# Revisiting Nonlocal Self-Similarity from Continuous Representation

arXiv: https://arxiv.org/abs/2401.00708 · HTML: https://mlsanity.com/paper/2401.00708/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 72 references that are in the map.
- First posted on arXiv 1 Jan 2024.

## Builds on (most cited first, 24 of 24)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Learning Continuous Image Representation with Local Implicit Image Function](https://mlsanity.com/paper/2012.09161/) (2020)
- [Implicit Functions in Feature Space for 3D Shape Reconstruction and Completion](https://mlsanity.com/paper/2003.01456/) (2020)
- [Rank Minimization for Snapshot Compressive Imaging](https://mlsanity.com/paper/1807.07837/) (2018)
- [Hyperspectral Image Restoration via Total Variation Regularized Low-rank Tensor Decomposition](https://mlsanity.com/paper/1707.02477/) (2017)
- [Hyperspectral Image Denoising Employing a Spatial-Spectral Deep Residual Convolutional Neural Network](https://mlsanity.com/paper/1806.00183/) (2018)
- [Meta-Learning Sparse Implicit Neural Representations](https://mlsanity.com/paper/2110.14678/) (2021)
- [Implicit Transformer Network for Screen Content Image Continuous Super-Resolution](https://mlsanity.com/paper/2112.06174/) (2021)
- [Low-Rank Tensor Function Representation for Multi-Dimensional Data Recovery](https://mlsanity.com/paper/2212.00262/) (2022)
- [Tensor Ring Decomposition with Rank Minimization on Latent Space: An Efficient Approach for Tensor Completion](https://mlsanity.com/paper/1809.02288/) (2018)
- [Guaranteed Tensor Recovery Fused Low-rankness and Smoothness](https://mlsanity.com/paper/2302.02155/) (2023)
- [Framelet Representation of Tensor Nuclear Norm for Third-Order Tensor Completion](https://mlsanity.com/paper/1909.06982/) (2019)
- [DDS2M: Self-Supervised Denoising Diffusion Spatio-Spectral Model for Hyperspectral Image Restoration](https://mlsanity.com/paper/2303.06682/) (2023)
- [Self-Supervised Arbitrary-Scale Point Clouds Upsampling via Implicit Neural Representation](https://mlsanity.com/paper/2204.08196/) (2022)
- [FastHyMix: Fast and Parameter-free Hyperspectral Image Mixed Noise Removal](https://mlsanity.com/paper/2109.08879/) (2021)
- [Implicit Neural Representation Learning for Hyperspectral Image Super-Resolution](https://mlsanity.com/paper/2112.10541/) (2021)
- [Fast Noise Removal in Hyperspectral Images via Representative Coefficient Total Variation](https://mlsanity.com/paper/2211.01825/) (2022)
- [Zero-shot Blind Image Denoising via Implicit Neural Representations](https://mlsanity.com/paper/2204.02405/) (2022)
- [Image Compressed Sensing Using Non-local Neural Network](https://mlsanity.com/paper/2112.03712/) (2021)
- [Nonlocal Patch-Based Fully-Connected Tensor Network Decomposition for Remote Sensing Image Inpainting](https://mlsanity.com/paper/2109.05889/) (2021)
- [Nonlocal Low-Rank Tensor Factor Analysis for Image Restoration](https://mlsanity.com/paper/1803.06795/) (2018)
- [Spherical Image Inpainting with Frame Transformation and Data-driven Prior Deep Networks](https://mlsanity.com/paper/2209.14604/) (2022)

## Built on by (most cited first, 14 of 14)

- [F-INR: Functional Tensor Decomposition for Implicit Neural Representations](https://mlsanity.com/paper/2503.21507/) (2025)
- [Continuous Representation Methods, Theories, and Applications: An Overview and Perspectives](https://mlsanity.com/paper/2505.15222/) (2025)
- [Lightweight Deep Unfolding Networks with Enhanced Robustness for Infrared Small Target Detection](https://mlsanity.com/paper/2509.08205/) (2025)
- [Cross-Frequency Implicit Neural Representation with Self-Evolving Parameters](https://mlsanity.com/paper/2504.10929/) (2025)
- [Calibrated Harmonic Overlaid Implicit Neural Representations for Multi-Dimensional Data](https://mlsanity.com/paper/2606.26763/) (2026)
- [It's Not the Target, It's the Background: Rethinking Infrared Small Target Detection via Deep Patch-Free Low-Rank Representations](https://mlsanity.com/paper/2506.10425/) (2025)
- [Low-Rank Tensor Recovery via Variational Schatten-p Quasi-Norm and Jacobian Regularization](https://mlsanity.com/paper/2506.22134/) (2025)
- [Beyond Motion Cues and Structural Sparsity: Revisiting Small Moving Target Detection](https://mlsanity.com/paper/2509.07654/) (2025)
- [Reparameterized Tensor Ring Functional Decomposition for Multi-Dimensional Data Recovery](https://mlsanity.com/paper/2603.01034/) (2026)
- [Accelerating Large-Scale Regularized High-Order Tensor Recovery](https://mlsanity.com/paper/2506.09594/) (2025)
- [Image Denoising Using Global and Local Circulant Representation](https://mlsanity.com/paper/2512.23569/) (2025)
- [Hyperbolic Distillation: Geometry-Guided Cross-Modal Transfer for Robust 3D Object Detection](https://mlsanity.com/paper/2605.09899/) (2026)
- [MG-SpaIR: Multi-grade Sparse-guided Implicit Representation for Training-Data-Free Image Restoration](https://mlsanity.com/paper/2607.00138/) (2026)
- [PICANet: Physics-Informed Cascaded Asymmetric Network for Infrared Small Target Detection](https://mlsanity.com/paper/2609.07515/) (2026)

## Abstract (arXiv)

Nonlocal self-similarity (NSS) is an important prior that has been successfully applied in multi-dimensional data processing tasks, e.g., image and video recovery. However, existing NSS-based methods are solely suitable for meshgrid data such as images and videos, but are not suitable for emerging off-meshgrid data, e.g., point cloud and climate data. In this work, we revisit the NSS from the continuous representation perspective and propose a novel Continuous Representation-based NonLocal method (termed as CRNL), which has two innovative features as compared with classical nonlocal methods. First, based on the continuous representation, our CRNL unifies the measure of self-similarity for on-meshgrid and off-meshgrid data and thus is naturally suitable for both of them. Second, the nonlocal continuous groups can be more compactly and efficiently represented by the coupled low-rank function factorization, which simultaneously exploits the similarity within each group and across different groups, while classical nonlocal methods neglect the similarity across groups. This elaborately designed coupled mechanism allows our method to enjoy favorable performance over conventional NSS methods in terms of both effectiveness and efficiency. Extensive multi-dimensional data processing experiments on-meshgrid (e.g., image inpainting and image denoising) and off-meshgrid (e.g., climate data prediction and point cloud recovery) validate the versatility, effectiveness, and efficiency of our CRNL as compared with state-of-the-art methods.