Quantization-aware Matrix Factorization for Low Bit Rate Image Compression

2024-08-22

AI Summary

Traditional SVD-based lossy image compression suffers from severe degradation in reconstruction quality at low bit rates (<0.25 bpp) due to high sensitivity to quantization errors. To address this, we propose Quantization-Aware Matrix Factorization (QMF), the first method to explicitly model integer quantization as an intrinsic constraint within low-rank matrix decomposition—rather than as a post-hoc step—enabling end-to-end differentiability and optimization. Our approach employs a block coordinate descent (BCD) algorithm with theoretical convergence guarantees, where each subproblem admits a closed-form solution, balancing computational efficiency and reconstruction accuracy. Evaluated on the Kodak and CLIC 2024 benchmarks, QMF significantly outperforms JPEG below 0.25 bpp: it achieves substantial PSNR gains and improves ImageNet classification Top-1 accuracy by over 5%, demonstrating superior semantic fidelity preservation.

Technology Category

• Computer Vision: Learning & Optimization for CV
• Machine Learning: Matrix & Tensor Methods
• Data Mining & Knowledge Management: Data Compression

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

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 .

Problem

• Integrates quantization with low-rank approximation for compression
• Improves reconstruction quality at low bit rates
• Preserves visual semantics better than traditional methods

Innovation

• Quantization-aware matrix factorization for compression
• Integer-constrained low-rank approximation integration
• Block coordinate descent with closed-form solutions