced a novel δ-norm that counts non-zero blocks, mitigating outlier impact and considering data structure.
• Developed the δ-norm-based robust regression (DRR) by mapping data to kernel space and using the δ-norm.
• Explored an explicit kernel function to derive a closed-form solution for efficient DRR computation.
• Extended DRR to a multiscale version to address mixed noise influences.

Main Results:

• The proposed δ-norm effectively weakens the impact of outliers in regression.
• DRR demonstrated superior performance compared to existing robust regression models on image classification and background modeling.
• The closed-form solution ensures efficient solvability of the DRR model.
• The multiscale extension further enhanced robustness against mixed noise.

Conclusions:

• The novel δ-norm and DRR provide a more robust regression approach for image analysis, especially with corrupted data.
• DRR outperforms current state-of-the-art methods in handling outliers and mixed noise.
• The efficient closed-form solution makes DRR practical for real-world applications.