Quaternion-Based Image Restoration via Saturation-Value Total Variation and Pseudo-Norm Regularization

Abstract

Color image restoration is a fundamental task in computer vision and image processing, with extensive real-world applications. In practice, color images often suffer from degradations caused by sensor noise, optical blur, compression artifacts, and data loss during the acquisition, transmission, or storage. Unlike grayscale images, color images exhibit high correlations among their RGB channels. Directly extending grayscale restoration methods to color images often leads to issues such as color distortion and structural artifacts. To address these challenges, this paper proposes a novel quaternion-based color image restoration framework. The method integrates low-rank pseudo-norm constraints with saturation-value total variation (SVTV) regularization, effectively enhancing restoration quality in tasks including denoising, deblurring, and inpainting of degraded color images. The proposed algorithm is efficiently solved using the alternating direction method of multipliers (ADMM), and restoration performance is rigorously evaluated through quantitative metrics including peak signal-to-noise ratio (PSNR), structural similarity index measure (SSIM), and S-CIELAB error. Extensive experimental results demonstrate the superior performance of our method compared to existing approaches.