Low Dimensional Manifold Model for Image Processing

DOI10.1137/16M1058686zbMath1401.49042OpenAlexW2763211003MaRDI QIDQ4689637

Zuoqiang Shi, Wei Zhu, Stanley J. Osher

Publication date: 17 October 2018

Published in: SIAM Journal on Imaging Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/16m1058686

zbMATH Keywords

Laplace-Beltrami operatorpoint integral methodnonlocal methodpatch manifold

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Numerical methods based on nonlinear programming (49M37) Image processing (compression, reconstruction, etc.) in information and communication theory (94A08)

Related Items (23)

Analysis of Asymptotic Escape of Strict Saddle Sets in Manifold Optimization ⋮ A Nonlocal Stokes System with Volume Constraints ⋮ Image colorization based on a generalization of the low dimensional manifold model ⋮ Generalization of the weighted nonlocal Laplacian in low dimensional manifold model ⋮ A Convergent Point Integral Method for Isotropic Elliptic Equations on a Point Cloud ⋮ Inverse problems on low-dimensional manifolds ⋮ Wasserstein-Based Projections with Applications to Inverse Problems ⋮ Group sparse representation for restoring blurred images with Cauchy noise ⋮ Iterative rank-one matrix completion via singular value decomposition and nuclear norm regularization ⋮ A second-order nonlocal approximation for Poisson model with Dirichlet boundary ⋮ Weighted nonlocal Laplacian on interpolation from sparse data ⋮ A Nonlocal Feature-Driven Exemplar-Based Approach for Image Inpainting ⋮ CURE: Curvature Regularization for Missing Data Recovery ⋮ Large region inpainting by re-weighted regularized methods ⋮ Manifold based low-rank regularization for image restoration and semi-supervised learning ⋮ Harmonic Extension on The Point Cloud ⋮ Unnamed Item ⋮ Point Integral Method for Elliptic Equations with Variable Coefficients on Point Cloud ⋮ Tensor train rank minimization with nonlocal self-similarity for tensor completion ⋮ RWRM: residual Wasserstein regularization model for image restoration ⋮ The Steerable Graph Laplacian and its Application to Filtering Image Datasets ⋮ Learning to scan: a deep reinforcement learning approach for personalized scanning in CT imaging ⋮ A Tale of Two Bases: Local-Nonlocal Regularization on Image Patches with Convolution Framelets

Cites Work

• Nonlinear total variation based noise removal algorithms
• Convergence of the point integral method for Laplace-Beltrami equation on point cloud
• Neighborhood filters and PDE's
• On the local behavior of spaces of natural images
• The nonlinear statistics of high-contrast patches in natural images
• Generalization of the weighted nonlocal Laplacian in low dimensional manifold model
• Nonlocal Operators with Applications to Image Processing
• Image Processing with Nonlocal Spectral Bases
• The Split Bregman Method for L1-Regularized Problems
• Nonlocal Linear Image Regularization and Supervised Segmentation
• Harmonic Extension on The Point Cloud
• Point Integral Method for Solving Poisson-Type Equations on Manifolds from Point Clouds with Convergence Guarantees
• A Convergent Point Integral Method for Isotropic Elliptic Equations on a Point Cloud
• Nonparametric Bayesian Dictionary Learning for Analysis of Noisy and Incomplete Images
• An Iterative Regularization Method for Total Variation-Based Image Restoration
• A Review of Image Denoising Algorithms, with a New One

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