# Quantization-aware Matrix Factorization for Low Bit Rate Image Compression

arXiv: https://arxiv.org/abs/2408.12691 · HTML: https://mlsanity.com/paper/2408.12691/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 40 references that are in the map.
- First posted on arXiv 22 Aug 2024.

## Builds on (most cited first, 7 of 7)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Variational image compression with a scale hyperprior](https://mlsanity.com/paper/1802.01436/) (2018)
- [Learned Image Compression with Discretized Gaussian Mixture Likelihoods and Attention Modules](https://mlsanity.com/paper/2001.01568/) (2020)
- [Learned Image Compression with Mixed Transformer-CNN Architectures](https://mlsanity.com/paper/2303.14978/) (2023)
- [Lossy Image Compression with Conditional Diffusion Models](https://mlsanity.com/paper/2209.06950/) (2022)
- [Image Compression Based on Compressive Sensing: End-to-End Comparison with JPEG](https://mlsanity.com/paper/1706.01000/) (2017)

## Abstract (arXiv)

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, where quantization errors cannot be incorporated into the compression process. The sensitivity of these methods, especially SVD-based ones, to quantization errors significantly degrades reconstruction quality. 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 factor 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 (BCD) scheme, with subproblems having closed-form solutions. Our experiments on the Kodak and CLIC 2024 datasets demonstrate that our QMF compression method consistently outperforms JPEG at low bit rates below 0.25 bits per pixel (bpp) and remains comparable at higher bit rates. We also assessed our method's capability to preserve visual semantics by evaluating an ImageNet pre-trained classifier on compressed images. Remarkably, our method improved top-1 accuracy by over 5 percentage points compared to JPEG at bit rates under 0.25 bpp. The project is available at https://github.com/pashtari/lrf .