用稀疏拉普拉斯场重建图像，速度快精度高。
Shared-kernel Wavelet Neural Networks for Poisson Image Reconstruction
- 用拉普拉斯场表示图像，通过求解泊松方程重建。
- 参数少于0.0002M，计算复杂度线性，实时重建。
- 适用于压缩、低光增强等场景，优于已有方法。
拉普拉斯算子将图像转换为稀疏且满足稳定分布的拉普拉斯场，且可通过求解带适当边界条件的泊松方程唯一重构图像。我们首先在数百张图像上验证了拉普拉斯场的稀疏性和稳定性分布特性，随后证明了图像可从其拉普拉斯场准确重建。针对重建任务，提出一种共享核小波神经网络，用于求解泊松方程，具有三大优势：参数量低于0.0002M，适合多数设备；计算复杂度为线性，支持实时重建；重建精度高于现有方法。多个数值实验验证了稀疏拉普拉斯场与所提泊松求解器的有效性与高效性。该方法可广泛应用于图像压缩、低光增强、目标追踪等领域。
原文摘要 · Abstract (English)
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.
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