用神经网络建模信号,实现连续表示与高效计算。
Implicit Neural Representations: A Signal Processing Perspective

- 将信号视为坐标函数,通过神经网络实现连续建模。
- 支持解析微分,避免离散近似误差,提升精度。
- 适合医学成像、3D重建等需高保真表示的场景。
隐式神经表示(INRs)标志着信号建模的根本转变,从离散采样数据转向连续函数表示。通过将信号参数化为神经网络,INRs提供了一个统一框架,用于将图像、音频、视频、3D几何等表示为坐标的连续函数。这种函数视角使信号操作(如微分)可通过自动微分进行解析计算,而非依赖离散近似。本文从信号处理视角审视INRs的发展,强调其频谱特性、采样理论与多尺度表示。我们追溯了从标准坐标网络(具有低频偏好)到先进设计的演进,后者通过周期性、局部化和自适应激活函数重塑逼近空间。同时讨论了分层分解、哈希网格编码等结构化表示,以提升空间自适应性和计算效率。文中还突出展示了INRs在医学与雷达成像反问题、压缩及3D场景表示中的广泛应用。通过将INRs视为可学习的信号模型,其逼近空间随数据自适应调整,本文厘清了该领域的核心概念进展,并指出了理论稳定性、权重空间可解释性与大规模泛化等开放挑战。
原文摘要 · Abstract (English)
Implicit neural representations (INRs) mark a fundamental shift in signal modeling, moving from discrete sampled data to continuous functional representations. By parameterizing signals as neural networks, INRs provide a unified framework for representing images, audio, video, 3D geometry, and beyond as continuous functions of their coordinates. This functional viewpoint enables signal operations such as differentiation to be carried out analytically through automatic differentiation rather than through discrete approximations. In this article, we examine the evolution of INRs from a signal processing perspective, emphasizing spectral behavior, sampling theory, and multiscale representation. We trace the progression from standard coordinate based networks, which exhibit a spectral bias toward low frequency components, to more advanced designs that reshape the approximation space through specialized activations, including periodic, localized, and adaptive functions. We also discuss structured representations, such as hierarchical decompositions and hash grid encodings, that improve spatial adaptivity and computational efficiency. We further highlight the utility of INRs across a broad range of applications, including inverse problems in medical and radar imaging, compression, and 3D scene representation. By interpreting INRs as learned signal models whose approximation spaces adapt to the underlying data, this article clarifies the field's core conceptual developments and outlines open challenges in theoretical stability, weight space interpretability, and large scale generalization.
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