Singular Value Decomposition for Image Processing: Methods and Applications

Abstract

Singular value decomposition (SVD) has significant practical value in image processing. It decomposes the image into different levels of information with varying amounts of information. The most important application is image compression. At the same time, it is also the mathematical basis for image denoising and watermark embedding, and is a classic tool for the underlying processing of digital images. This paper first introduces the mathematical form and geometric meaning of SVD. Subsequently, at the application level, it reviews six typical methods: fingerprint recognition, image denoising, watermark embedding, image compression, super-resolution enhancement, and ground-penetrating radar images. Each method is based on the energy concentration characteristic and low-rank approximation ability of SVD, and designs corresponding singular value processing strategies for different tasks. As a core tool of linear algebra, SVD demonstrates strong low-rank representation and feature extraction capabilities in image compression, denoising, watermarking, and enhancement, with remarkable effects. However, computational efficiency, geometric robustness, and adaptive threshold selection remain key bottlenecks. In the future, it is necessary to combine randomized algorithms, GPU parallelization, invariant feature alignment, and data-driven threshold learning to promote the in-depth application of SVD in real-time and complex scenarios.