scholarly journals An Interpretation Of Regularization By Denoising And Its Application With The Back-Projected Fidelity Term

2021 ◽  
Author(s):  
Einav Yogev-Ofer ◽  
Tom Tirer ◽  
Raja Giryes
Keyword(s):  
Fidelity Term

scholarly journals Exact solutions for the total variation denoising problem of piecewise constant images in dimension one

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Riccardo Cristoferi
Keyword(s):  
Exact Solution ◽  
Exact Solutions ◽  
Total Variation ◽  
Piecewise Constant ◽  
Geometrical Properties ◽  
Total Variation Denoising ◽  
Fidelity Term ◽  
Dimension One

AbstractA method for obtaining the exact solution for the total variation denoising problem of piecewise constant images in dimension one is presented. The validity of the algorithm relies on some results concerning the behavior of the solution when the parameter λ in front of the fidelity term varies. Albeit some of them are well-known in the community, here they are proved with simple techniques based on qualitative geometrical properties of the solutions.

scholarly journals A derivation of Griffith functionals from discrete finite-difference models

2020 ◽  
Vol 59 (6) ◽  
Author(s):  
Vito Crismale ◽  
Giovanni Scilla ◽  
Francesco Solombrino
Keyword(s):  
Finite Difference ◽  
Continuum Limit ◽  
Dirichlet Boundary ◽  
Two Dimensions ◽  
Dirichlet Boundary Conditions ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Discretization Step ◽  
Fidelity Term ◽  
Ellipticity Parameter

AbstractWe analyze a finite-difference approximation of a functional of Ambrosio–Tortorelli type in brittle fracture, in the discrete-to-continuum limit. In a suitable regime between the competing scales, namely if the discretization step $$\delta $$ δ is smaller than the ellipticity parameter $$\varepsilon $$ ε , we show the $$\varGamma $$ Γ -convergence of the model to the Griffith functional, containing only a term enforcing Dirichlet boundary conditions and no $$L^p$$ L p fidelity term. Restricting to two dimensions, we also address the case in which a (linearized) constraint of non-interpenetration of matter is added in the limit functional, in the spirit of a recent work by Chambolle, Conti and Francfort.

A multi-frame super-resolution based on new variational data fidelity term

2020 ◽  
Vol 87 ◽  
pp. 446-467
Author(s):  
M. Hakim ◽  
A. Ghazdali ◽  
A. Laghrib
Keyword(s):  
Super Resolution ◽  
Data Fidelity ◽  
Fidelity Term

Automatic Binary Data Classification Using a Modified Allen–Cahn Equation

2020 ◽  
pp. 2150013
Author(s):  
Sangkwon Kim ◽  
Junseok Kim
Keyword(s):  
Binary Data ◽  
Data Classification ◽  
Coarse Grid ◽  
Computational Results ◽  
Trial And Error ◽  
Hybrid Scheme ◽  
Cahn Equation ◽  
Fidelity Term ◽  
2D And 3D ◽  
The Given

In this paper, we propose an automatic binary data classification method using a modified Allen–Cahn (AC) equation. The modified AC equation was originally developed for image segmentation. The equation consists of the AC equation with a fidelity term which enforces the solution to be the given data. In the proposed method, we start from a coarse grid and refine the grid until the accuracy of the data classification reaches a given tolerance. Therefore, we can avoid a laborious trial and error procedure. For a numerical method for the modified AC equation, we use a recently developed explicit hybrid scheme. We perform several 2D and 3D computational tests to demonstrate the performance of the proposed method. The computational results confirm that the proposed algorithm is automatic.

Sign in / Sign up

Export Citation Format

Share Document