scholarly journals On the definition of solution to the total variation flow

2022 ◽  
Vol 61 (1) ◽  
Author(s):  
Juha Kinnunen ◽  
Christoph Scheven
Keyword(s):  
Weak Solution ◽  
Variational Inequality ◽  
Total Variation ◽  
Boundary Data ◽  
Duality Result ◽  
Total Variation Flow ◽  
Definition Of

AbstractWe show that the notions of weak solution to the total variation flow based on the Anzellotti pairing and the variational inequality coincide under some restrictions on the boundary data. The key ingredient in the argument is a duality result for the total variation functional, which is based on an approximation of the total variation by area-type functionals.

scholarly journals The convergence of a numerical method for total variation flow

2021 ◽  
Vol 15 ◽  
pp. 174830262110113
Author(s):  
Qianying Hong ◽  
Ming-jun Lai ◽  
Jingyue Wang
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Numerical Method ◽  
Convergence Analysis ◽  
Total Variation ◽  
Iterative Algorithm ◽  
Finite Difference Scheme ◽  
Gradient Flow ◽  
Time Dependent ◽  
Total Variation Flow

We present a convergence analysis for a finite difference scheme for the time dependent partial different equation called gradient flow associated with the Rudin-Osher-Fetami model. We devise an iterative algorithm to compute the solution of the finite difference scheme and prove the convergence of the iterative algorithm. Finally computational experiments are shown to demonstrate the convergence of the finite difference scheme.

Quantifying image structures in high-throughput microscopy with total variation flow

2016 ◽  
Author(s):  
Shekoufeh Gorgi Zadeh ◽  
Max Hermann ◽  
Elisa Merklingen ◽  
Jan-Gero Schloetel ◽  
Thomas Schultz
Keyword(s):  
Total Variation ◽  
High Throughput ◽  
Total Variation Flow

scholarly journals Moving Heat Source Reconstruction from Cauchy Boundary Data: The Cartesian Coordinates Case

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
Nilson C. Roberty ◽  
Denis M. de Sousa ◽  
Marcelo L. S. Rainha
Keyword(s):  
Helmholtz Equation ◽  
Boundary Data ◽  
Representation Formula ◽  
Transient Heat Conduction ◽  
Thermal Source ◽  
Source Reconstruction ◽  
Modified Helmholtz Equation ◽  
Time Space ◽  
Definition Of ◽  
Characteristic Interval

We consider the problem of reconstruction of an unknown characteristic interval and block transient thermal source inside a domain. By exploring the definition of an Extended Dirichlet to Neumann map in the time space cylinder that has been introduced in Roberty and Rainha (2010a), we can treat the problem with methods similar to that used in the analysis of the stationary source reconstruction problem. Further, the finite differenceθ-scheme applied to the transient heat conduction equation leads to a model based on a sequence of modified Helmholtz equation solutions. For each modified Helmholtz equation the characteristic interval and parallelepiped source function may be reconstructed uniquely from the Cauchy boundary data. Using representation formula we establish reciprocity functional mapping functions that are solutions of the modified Helmholtz equation to their integral in the unknown characteristic support. Numerical experiment for capture of an interval and an rectangular parallelepiped characteristic source inside a cubic box domain from boundary data are presented in threedimensional and one-dimensional implementations. The problem of centroid determination is addressed and questions are discussed from an computational points of view.

The nonlocal total variation flow

2010 ◽  
pp. 163-189 ◽  
Author(s):  
Fuensanta Andreu-Vaillo ◽  
José Mazón ◽  
Julio Rossi ◽  
J. Julián Toledo-Melero
Keyword(s):  
Total Variation ◽  
Total Variation Flow ◽  
Nonlocal Total Variation

scholarly journals On the Jump set of Solutions of the Total Variation Flow

2013 ◽  
Vol 130 ◽  
pp. 155-168 ◽  
Author(s):  
Vicent Caselles ◽  
Khalid Jalalzai ◽  
Matteo Novaga
Keyword(s):  
Total Variation ◽  
Total Variation Flow ◽  
Jump Set
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