A discrete theory and efficient algorithms for forward-and-backward diffusion filtering

DOI10.1007/s10851-018-0847-4zbMath1433.94017OpenAlexW2892662896MaRDI QIDQ1799615

Guy Gilboa, Martin Welk, Joachim Weickert

Publication date: 19 October 2018

Published in: Journal of Mathematical Imaging and Vision (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10851-018-0847-4

zbMATH Keywords

dynamical systemsill-posed problemsimage enhancementdiffusion filteringbackward parabolic pdesnon-standard finite differences

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) Image processing (compression, reconstruction, etc.) in information and communication theory (94A08) PDEs in connection with information and communication (35Q94) Quasilinear parabolic equations (35K59)

Related Items (4)

Diffusion, pre-smoothing and gradient descent ⋮ Enhanced total variation minimization for stable image reconstruction ⋮ Stable backward diffusion models that minimise convex energies ⋮ Stochastic block models are a discrete surface tension

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Iterations of a non-linear transformation for enhancement of digital images
• Image sharpening by flows based on triple well potentials
• Staircasing in semidiscrete stabilised inverse linear diffusion algorithms
• A numerical scheme for solving nonlinear backward parabolic problems
• Locally analytic schemes: a link between diffusion filtering and wavelet shrinkage
• Diffusion-inspired shrinkage functions and stability results for wavelet denoising
• Image segmentation and edge enhancement with stabilized inverse diffusion equations
• Stable explicit time marching in well-posed or ill-posed nonlinear parabolic equations
• Feature-Oriented Image Enhancement Using Shock Filters
• Uniqueness of the Gaussian Kernel for Scale-Space Filtering
• Local Strong Homogeneity of a Regularized Estimator
• Stabilized Richardson leapfrog scheme in explicit stepwise computation of forward or backward nonlinear parabolic equations
• On the Equivalence of Soft Wavelet Shrinkage, Total Variation Diffusion, Total Variation Regularization, and SIDEs
• Minimizers of Cost-Functions Involving Nonsmooth Data-Fidelity Terms. Application to the Processing of Outliers
• An Efficient and Stable Two-Pixel Scheme for 2D Forward-and-Backward Diffusion
• Algorithms and Data Structures

This page was built for publication: A discrete theory and efficient algorithms for forward-and-backward diffusion filtering