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.

翻译：本文提出了一种名为隐式神经表示正则化器（INRR）的正则化方法，旨在提升隐式神经表示（INR）的泛化能力。INR是一种全连接网络，能够以不受网格分辨率限制的细节程度表示信号，但其泛化能力（尤其在非均匀采样数据上）仍有改进空间。所提出的INRR基于学习的狄利克雷能量（DE），该能量可度量矩阵行/列之间的相似性。通过使用小型INR参数化DE，进一步融入了拉普拉斯矩阵的平滑性。INRR通过巧妙结合信号的自相似性与拉普拉斯的平滑性，显著提升了INR在信号表示中的泛化性能。通过精心设计的数值实验，本文还揭示了INRR衍生的一系列特性，包括类似动量法的收敛轨迹以及多尺度相似性。此外，所提方法可有效改善其他信号表示方法的性能表现。