ERROR BOUNDS FOR FINITE-DIFFERENCE METHODS FOR RUDIN—OSHER—FATEMI IMAGE SMOOTHING

ERROR BOUNDS FOR FINITE-DIFFERENCE METHODS FOR RUDIN—OSHER—FATEMI IMAGE SMOOTHING

We bound the difference between the solution to the continuous Rudin—Osher—Fatemi (ROF) image smoothing model and the solutions to various finite-difference approximations to this model. These bounds apply to "typical" images, i.e., images with edges or with fractal structure. These are th...

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Veröffentlicht in:SIAM journal on numerical analysis 2011-01, Vol.49 (1/2), p.845-868
Hauptverfasser: WANG, JINGYUE, LUCIER, BRADLEY J.
Format: Artikel
Sprache:eng
Schlagworte:
Approximation
Calculus of variations and optimal control
Convergence
Data smoothing
Discrete functions
Eigenfunctions
Error analysis
Error bounds
Errors
Exact sciences and technology
Finite difference method
Integers
Mathematical analysis
Mathematical functions
Mathematical models
Mathematical vectors
Mathematics
Measure and integration
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in mathematical programming, optimization and calculus of variations
Numerical methods in optimization and calculus of variations
Numerical methods in probability and statistics
Sciences and techniques of general use
Smoothing
Studies
Triangles
Upwind schemes
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Zusammenfassung:We bound the difference between the solution to the continuous Rudin—Osher—Fatemi (ROF) image smoothing model and the solutions to various finite-difference approximations to this model. These bounds apply to "typical" images, i.e., images with edges or with fractal structure. These are the first bounds on the error in numerical methods for ROF smoothing.
ISSN:0036-1429
1095-7170
DOI:10.1137/090769594