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Approximately Invertible Neural Network for Learned Image Compression

Yanbo Gao, Meng Fu, Shuai Li, Chong Lv, Xun Cai, Hui Yuan, Mao Ye

TL;DR

The paper tackles the challenge of achieving high-quality, learned image compression when using invertible neural networks under quantization. It introduces Approximately Invertible Neural Network (A-INN), an RD-optimized framework that accounts for quantization noise by modeling the distortion bound with the Jacobian of the inverse transform and incorporating an Lagrangian RD objective $J = R + \lambda D$. To suppress quantization-induced errors and preserve detail, the authors propose three plug-in modules: Progressive Denoising Module (PDM) to reduce noise in latent features, Cascaded Feature Recovery Module (CFRM) to restore high-dimensional information from reduced channels, and Frequency-enhanced Decomposition and Synthesis Module (FDSM) with a Frequency-decomposition (FDSM-D) and a Dual-Frequency Attention Synthesis (FDSM-S) to better recover high-frequency content. The architecture integrates these components with an invertible transform, along with a joint hyperprior and context-based entropy model, to achieve superior rate-distortion performance on standard benchmarks, including Kodak, Tecnick, and CLIC datasets. Ablation studies corroborate the contribution of each module, with notable improvements from structure-based denoising and CFRM, and the approach demonstrates substantial BD-rate improvements over both traditional codecs and prior INN-based methods. Overall, A-INN provides a principled and practical foundation for INN-based lossy compression, enabling more reliable high-quality reconstructions in real-world scenarios.

Abstract

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.

Approximately Invertible Neural Network for Learned Image Compression

TL;DR

The paper tackles the challenge of achieving high-quality, learned image compression when using invertible neural networks under quantization. It introduces Approximately Invertible Neural Network (A-INN), an RD-optimized framework that accounts for quantization noise by modeling the distortion bound with the Jacobian of the inverse transform and incorporating an Lagrangian RD objective . To suppress quantization-induced errors and preserve detail, the authors propose three plug-in modules: Progressive Denoising Module (PDM) to reduce noise in latent features, Cascaded Feature Recovery Module (CFRM) to restore high-dimensional information from reduced channels, and Frequency-enhanced Decomposition and Synthesis Module (FDSM) with a Frequency-decomposition (FDSM-D) and a Dual-Frequency Attention Synthesis (FDSM-S) to better recover high-frequency content. The architecture integrates these components with an invertible transform, along with a joint hyperprior and context-based entropy model, to achieve superior rate-distortion performance on standard benchmarks, including Kodak, Tecnick, and CLIC datasets. Ablation studies corroborate the contribution of each module, with notable improvements from structure-based denoising and CFRM, and the approach demonstrates substantial BD-rate improvements over both traditional codecs and prior INN-based methods. Overall, A-INN provides a principled and practical foundation for INN-based lossy compression, enabling more reliable high-quality reconstructions in real-world scenarios.

Abstract

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.
Paper Structure (16 sections, 17 equations, 8 figures, 3 tables)

This paper contains 16 sections, 17 equations, 8 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Lossy Image Compression
  4. Invertible Neural Network based image compression methods
  5. Proposed Approximately Invertible Neural Network (A-INN): Formulation
  6. Proposed Approximately Invertible Neural Network (A-INN): Architecture
  7. A-INN with Progressive Denoising Modules
  8. Cascaded Feature Recovery Module
  9. Frequency-enhanced Decomposition and Synthesis Module
  10. Frequency-enhanced Decomposition Module
  11. Dual-Frequency Attention based Synthesis Module
  12. Experiments
  13. Experimental setup
  14. Rate-Distortion Performance Comparison with State-of-the-art Methods
  15. Ablation Studies
  16. ...and 1 more sections

Figures (8)

  • Figure 1: Diagram of the proposed A-INN based image compression in comparison with the existing learned image compression frameworks.
  • Figure 2: Overview of the proposed Approximately Invertible Neural Network (A-INN) based image compression framework. It includes the invertible block as the main transform, the proposed FDSM containing the frequency enchanced decomposition (FDSM-D) and synthesis (FDSM-S), PDM for denoising due to quantization, CFRM and the optional MS-CFRM for denoising due to channel squeeze. Q represents quantization, AE and AD represent the arithmetic encoder and arithmetic decoder, respectively, and Entropy Model represents the joint hyperprior and context based model.
  • Figure 3: Proposed Cascaded Feature Recovery Module (CFRM). ReLU is used after the $3\times 3$ convolution while $1\times 1$ convolution is only used for channel processing and no activation is used. $sC$ represents the split concatenation to concatenate the feature channels by group corresponding to the channel squeeze at the encoder side.
  • Figure 4: Frequency-enhanced Decomposition and Synthesis Module (FDSM). ReLU is used after the convolution block except the $1\times 1$ convolution used in the end of synthesis which uses Sigmoid as activation to produce the attention map.
  • Figure 5: RD curve comparison of the proposed A-INN against the existing methods, including the traditional methods (first row (a)-(d)) and the learned image compression methods (second row (e)-(h)), on Kodak, CLIC Mobile, CLIC Professional and Tecnick dataset.
  • ...and 3 more figures