用奇异值分解压缩图像，效果不如主流格式
Image Compression Using Singular Value Decomposition
- 通过低秩矩阵近似实现图像压缩
- 在相同误差下压缩比低于JPEG等标准格式
- 适合理解压缩原理，不适合实际应用
图像占互联网数据的很大比例，高效压缩对降低存储和带宽需求至关重要。本研究探讨了利用奇异值分解和低秩矩阵近似进行图像压缩的方法，采用相对Frobenius误差和压缩比评估性能。该方法应用于灰度图和多通道图像，以检验其通用性。结果表明，低秩近似通常能生成视觉上与原图相似的图像，但在相同误差水平下，压缩效率始终低于JPEG、JPEG2000和WEBP等成熟格式。在低允许误差条件下，奇异值分解产生的压缩表示甚至可能大于原始图像尺寸，说明该方法在实际图像压缩中不具备与行业标准编码器竞争的能力。
原文摘要 · Abstract (English)
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.
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