Learning Optimal Linear Block Transform by Rate Distortion Minimization
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arXiv
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| Format: | Preprint |
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2024
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| author | Gnutti, Alessandro Kao, Chia-Hao Peng, Wen-Hsiao Leonardi, Riccardo |
| author_facet | Gnutti, Alessandro Kao, Chia-Hao Peng, Wen-Hsiao Leonardi, Riccardo |
| contents | Linear block transform coding remains a fundamental component of image and video compression. Although the Discrete Cosine Transform (DCT) is widely employed in all current compression standards, its sub-optimality has sparked ongoing research into discovering more efficient alternative transforms even for fields where it represents a consolidated tool. In this paper, we introduce a novel linear block transform called the Rate Distortion Learned Transform (RDLT), a data-driven transform specifically designed to minimize the rate-distortion (RD) cost when approximating residual blocks. Our approach builds on the latest end-to-end learned compression frameworks, adopting back-propagation and stochastic gradient descent for optimization. However, unlike the nonlinear transforms used in variational autoencoder (VAE)-based methods, the goal is to create a simpler yet optimal linear block transform, ensuring practical integration into existing image and video compression standards. Differently from existing data-driven methods that design transforms based on sample covariance matrices, such as the Karhunen-Loève Transform (KLT), the proposed RDLT is directly optimized from an RD perspective. Experimental results show that this transform significantly outperforms the DCT or other existing data-driven transforms. Additionally, it is shown that when simulating the integration of our RDLT into a VVC-like image compression framework, the proposed transform brings substantial improvements. All the code used in our experiments has been made publicly available at [1]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_18494 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Learning Optimal Linear Block Transform by Rate Distortion Minimization Gnutti, Alessandro Kao, Chia-Hao Peng, Wen-Hsiao Leonardi, Riccardo Image and Video Processing Linear block transform coding remains a fundamental component of image and video compression. Although the Discrete Cosine Transform (DCT) is widely employed in all current compression standards, its sub-optimality has sparked ongoing research into discovering more efficient alternative transforms even for fields where it represents a consolidated tool. In this paper, we introduce a novel linear block transform called the Rate Distortion Learned Transform (RDLT), a data-driven transform specifically designed to minimize the rate-distortion (RD) cost when approximating residual blocks. Our approach builds on the latest end-to-end learned compression frameworks, adopting back-propagation and stochastic gradient descent for optimization. However, unlike the nonlinear transforms used in variational autoencoder (VAE)-based methods, the goal is to create a simpler yet optimal linear block transform, ensuring practical integration into existing image and video compression standards. Differently from existing data-driven methods that design transforms based on sample covariance matrices, such as the Karhunen-Loève Transform (KLT), the proposed RDLT is directly optimized from an RD perspective. Experimental results show that this transform significantly outperforms the DCT or other existing data-driven transforms. Additionally, it is shown that when simulating the integration of our RDLT into a VVC-like image compression framework, the proposed transform brings substantial improvements. All the code used in our experiments has been made publicly available at [1]. |
| title | Learning Optimal Linear Block Transform by Rate Distortion Minimization |
| topic | Image and Video Processing |
| url | https://arxiv.org/abs/2411.18494 |