# Learning Scalable ℓ_∞-constrained Near-lossless Image Compression via Joint Lossy Image and Residual Compression

arXiv: https://arxiv.org/abs/2103.17015 · HTML: https://mlsanity.com/paper/2103.17015/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 53 references that are in the map.
- First posted on arXiv 31 Mar 2021.

## Builds on (most cited first, 26 of 26)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Variational image compression with a scale hyperprior](https://mlsanity.com/paper/1802.01436/) (2018)
- [Conditional Image Generation with PixelCNN Decoders](https://mlsanity.com/paper/1606.05328/) (2016)
- [Pixel Recurrent Neural Networks](https://mlsanity.com/paper/1601.06759/) (2016)
- [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)
- [Learned Image Compression with Discretized Gaussian Mixture Likelihoods and Attention Modules](https://mlsanity.com/paper/2001.01568/) (2020)
- [PixelCNN++: Improving the PixelCNN with Discretized Logistic Mixture Likelihood and Other Modifications](https://mlsanity.com/paper/1701.05517/) (2017)
- [High-Fidelity Generative Image Compression](https://mlsanity.com/paper/2006.09965/) (2020)
- [Lossy Image Compression with Compressive Autoencoders](https://mlsanity.com/paper/1703.00395/) (2017)
- [Full Resolution Image Compression with Recurrent Neural Networks](https://mlsanity.com/paper/1608.05148/) (2016)
- [Variable Rate Image Compression with Recurrent Neural Networks](https://mlsanity.com/paper/1511.06085/) (2015)
- [Context-adaptive Entropy Model for End-to-end Optimized Image Compression](https://mlsanity.com/paper/1809.10452/) (2018)
- [Conditional Probability Models for Deep Image Compression](https://mlsanity.com/paper/1801.04260/) (2018)
- [Real-Time Adaptive Image Compression](https://mlsanity.com/paper/1705.05823/) (2017)
- [Variable Rate Deep Image Compression With a Conditional Autoencoder](https://mlsanity.com/paper/1909.04802/) (2019)
- [Practical Full Resolution Learned Lossless Image Compression](https://mlsanity.com/paper/1811.12817/) (2018)
- [Practical Lossless Compression with Latent Variables using Bits Back Coding](https://mlsanity.com/paper/1901.04866/) (2019)
- [Integer Discrete Flows and Lossless Compression](https://mlsanity.com/paper/1905.07376/) (2019)
- [Learning Convolutional Networks for Content-weighted Image Compression](https://mlsanity.com/paper/1703.10553/) (2017)
- [Bit-Swap: Recursive Bits-Back Coding for Lossless Compression with Hierarchical Latent Variables](https://mlsanity.com/paper/1905.06845/) (2019)
- [Learning Better Lossless Compression Using Lossy Compression](https://mlsanity.com/paper/2003.10184/) (2020)
- [Learning Content-Weighted Deep Image Compression](https://mlsanity.com/paper/1904.00664/) (2019)
- [3-D Context Entropy Model for Improved Practical Image Compression](https://mlsanity.com/paper/2004.08273/) (2020)
- [Near-lossless ℓ_∞-constrained Image Decompression via Deep Neural Network](https://mlsanity.com/paper/1801.07987/) (2018)

## Built on by (most cited first, 16 of 16)

- [3DAC: Learning Attribute Compression for Point Clouds](https://mlsanity.com/paper/2203.09931/) (2022)
- [Deep Lossy Plus Residual Coding for Lossless and Near-lossless Image Compression](https://mlsanity.com/paper/2209.04847/) (2022)
- [Once-for-All: Controllable Generative Image Compression with Dynamic Granularity Adaptation](https://mlsanity.com/paper/2406.00758/) (2024)
- [LC-FDNet: Learned Lossless Image Compression with Frequency Decomposition Network](https://mlsanity.com/paper/2112.06417/) (2021)
- [Exploring Resolution Fields for Scalable Image Compression with Uncertainty Guidance](https://mlsanity.com/paper/2306.08941/) (2023)
- [GroupedMixer: An Entropy Model with Group-wise Token-Mixers for Learned Image Compression](https://mlsanity.com/paper/2405.01170/) (2024)
- [CALLIC: Content Adaptive Learning for Lossless Image Compression](https://mlsanity.com/paper/2412.17464/) (2024)
- [Joint Lossless Compression and Steganography for Medical Images via Large Language Models](https://mlsanity.com/paper/2508.01782/) (2025)
- [Learning Lossless Compression for High Bit-Depth Volumetric Medical Image](https://mlsanity.com/paper/2410.17814/) (2024)
- [L3C-Stereo: Lossless Compression for Stereo Images](https://mlsanity.com/paper/2108.09422/) (2021)
- [End-to-end lossless compression of high precision depth maps guided by pseudo-residual](https://mlsanity.com/paper/2201.03195/) (2022)
- [Semantic Ensemble Loss and Latent Refinement for High-Fidelity Neural Image Compression](https://mlsanity.com/paper/2401.14007/) (2024)
- [SEEC: Segmentation-Assisted Multi-Entropy Models for Learned Lossless Image Compression](https://mlsanity.com/paper/2509.07704/) (2025)
- [FLLIC: Functionally Lossless Image Compression](https://mlsanity.com/paper/2401.13616/) (2024)
- [RAWIC: Bit-Depth Adaptive Lossless Raw Image Compression](https://mlsanity.com/paper/2603.28105/) (2026)
- [Practical Lossless Volumetric Medical Image Compression via Tri-plane Context Tree Learning](https://mlsanity.com/paper/2608.13897/) (2026)

## Abstract (arXiv)

We propose a novel joint lossy image and residual compression framework for learning ℓ_∞-constrained near-lossless image compression. Specifically, we obtain a lossy reconstruction of the raw image through lossy image compression and uniformly quantize the corresponding residual to satisfy a given tight ℓ_∞ error bound. Suppose that the error bound is zero, i.e., lossless image compression, we formulate the joint optimization problem of compressing both the lossy image and the original residual in terms of variational auto-encoders and solve it with end-to-end training. To achieve scalable compression with the error bound larger than zero, we derive the probability model of the quantized residual by quantizing the learned probability model of the original residual, instead of training multiple networks. We further correct the bias of the derived probability model caused by the context mismatch between training and inference. Finally, the quantized residual is encoded according to the bias-corrected probability model and is concatenated with the bitstream of the compressed lossy image. Experimental results demonstrate that our near-lossless codec achieves the state-of-the-art performance for lossless and near-lossless image compression, and achieves competitive PSNR while much smaller ℓ_∞ error compared with lossy image codecs at high bit rates.