Publication

Abstract : The rapid growth of digital images in communication, storage, and edge-device applications has sustained interest in compression methods that are both interpretable and quality-aware. Singular Value Decomposition (SVD) is a mathematically grounded approach to lossy image compression because it exploits the low-rank structure of image matrices and provides the optimal rank- k approximation in the Frobenius-norm sense. Although SVD is widely used in image-processing research, the compression literature is scattered across pure rank truncation, hybrid transform methods, optimization-guided rank selection, and learning-assisted variants. This survey reviews more than 50 SVD-centered works from 2007 to 2024. Additional contextual references published after 2024 were added during revision but were not counted in the primary 2007–2024 corpus. The retained works are organized into a revised five-category taxonomy: (C1) pure SVD rank- k approximation, (C2) hybrid SVD-DCT methods, (C3) hybrid SVD-DWT methods, (C4) optimization-assisted SVD, and (C5) learning-assisted SVD. Application-area papers outside the core compression mechanism are treated only as related evaluation contexts unless SVD is the central compression mechanism. The paper expands the compression pipeline from input image to stored singular triplets and reconstructed output, adds visual rank- k reconstruction examples, and compares compression ratio, PSNR, SSIM, MSE, and computational complexity across method families. The analysis also positions SVD relative to modern codecs such as JPEG XL, HEVC, AV1/AVIF, and neural compression. The synthesis shows that hybrid SVD methods typically improve PSNR over pure SVD at comparable compression ratios, while optimization-guided and patch-adaptive approaches provide the strongest quality-control mechanisms. Finally, the survey identifies open challenges in real-time high-resolution processing, adaptive color-channel rank allocation, perceptual metrics beyond PSNR, standardized benchmarking, and practical integration of SVD modules with modern compression standards.