Quantization-aware matrix factorization for low bit rate image compression

Lossy image compression is essential for efficient transmission and storage. Traditional compression methods mainly rely on discrete cosine transform (DCT) or singular value decomposition (SVD), both of which represent image data in continuous domains and, therefore, necessitate carefully designed quantizers. Notably, these methods consider quantization as a separate step, which prevents quantization errors from being incorporated into the compression process and degrades the reconstruction quality, particularly in SVD-based methods. To address this issue, we introduce a quantization-aware matrix factorization (QMF) to develop a novel lossy image compression method. QMF provides a low-rank representation of the image data as a product of two smaller matrices, with elements constrained to bounded integer values, thereby effectively integrating quantization with low-rank approximation. We propose an efficient, provably convergent iterative algorithm for QMF using a block coordinate descent scheme, with subproblems having closed-form solutions. Our experiments demonstrate that our method consistently outperforms JPEG at low bit rates below 0.25 bits per pixel. We also demonstrated that our method has an improved capability to preserve visual semantics compared to JPEG at low bit rates by evaluating an ImageNet pre-trained classifier on compressed images. The project is available at https://github.com/pashtari/qmf .