Quantization-aware Matrix Factorization for Low Bit Rate Image Compression

TL;DR

This paper introduces a quantization-aware matrix factorization approach for low bit rate image compression, effectively integrating quantization into the low-rank approximation process to improve reconstruction quality and semantic preservation.

Contribution

It proposes a novel quantization-aware matrix factorization method with an efficient algorithm, outperforming JPEG at very low bit rates and maintaining competitive quality at higher bit rates.

Findings

Outperforms JPEG below 0.25 bpp in image quality

Improves top-1 classification accuracy by over 5% at low bit rates

Provides a convergent iterative algorithm with closed-form solutions

Abstract

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 .