# Approximately Invertible Neural Network for Learned Image Compression

arXiv: https://arxiv.org/abs/2408.17073 · HTML: https://mlsanity.com/paper/2408.17073/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 79 references that are in the map.
- First posted on arXiv 30 Aug 2024.

## Builds on (most cited first, 30 of 42)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [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)
- [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)
- [CompressAI: a PyTorch library and evaluation platform for end-to-end compression research](https://mlsanity.com/paper/2011.03029/) (2020)
- [Channel-wise Autoregressive Entropy Models for Learned Image Compression](https://mlsanity.com/paper/2007.08739/) (2020)
- [Learned Image Compression with Mixed Transformer-CNN Architectures](https://mlsanity.com/paper/2303.14978/) (2023)
- [Checkerboard Context Model for Efficient Learned Image Compression](https://mlsanity.com/paper/2103.15306/) (2021)
- [Low-Light Image Enhancement with Normalizing Flow](https://mlsanity.com/paper/2109.05923/) (2021)
- [Full Resolution Image Compression with Recurrent Neural Networks](https://mlsanity.com/paper/1608.05148/) (2016)
- [The Devil Is in the Details: Window-based Attention for Image Compression](https://mlsanity.com/paper/2203.08450/) (2022)
- [Context-adaptive Entropy Model for End-to-end Optimized Image Compression](https://mlsanity.com/paper/1809.10452/) (2018)
- [Real-Time Adaptive Image Compression](https://mlsanity.com/paper/1705.05823/) (2017)
- [Enhanced Invertible Encoding for Learned Image Compression](https://mlsanity.com/paper/2108.03690/) (2021)
- [Improved Lossy Image Compression with Priming and Spatially Adaptive Bit Rates for Recurrent Networks](https://mlsanity.com/paper/1703.10114/) (2017)
- [Non-local Attention Optimized Deep Image Compression](https://mlsanity.com/paper/1904.09757/) (2019)
- [Image and Video Compression with Neural Networks: A Review](https://mlsanity.com/paper/1904.03567/) (2019)
- [Causal Contextual Prediction for Learned Image Compression](https://mlsanity.com/paper/2011.09704/) (2020)
- [Hierarchical Conditional Flow: A Unified Framework for Image Super-Resolution and Image Rescaling](https://mlsanity.com/paper/2108.05301/) (2021)
- [Invertible Denoising Network: A Light Solution for Real Noise Removal](https://mlsanity.com/paper/2104.10546/) (2021)
- [Augmented Normalizing Flows: Bridging the Gap Between Generative Flows and Latent Variable Models](https://mlsanity.com/paper/2002.07101/) (2020)
- [A Unified End-to-End Framework for Efficient Deep Image Compression](https://mlsanity.com/paper/2002.03370/) (2020)

## Built on by (most cited first, 2 of 2)

- [Leveraging Second-Order Curvature for Efficient Learned Image Compression: Theory and Empirical Evidence](https://mlsanity.com/paper/2601.20769/) (2026)
- [High-Fidelity Video Compression based on Invertible Neural Transform and Implicit Conditioning](https://mlsanity.com/paper/2606.13957/) (2026)

## Abstract (arXiv)

Learned image compression have attracted considerable interests in recent years. It typically comprises an analysis transform, a synthesis transform, quantization and an entropy coding model. The analysis transform and synthesis transform are used to encode an image to latent feature and decode the quantized feature to reconstruct the image, and can be regarded as coupled transforms. However, the analysis transform and synthesis transform are designed independently in the existing methods, making them unreliable in high-quality image compression. Inspired by the invertible neural networks in generative modeling, invertible modules are used to construct the coupled analysis and synthesis transforms. Considering the noise introduced in the feature quantization invalidates the invertible process, this paper proposes an Approximately Invertible Neural Network (A-INN) framework for learned image compression. It formulates the rate-distortion optimization in lossy image compression when using INN with quantization, which differentiates from using INN for generative modelling. Generally speaking, A-INN can be used as the theoretical foundation for any INN based lossy compression method. Based on this formulation, A-INN with a progressive denoising module (PDM) is developed to effectively reduce the quantization noise in the decoding. Moreover, a Cascaded Feature Recovery Module (CFRM) is designed to learn high-dimensional feature recovery from low-dimensional ones to further reduce the noise in feature channel compression. In addition, a Frequency-enhanced Decomposition and Synthesis Module (FDSM) is developed by explicitly enhancing the high-frequency components in an image to address the loss of high-frequency information inherent in neural network based image compression. Extensive experiments demonstrate that the proposed A-INN outperforms the existing learned image compression methods.