Image Compression Using Singular Value Decomposition

TL;DR

This paper explores using Singular Value Decomposition for image compression, finding it produces visually similar images but is less efficient than standard codecs like JPEG and WEBP.

Contribution

It evaluates the effectiveness of SVD-based low-rank approximations for image compression across different image types and compares performance with industry-standard methods.

Findings

SVD produces visually similar images at certain error levels.

SVD compression is less efficient than JPEG, JPEG2000, and WEBP.

At low error tolerances, SVD can result in larger file sizes than original images.

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.