Some Variations on Total Variation-Based Image Smoothing

Abstract

In this paper we study finite-difference approximations to the variational problem using the BV smoothness penalty that was introduced in an image smoothing context by Rudin, Osher, and Fatemi. We give a dual formulation for an "upwind" finite-difference approximation for the BV seminorm; this formulation is in the same spirit as one popularized by Chambolle for a simpler, more anisotropic, finite-difference approximation to the BV seminorm. We introduce a multiscale method for speeding the approximation of both Chambolle's original method and of the new formulation of the upwind scheme. We demonstrate numerically that the multiscale method is effective, and we provide numerical examples that illustrate both the qualitative and quantitative behavior of the solutions of the numerical formulations.

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 2009
Accession Number
ADA513218

Entities

People

  • Antonin Chambolle
  • Bradley J. Lucier
  • Stacey E. Levine

Organizations

  • University of Minnesota

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Algorithms
  • Boundaries
  • Computations
  • Computer Science
  • Convergence
  • Convex Sets
  • Differential Equations
  • Discontinuities
  • Equations
  • Image Processing
  • Injectors
  • Iterations
  • Mathematics
  • Minnesota
  • Partial Differential Equations
  • Scalar Functions
  • Universities

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)