用复正弦调制激活函数,提升隐式神经表示的频率建模能力。
COSMO-INR: Complex Sinusoidal Modulation for Implicit Neural Representations
- 引入复正弦调制激活函数,增强网络频谱表达能力。
- 图像重建平均提升5.67 dB,6倍超分优于现有最佳方法0.64 dB。
- 适合需要高保真重建与抗噪能力的视觉任务研究者。
隐式神经表示(INRs)是一种强大的数据建模范式,提供连续的信号表示替代离散方式。其紧凑编码复杂信号的能力在众多视觉任务中表现优异。已有研究表明,INR性能高度依赖多层感知机中的激活函数选择,但理论机制尚不明确。现存关键限制包括谱偏差(对高频内容敏感度低)、噪声鲁棒性差,以及难以同时捕捉局部与全局结构。本文通过谐波分析与切比雪夫多项式解析INR信号表示,证明用复正弦项调制激活函数可实现更丰富完整的频谱支持。基于此,提出专为INRs设计的新激活函数,并通过切比雪夫分析与大量实验验证理论。此外,采用任务特定模型提取的正则化深层先验来调整激活,进一步提升收敛速度与稳定性。在图像重建(多样数据集上平均提升+5.67 dB PSNR)、去噪(+0.46 dB)、超分辨率(6倍缩放下优于最先进方法+0.64 dB)、修复与3D形状重建中,该激活函数始终优于现有最优方案。
原文摘要 · Abstract (English)
Implicit neural representations (INRs) are a powerful paradigm for modeling data, offering a continuous alternative to discrete signal representations. Their ability to compactly encode complex signals has led to strong performance in many vision tasks. Prior work shows INR performance is highly sensitive to the choice of activation function in the underlying multilayer perceptron, yet the theoretical reasons remain unclear. Key limitations also persist, including spectral bias (reduced sensitivity to high-frequency content), limited robustness to noise, and difficulty capturing local and global structure jointly. We analyze INR signal representation using harmonic analysis and Chebyshev polynomials. We prove that modulating activation functions with a complex sinusoidal term yields richer and more complete spectral support throughout the network. Building on this, we introduce a new activation function tailored to INRs and validate our theory using Chebyshev analysis and extensive experiments. We additionally use a regularized deep prior, extracted from a task-specific model, to adapt the activations, further improving convergence speed and stability. Across image reconstruction (average PSNR gain of +5.67 dB over the nearest counterpart on a diverse dataset), denoising (+0.46 dB PSNR), super-resolution (+0.64 dB over the nearest SOTA method for 6X upscaling), inpainting, and 3D shape reconstruction, our activation consistently outperforms existing state-of-the-art alternatives.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品;中文卡片由大模型生成,请以原文为准。