Reverse Convolution and Its Applications to Image Restoration

2025-08-13

AI Summary

Existing transposed convolutions do not constitute mathematically exact inverses of convolutional operators, limiting their capacity for reversible modeling. To address this, we propose a depthwise separable deconvolution operator, which approximates the inverse of depthwise convolution via regularized least-squares optimization. Building upon this, we design a lightweight deconvolution module incorporating layer normalization, 1×1 convolution, and GELU activation, and integrate it into a Transformer-like architecture named ConverseNet. Crucially, ConverseNet supports end-to-end training and—uniquely among backbone architectures—adopts learnable deconvolution as a universal, invertible primitive. Extensive experiments on Gaussian denoising, single-image super-resolution, and motion deblurring demonstrate that all ConverseNet variants achieve state-of-the-art performance, validating the effectiveness, generalizability, and architectural versatility of the proposed operator.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Deep Neural Architectures and Foundation Models
• Search and Optimization: Non-convex Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Responsible Web: Measurement, analysis, and circumvention of Web censorship

Abstract

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$ imes$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.

Problem

• Proposes a novel depthwise reverse convolution operator
• Aims to effectively reverse depthwise convolution mathematically
• Enhances image restoration tasks like denoising and super-resolution

Innovation

• Proposed depthwise reverse convolution operator
• Solved regularized least-squares optimization problem
• Constructed Transformer-like reverse convolution block