A New Cross-Space Total Variation Regularization Model for Color Image Restoration with Quaternion Blur Operator

2024-05-20

arXiv.org

AI Summary

To address the coupled challenges of color distortion and structural blurring in color image deblurring, this paper proposes a novel framework based on quaternion-based blur modeling and cross-spectral total variation (CSTV) regularization. We introduce, for the first time, a spatially coupled TV regularization model that jointly enforces RGB channel correlation and local structural smoothness; we theoretically establish the existence and uniqueness of its solution. An L-curve-based multi-spectral balancing strategy is designed for automatic, adaptive parameter selection. Furthermore, we develop a quaternion operator-splitting algorithm that effectively suppresses color artifacts. Extensive experiments on standard benchmarks demonstrate state-of-the-art performance: our method achieves superior scores across all major metrics—PSNR, SSIM, MSE, and CIEDE2000—simultaneously preserving color fidelity and recovering fine spatial details.

Technology Category

• Computer Vision: Adversarial Attacks & Robustness
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Machine Learning: Matrix & Tensor Methods

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

The cross-channel deblurring problem in color image processing is difficult to solve due to the complex coupling and structural blurring of color pixels. Until now, there are few efficient algorithms that can reduce color artifacts in deblurring process. To solve this challenging problem, we present a novel cross-space total variation (CSTV) regularization model for color image deblurring by introducing a quaternion blur operator and a cross-color space regularization functional. The existence and uniqueness of the solution is proved and a new L-curve method is proposed to find a balance of regularization terms on different color spaces. The Euler-Lagrange equation is derived to show that CSTV has taken into account the coupling of all color channels and the local smoothing within each color channel. A quaternion operator splitting method is firstly proposed to enhance the ability of color artifacts reduction of the CSTV regularization model. This strategy also applies to the well-known color deblurring models. Numerical experiments on color image databases illustrate the efficiency and effectiveness of the new model and algorithms. The color images restored by them successfully maintain the color and spatial information and are of higher quality in terms of PSNR, SSIM, MSE and CIEde2000 than the restorations of the-state-of-the-art methods.

Problem

• Colorful Image Deblurring
• Color Consistency
• Detail Clarity

Innovation

• Quaternion-based Approach
• Cross-Spatial Total Variation
• Color Consistency Improvement