# Reverse Convolution and Its Applications to Image Restoration

arXiv: https://arxiv.org/abs/2508.09824 · HTML: https://mlsanity.com/paper/2508.09824/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 60 references that are in the map.
- First posted on arXiv 13 Aug 2025.

## Builds on (most cited first, 30 of 39)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Fully Convolutional Networks for Semantic Segmentation](https://mlsanity.com/paper/1411.4038/) (2014)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Aggregated Residual Transformations for Deep Neural Networks](https://mlsanity.com/paper/1611.05431/) (2016)
- [Xception: Deep Learning with Depthwise Separable Convolutions](https://mlsanity.com/paper/1610.02357/) (2016)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Multi-Scale Context Aggregation by Dilated Convolutions](https://mlsanity.com/paper/1511.07122/) (2015)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [Semantic Image Segmentation with Deep Convolutional Nets and Fully Connected CRFs](https://mlsanity.com/paper/1412.7062/) (2014)
- [Plug-and-Play Image Restoration with Deep Denoiser Prior](https://mlsanity.com/paper/2008.13751/) (2020)
- [From Big to Small: Multi-Scale Local Planar Guidance for Monocular Depth Estimation](https://mlsanity.com/paper/1907.10326/) (2019)
- [Learning Deconvolution Network for Semantic Segmentation](https://mlsanity.com/paper/1505.04366/) (2015)
- [Invertible Residual Networks](https://mlsanity.com/paper/1811.00995/) (2018)
- [Residual Flows for Invertible Generative Modeling](https://mlsanity.com/paper/1906.02735/) (2019)
- [Deep Unfolding Network for Image Super-Resolution](https://mlsanity.com/paper/2003.10428/) (2020)
- [CondenseNet: An Efficient DenseNet using Learned Group Convolutions](https://mlsanity.com/paper/1711.09224/) (2017)
- [Deep Generalized Unfolding Networks for Image Restoration](https://mlsanity.com/paper/2204.13348/) (2022)
- [MixConv: Mixed Depthwise Convolutional Kernels](https://mlsanity.com/paper/1907.09595/) (2019)
- [Fast Training of Convolutional Networks through FFTs](https://mlsanity.com/paper/1312.5851/) (2013)
- [Iterative Filter Adaptive Network for Single Image Defocus Deblurring](https://mlsanity.com/paper/2108.13610/) (2021)

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

- [A Weak Signal Learning Dataset and Its Baseline Method](https://mlsanity.com/paper/2512.23160/) (2025)
- [Weighted Reverse Convolution for Feature Upsampling](https://mlsanity.com/paper/2605.17472/) (2026)

## Abstract (arXiv)

Convolution and transposed convolution are fundamental operators widely used in neural networks. However, transposed convolution (a.k.a. deconvolution) does not serve as a true inverse of convolution due to inherent differences in their mathematical formulations. To date, no reverse convolution operator has been established as a standard component in neural architectures. In this paper, we propose a novel depthwise reverse convolution operator as an initial attempt to effectively reverse depthwise convolution by formulating and solving a regularized least-squares optimization problem. We thoroughly investigate its kernel initialization, padding strategies, and other critical aspects to ensure its effective implementation. Building upon this operator, we further construct a reverse convolution block by combining it with layer normalization, 1×1 convolution, and GELU activation, forming a Transformer-like structure. The proposed operator and block can directly replace conventional convolution and transposed convolution layers in existing architectures, leading to the development of ConverseNet. Corresponding to typical image restoration models such as DnCNN, SRResNet and USRNet, we train three variants of ConverseNet for Gaussian denoising, super-resolution and deblurring, respectively. Extensive experiments demonstrate the effectiveness of the proposed reverse convolution operator as a basic building module. We hope this work could pave the way for developing new operators in deep model design and applications.