RobOMP: Robust variants of Orthogonal Matching Pursuit for sparse representations

Area of Science:

• Signal Processing
• Machine Learning
• Computer Vision

Background:

• Sparse coding seeks efficient data representations using dictionaries.
• Orthogonal Matching Pursuit (OMP) is a fast sparse coding algorithm.
• OMP's Mean Squared Error (MSE) minimization is sensitive to outliers.

Purpose of the Study:

• Introduce robust variants of OMP (RobOMP) to address outlier sensitivity.
• Develop adaptive methods for sparse coding that are resilient to data imperfections.
• Enhance sparse representation performance in the presence of noise and missing data.

Main Methods:

• Developed five RobOMP variants based on M-estimators and linear models.
• Employed Iteratively Reweighted Least Squares (IRLS) for robust weight adaptation.
• Utilized a learned weight vector to model data distribution robustly.

Main Results:

• RobOMP variants significantly outperform MSE-based OMP and other robust methods.
• Demonstrated superior performance on synthetic data with various noise distributions.
• Showcased effectiveness in image recognition tasks with occlusions and missing pixels.

Conclusions:

• RobOMP provides principled, parameter-free alternatives to standard OMP.
• The proposed robust sparse coding framework is effective for denoising and other applications.
• RobOMP enhances sparse representation accuracy and reliability in real-world scenarios.