Total Variation Based Image Cartoon-Texture Decomposition

Abstract

This paper studies algorithms for decomposing a real image into the sum of cartoon and texture based on total variation minimization and second-order cone programming (SOCP). The cartoon is represented as a function of bounded variation while texture (and noise) is represented by elements in the space of oscillating functions, as proposed by Yves Meyer. Our approach gives more accurate results than those obtained previously by Vese-Osher's approximation to Meyer's model, which we also formulate and solve as an SOCP. The model of minimizing total variation with an L1-norm fidelity term is also considered and empirically shown to achieve even better results when there is no noise. This model is analyzed and shown to be able to select features of an image according to their scales.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2005
Accession Number
ADA478457

Entities

People

  • Donald Goldfarb
  • Stanley Osher
  • Wotao Yin

Organizations

  • Columbia University

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Banach Space
  • Boundaries
  • Computer Programming
  • Computer Science
  • Decomposition
  • Differential Equations
  • Equations
  • Evolutionary Algorithms
  • Inequalities
  • Linear Algebra
  • Mathematics
  • Operations Research
  • Partial Differential Equations
  • Reliability
  • Second Order Cone Programming
  • Three Dimensional

Fields of Study

  • Computer science

Readers

  • Computational Modeling and Simulation
  • Fault Tolerant Diagnosis of Black and White Balloon Isolation Tests Using ¥.
  • Mathematical Modeling and Probability Theory.

Technology Areas

  • Space