A Class of Second-Order Geometric Quasilinear Hyperbolic PDEs and Their Application in Imaging
DOI10.1137/20M1366277zbMath1478.35150arXiv1905.01457OpenAlexW3162042754WikidataQ114074154 ScholiaQ114074154MaRDI QIDQ5860338
Ye Zhang, Guozhi Dong, Michael Hintermüller
Publication date: 19 November 2021
Published in: SIAM Journal on Imaging Sciences (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1905.01457
mean curvature flowlevel setimage denoisingsecond-order dynamicsgeometric PDEstotal variation flowsecond-order quasilinear hyperbolic equationdisplacement error correctionnonsmooth and nonconvex variational methods
Optimality conditions for problems involving partial differential equations (49K20) Nonsmooth analysis (49J52) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Degenerate hyperbolic equations (35L80) Second-order quasilinear hyperbolic equations (35L72)
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Cites Work
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- Nonlinear total variation based noise removal algorithms
- Wave-type threshold dynamics and the hyperbolic mean curvature flow
- Partial differential equations for zooming, deinterlacing and dejittering
- Decay estimates for quasi-linear evolution equations
- The total variation flow in \(\mathbb R^N\)
- Motion of level sets by mean curvature. I
- Gevrey well posedness for a second order weakly hyperbolic equation with non regular in time coefficients
- Gevrey well-posedness of an abstract Cauchy problem of weakly hyperbolic type
- Variational methods in imaging
- Applied functional analysis. Functional analysis, Sobolev spaces and elliptic differential equations
- Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
- Level set approach to mean curvature flow in arbitrary codimension
- Global existence and asymptotics of the solutions of the second-order quasilinear hyperbolic equations with the first-order dissipation
- Image recovery via total variation minimization and related problems
- A second-order gradient-like dissipative dynamical system with Hessian-driven damping. Application to optimization and mechanics.
- Introductory lectures on convex optimization. A basic course.
- Parabolic quasilinear equations minimizing linear growth functionals
- Asymptotic stabilization of inertial gradient dynamics with time-dependent viscosity
- A first-order primal-dual algorithm for convex problems with applications to imaging
- Nonlinear spectral decompositions by gradient flows of one-homogeneous functionals
- Accelerated variational PDEs for efficient solution of regularized inversion problems
- Hyperbolic mean curvature flow
- Combining fast inertial dynamics for convex optimization with Tikhonov regularization
- Fast convergence of inertial dynamics and algorithms with asymptotic vanishing viscosity
- Nonlinear inverse scale space methods
- The hyperbolic mean curvature flow
- Sur les problèmes de Cauchy hyperboliques bien posés
- A Differential Equation for Modeling Nesterov's Accelerated Gradient Method: Theory and Insights
- Spectral Decompositions Using One-Homogeneous Functionals
- Infinite Dimensional Optimization Models and PDEs for Dejittering
- Computation of geometric partial differential equations and mean curvature flow
- Numerical approximation of anisotropic geometric evolution equations in the plane
- Evolution by Non-Convex Functionals
- On the long time behavior of second order differential equations with asymptotically small dissipation
- Delayed singularity formation in solution of nonlinear wave equations in higher dimensions
- Global existence for nonlinear wave equations
- On the Minimizing Property of a Second Order Dissipative System in Hilbert Spaces
- THE HEAVY BALL WITH FRICTION METHOD, I. THE CONTINUOUS DYNAMICAL SYSTEM: GLOBAL EXPLORATION OF THE LOCAL MINIMA OF A REAL-VALUED FUNCTION BY ASYMPTOTIC ANALYSIS OF A DISSIPATIVE DYNAMICAL SYSTEM
- Unconditional Stability of Semi-Implicit Discretizations of Singular Flows
- Functional-analytic and numerical issues in splitting methods for total variation-based image reconstruction
- On the second-order asymptotical regularization of linear ill-posed inverse problems
- A Total Variation Spectral Framework for Scale and Texture Analysis
- Damped second order flow applied to image denoising
- Nonlinear Flows for Displacement Correction and Applications in Tomography
- Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations
- Review of geometry and analysis
- The Dirichlet problem for the total variation flow