Image Compression Using Singular Value Decomposition
This is an incremental analysis for image compression researchers, showing SVD is not practical compared to existing codecs.
The study tackled image compression using Singular Value Decomposition and low-rank approximations, finding that the method consistently underperformed standard formats like JPEG and JPEG2000, with compression ratios worse and sometimes exceeding original image sizes at low error levels.
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.