LNRR: Learnable Nonlocal Relation Regularization for Implicit Neural Representations

Implicit neural representations (INRs) model discrete observations as samples of a continuous signal and provide compact, resolution-independent representations. However, an INR is supervised only at observed locations and generalizes poorly to unobserved ones, especially inside large missing regions. Local smoothness priors only propagate information inward from the boundary of a missing region, so the interior of a large region degrades into a blur that loses the original edges and textures. These structures can only be borrowed from similar ones elsewhere in the image, yet INRs have no built-in mechanism to exploit such nonlocal relations. We propose Learnable Nonlocal Relation Regularization (LNRR), which brings nonlocal relations between image patches into INR training to improve completion under large missing regions. LNRR learns patch relations with a patch feature network and uses them to constrain the reconstruction of missing regions through a robust graph-residual regularizer in the wavelet domain. LNRR changes only the regularization term and applies to a range of INR backbones. Across multiple natural-image datasets and missing patterns, LNRR achieves state-of-the-art completion among existing INR regularization methods.