Abstract
Images are a substantial portion of the internet, making efficient compression important for reducing storage and bandwidth demands. This study investigates the use of Singular Value Decomposition and low-rank matrix approximations for image compression, evaluating performance using relative Frobenius error and compression ratio. The approach is applied to both grayscale and multichannel images to assess its generality. Results show that the low-rank approximations often produce images that appear visually similar to the originals, but the compression efficiency remains consistently worse than established formats such as JPEG, JPEG2000, and WEBP at comparable error levels. At low tolerated error levels, the compressed representation produced by Singular Value Decomposition can even exceed the size of the original image, indicating that this method is not competitive with industry-standard codecs for practical image compression.
Abstract (translated)
图像构成了互联网的很大一部分，因此高效的压缩技术对于减少存储和带宽需求至关重要。本研究探讨了使用奇异值分解（SVD）和低秩矩阵近似来实现图像压缩的方法，并通过相对弗罗贝尼乌斯误差和压缩比来评估其性能。该方法被应用于灰度图和多通道图像，以测试其广泛适用性。 结果表明，在视觉效果上，低秩近似的图像通常与原始图像非常相似；然而，这种压缩技术在相同误差水平下仍然不如JPEG、JPEG2000和WEBP等成熟格式高效。当容许的误差水平较低时，通过奇异值分解生成的压缩表示甚至可能超过原图大小，这表明此方法在实际图像压缩方面与行业标准编解码器相比不具备竞争力。
URL
https://arxiv.org/abs/2512.16226
