A vector-valued PDE model unifying anisotropic diffusion and shock filter for color images denoising and deblurring

Abstract

This paper proposes a novel and efficient method for the restoration of color images degraded by the combined effects of noise and blur. To address this challenging inverse problem, a mixed partial differential equation (PDE) model based on a semi-implicit numerical scheme is developed for color image restoration. The proposed approach integrates anisotropic diffusion and shock filtering within a unified vector-valued framework, allowing the different color channels to be processed jointly while preserving their mutual correlation. This formulation enables selective smoothing that efficiently suppresses noise in homogeneous regions while simultaneously enhancing and preserving significant edge and structural features. Extensive experimental results on various color images demonstrate that the proposed method consistently outperforms existing color image restoration techniques. Quantitative evaluations based on standard image quality assessment metrics, including peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM), confirm the superior restoration performance of the proposed approach. Furthermore, the proposed model maintains chromatic consistency across color channels during simultaneous denoising and deblurring, effectively preventing the introduction of color artifacts and ensuring visually faithful restoration results. The numerical implementation of the proposed method is based on a semi-implicit scheme.