Sparse modeling for image inpainting: A multi-scale morphological patch-based k-SVD and group-based PCA

Abstract

Image inpainting, a crucial task in image restoration, aims to reconstruct highly degraded images with missing pixels while preserving structural and textural integrity. Traditional patch-based and group-based sparse representation methods often struggle with visual artifacts and over-smoothing, limiting their effectiveness. To address these challenges, we propose a novel multi-scale morphological patch-based and group-based sparse representation learning approach for image inpainting. Our method enhances image inpainting by integrating morphological patch-based sparse representation (M-PSR) learning using k-singular value decomposition (k-SVD) and group-based sparse representation using principal component analysis (PCA) to construct adaptive dictionaries for improved reconstruction accuracy. Additionally, we employ the alternating direction method of multipliers (ADMM) to optimize the integration of morphological patch and group based sparse representations, enhancing restoration quality. Extensive experiments on various degraded images demonstrate that our approach outperforms state-of-the-art methods in terms of the peak signal-to-noise ratio (PSNR) and the structural similarity index measure (SSIM). The proposed method effectively reconstructs images corrupted by missing pixels, scratches, and text inlays, achieving superior structural coherence and perceptual quality. This work contributes a robust and efficient solution for image inpainting, offering significant advances in sparse modeling and morphological image processing.