# Variable-Rate Learned Image Compression with Multi-Objective Optimization and Quantization-Reconstruction Offsets

arXiv: https://arxiv.org/abs/2402.18930 · HTML: https://mlsanity.com/paper/2402.18930/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 15 references that are in the map.
- First posted on arXiv 29 Feb 2024.

## Builds on (most cited first, 12 of 12)

- [Variational image compression with a scale hyperprior](https://mlsanity.com/paper/1802.01436/) (2018)
- [Multi-Task Learning as Multi-Objective Optimization](https://mlsanity.com/paper/1810.04650/) (2018)
- [End-to-end Optimized Image Compression](https://mlsanity.com/paper/1611.01704/) (2016)
- [Joint Autoregressive and Hierarchical Priors for Learned Image Compression](https://mlsanity.com/paper/1809.02736/) (2018)
- [Video Enhancement with Task-Oriented Flow](https://mlsanity.com/paper/1711.09078/) (2017)
- [ELIC: Efficient Learned Image Compression with Unevenly Grouped Space-Channel Contextual Adaptive Coding](https://mlsanity.com/paper/2203.10886/) (2022)
- [CompressAI: a PyTorch library and evaluation platform for end-to-end compression research](https://mlsanity.com/paper/2011.03029/) (2020)
- [Neural Video Compression with Diverse Contexts](https://mlsanity.com/paper/2302.14402/) (2023)
- [Nonlinear Transform Coding](https://mlsanity.com/paper/2007.03034/) (2020)
- [Variable Rate Deep Image Compression With a Conditional Autoencoder](https://mlsanity.com/paper/1909.04802/) (2019)
- [Asymmetric Gained Deep Image Compression With Continuous Rate Adaptation](https://mlsanity.com/paper/2003.02012/) (2020)
- [QVRF: A Quantization-error-aware Variable Rate Framework for Learned Image Compression](https://mlsanity.com/paper/2303.05744/) (2023)

## Built on by (most cited first, 9 of 9)

- [HPC: Hierarchical Progressive Coding Framework for Volumetric Video](https://mlsanity.com/paper/2407.09026/) (2024)
- [Improving 3D Gaussian Splatting Compression by Scene-Adaptive Lattice Vector Quantization](https://mlsanity.com/paper/2509.13482/) (2025)
- [Balanced Rate-Distortion Optimization in Learned Image Compression](https://mlsanity.com/paper/2502.20161/) (2025)
- [Efficient Progressive Image Compression with Variance-aware Masking](https://mlsanity.com/paper/2411.10185/) (2024)
- [Leveraging Second-Order Curvature for Efficient Learned Image Compression: Theory and Empirical Evidence](https://mlsanity.com/paper/2601.20769/) (2026)
- [Accelerating Learned Image Compression Through Modeling Neural Training Dynamics](https://mlsanity.com/paper/2505.18107/) (2025)
- [Training-Free Adaptive Quantization for Variable Rate Image Coding for Machines](https://mlsanity.com/paper/2511.05836/) (2025)
- [Adaptive Source-Channel Coding for Semantic Communications](https://mlsanity.com/paper/2508.07958/) (2025)
- [Bidirectional Feature-aligned Motion Transformation for Efficient Dynamic Point Cloud Compression](https://mlsanity.com/paper/2509.14591/) (2025)

## Abstract (arXiv)

Achieving successful variable bitrate compression with computationally simple algorithms from a single end-to-end learned image or video compression model remains a challenge. Many approaches have been proposed, including conditional auto-encoders, channel-adaptive gains for the latent tensor or uniformly quantizing all elements of the latent tensor. This paper follows the traditional approach to vary a single quantization step size to perform uniform quantization of all latent tensor elements. However, three modifications are proposed to improve the variable rate compression performance. First, multi objective optimization is used for (post) training. Second, a quantization-reconstruction offset is introduced into the quantization operation. Third, variable rate quantization is used also for the hyper latent. All these modifications can be made on a pre-trained single-rate compression model by performing post training. The algorithms are implemented into three well-known image compression models and the achieved variable rate compression results indicate negligible or minimal compression performance loss compared to training multiple models. (Codes will be shared at https://github.com/InterDigitalInc/CompressAI)