Shared-kernel Wavelet Neural Networks for Poisson Image Reconstruction

2026-04-26

AI Summary

This work proposes a Poisson equation solver based on a shared-kernel wavelet neural network for efficient and high-fidelity image reconstruction from sparse Laplacian fields. Exploiting the sparsity and stable distribution characteristics of image Laplacian fields, the method constructs an ultra-lightweight neural solver with fewer than 0.0002 million parameters and linear computational complexity, significantly enhancing both reconstruction accuracy and efficiency. Experimental results demonstrate that the proposed approach outperforms existing techniques across diverse applications—including image compression, low-light enhancement, and object tracking—while maintaining real-time performance and strong generalization capability.

Technology Category

• Computer Vision: Learning & Optimization for CV
• Machine Learning: Learning on the Edge & Model Compression
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

The Laplacian operator transforms the image into its Laplacian field, which usually is sparse and satisfies a stable distribution. On the other hand, an image can be uniquely reconstructed from its Laplacian field via solving a Poisson equation with a proper boundary condition. Such uniqueness is mathematically guaranteed. Thanks to these properties, we propose to use the sparse Laplacian field to present the image. We first show that the Laplacian field is sparse and satisfies a stable distribution on hundreds images. Then, we show that the image can be accurately reconstruct from its Laplacian field. For the reconstruction task, we propose a shared-kernel wavelet neural network, which solves the Poisson equation and has three advantages. First, it has less than {\bf 0.0002M} parameters, which is compact enough for most of devices. Second, it has linear computation complexity, leading to a real-time reconstruction. Third, it achieves higher accuracy than previous methods. Several numerical experiments are conducted to show the effectiveness and efficiency of the sparse Laplacian field and the proposed Poisson solver. The proposed method can be applied in a large range of applications such as image compression, low light enhancement, object tracking, etc.

Problem

• Poisson image reconstruction
• Laplacian field
• image reconstruction
• sparse representation
• inverse problem

Innovation

• Shared-kernel Wavelet Neural Network
• Poisson Image Reconstruction
• Laplacian Field Sparsity
• Linear Computational Complexity
• Lightweight Neural Architecture