# LC-FDNet: Learned Lossless Image Compression with Frequency Decomposition Network

arXiv: https://arxiv.org/abs/2112.06417 · HTML: https://mlsanity.com/paper/2112.06417/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 52 references that are in the map.
- First posted on arXiv 13 Dec 2021.

## Builds on (most cited first, 30 of 35)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Enhanced Deep Residual Networks for Single Image Super-Resolution](https://mlsanity.com/paper/1707.02921/) (2017)
- [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)
- [Checkerboard Context Model for Efficient Learned Image Compression](https://mlsanity.com/paper/2103.15306/) (2021)
- [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)
- [Asymmetric Gained Deep Image Compression With Continuous Rate Adaptation](https://mlsanity.com/paper/2003.02012/) (2020)
- [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)
- [Parallel Multiscale Autoregressive Density Estimation](https://mlsanity.com/paper/1703.03664/) (2017)
- [Variable-Rate Deep Image Compression through Spatially-Adaptive Feature Transform](https://mlsanity.com/paper/2108.09551/) (2021)
- [Slimmable Compressive Autoencoders for Practical Neural Image Compression](https://mlsanity.com/paper/2103.15726/) (2021)
- [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)
- [Learning Image and Video Compression through Spatial-Temporal Energy Compaction](https://mlsanity.com/paper/1906.09683/) (2019)
- [Lossless Image Compression through Super-Resolution](https://mlsanity.com/paper/2004.02872/) (2020)
- [Attention-guided Image Compression by Deep Reconstruction of Compressive Sensed Saliency Skeleton](https://mlsanity.com/paper/2103.15368/) (2021)

## Built on by (most cited first, 12 of 12)

- [Language Modeling Is Compression](https://mlsanity.com/paper/2309.10668/) (2023)
- [Lossless data compression by large models](https://mlsanity.com/paper/2407.07723/) (2024)
- [Compression via Pre-trained Transformers: A Study on Byte-Level Multimodal Data](https://mlsanity.com/paper/2410.05078/) (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)
- [WISE: A Framework for Gigapixel Whole-Slide-Image Lossless Compression](https://mlsanity.com/paper/2503.18074/) (2025)
- [Frequency Regularization: Restricting Information Redundancy of Convolutional Neural Networks](https://mlsanity.com/paper/2304.07973/) (2023)
- [FLLIC: Functionally Lossless Image Compression](https://mlsanity.com/paper/2401.13616/) (2024)
- [SSFMamba: Learning Symmetry-driven Spatial-Frequency Modeling for Physically Consistent 3D Medical Image Segmentation](https://mlsanity.com/paper/2508.03069/) (2025)
- [A Model-Driven Lossless Compression Algorithm Resistant to Mismatch](https://mlsanity.com/paper/2601.17684/) (2026)
- [End-to-End Image Compression with Segmentation Guided Dual Coding for Wind Turbines](https://mlsanity.com/paper/2603.29927/) (2026)

## Abstract (arXiv)

Recent learning-based lossless image compression methods encode an image in the unit of subimages and achieve comparable performances to conventional non-learning algorithms. However, these methods do not consider the performance drop in the high-frequency region, giving equal consideration to the low and high-frequency areas. In this paper, we propose a new lossless image compression method that proceeds the encoding in a coarse-to-fine manner to separate and process low and high-frequency regions differently. We initially compress the low-frequency components and then use them as additional input for encoding the remaining high-frequency region. The low-frequency components act as a strong prior in this case, which leads to improved estimation in the high-frequency area. In addition, we design the frequency decomposition process to be adaptive to color channel, spatial location, and image characteristics. As a result, our method derives an image-specific optimal ratio of low/high-frequency components. Experiments show that the proposed method achieves state-of-the-art performance for benchmark high-resolution datasets.