The Total Variation Regularized L1 Model for Multiscale Decomposition

Abstract

This paper studies the total variation regularization model with an L1 fidelity term (TV-L1) for decomposing an image into features of different scales. We first show that the images produced by this model can be formed from the minimizers of a sequence of decoupled geometry sub-problems. Using this result we show that the TV-L1 model is able to separate image features according to their scales, where the scale is analytically defined by the G-value. A number of other properties including the geometric and morphological invariance of the TV-L1 model are also proved and their applications discussed.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2006
Accession Number
ADA460529

Entities

People

  • Donald Goldfarb
  • Stanley Osher
  • Wotao Yin

Organizations

  • Rice University

Tags

Communities of Interest

  • Biomedical
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Applied Mathematics
  • Banach Space
  • Boundaries
  • Decomposition
  • Feature Selection
  • Geometry
  • Gray Scale
  • Illumination
  • Image Processing
  • Image Registration
  • Industrial Engineering
  • Inequalities
  • Operations Research
  • Recognition
  • Signal Processing
  • Two Dimensional

Readers

  • Ocean-Atmosphere Mesoscale Modeling, Data Assimilation, and Flux Boundary Layers
  • Operations Research
  • Theoretical Analysis.