arXiv:2602.20535eess.SPeess.IV2026-02被引 1

对比神经网络与样条函数在稀疏数据拟合中的表现,发现前者更优。

Comparing Implicit Neural Representations and B-Splines for Continuous Function Fitting from Sparse Samples

  • 用坐标编码的隐式神经表示法拟合连续函数
  • 在理想参数下,神经网络误差更低、边缘更清晰
  • 提出实用优化方法,逼近理想效果,适合图像重建研究者

连续信号表示天然适用于逆问题,如磁共振成像(MRI)和计算机断层扫描,因为测量依赖于潜在的物理连续信号。传统方法依赖预定义的解析基(如三次样条),而隐式神经表示(INRs)则使用基于坐标的网络,以隐式方式参数化连续函数。尽管经验上成功,但其与传统模型的内在表征能力对比仍有限。本初步实证研究比较了位置编码的INR与三次样条模型在稀疏随机采样下的连续函数拟合能力,仅使用系数域Tikhonov正则化来隔离表征能力差异。结果表明,在最优超参数设置下,INR的归一化均方根误差更低,边缘过渡更锐利,振荡伪影更少。此外,我们展示了一种基于测量数据划分的双层优化框架,可有效逼近理想性能。这些发现从实证角度支持了INRs在稀疏数据拟合中的更强表征能力。

原文摘要 · Abstract (English)

Continuous signal representations are naturally suited for inverse problems, such as magnetic resonance imaging (MRI) and computed tomography, because the measurements depend on an underlying physically continuous signal. While classical methods rely on predefined analytical bases like B-splines, implicit neural representations (INRs) have emerged as a powerful alternative that use coordinate-based networks to parameterize continuous functions with implicitly defined bases. Despite their empirical success, direct comparisons of their intrinsic representation capabilities with conventional models remain limited. This preliminary empirical study compares a positional-encoded INR with a cubic B-spline model for continuous function fitting from sparse random samples, isolating the representation capacity difference by only using coefficient-domain Tikhonov regularization. Results demonstrate that, under oracle hyperparameter selection, the INR achieves a lower normalized root-mean-squared error, yielding sharper edge transitions and fewer oscillatory artifacts than the oracle-tuned B-spline model. Additionally, we show that a practical bilevel optimization framework for INR hyperparameter selection based on measurement data split effectively approximates oracle performance. These findings empirically support the superior representation capacity of INRs for sparse data fitting.

隐式表示函数拟合稀疏数据神经渲染

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。