This paper proposes a regularizer called Implicit Neural Representation
Regularizer (INRR) to improve the generalization ability of the Implicit Neural
Representation (INR). The INR is a fully connected network that can represent
signals with details not restricted by grid resolution. However, its
generalization ability could be improved, especially with non-uniformly sampled
data. The proposed INRR is based on learned Dirichlet Energy (DE) that measures
similarities between rows/columns of the matrix. The smoothness of the
Laplacian matrix is further integrated by parameterizing DE with a tiny INR.
INRR improves the generalization of INR in signal representation by perfectly
integrating the signal's self-similarity with the smoothness of the Laplacian
matrix. Through well-designed numerical experiments, the paper also reveals a
series of properties derived from INRR, including momentum methods like
convergence trajectory and multi-scale similarity. Moreover, the proposed
method could improve the performance of other signal representation methods.

本文提出了一个称为隐式神经表示正则化器的正则化器 (INRR)，以提高隐式神经表示 (INR) 的泛化能力。 INRR 通过将归一化的 Dirichlet 能量 (DE) 与 INR 集成来改善信号表示中的泛化性能，从而更好地集成了信号的自相似性和 Laplacian 矩阵的光滑度。作者进一步设计了一系列实验来论证 INRR 的性质，如收敛轨迹和多尺度相似性，并表明该方法可以提高其他信号表示方法的性能。