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Bregman implementation of Meyer's $G-$norm for cartoon + textures decomposition

Jerome Gilles, Stanley Osher

TL;DR

A very simple algorithm based on Split Bregman iterations to numerically solve the cartoon + textures decomposition model of Meyer results in a significant gain in speed compared to Chambolle's nonlinear projectors.

Abstract

In this paper, we design a very simple algorithm based on Split Bregman iterations to numerically solve the cartoon + textures decomposition model of Meyer. This results in a significant gain in speed compared to Chambolle's nonlinear projectors.

Bregman implementation of Meyer's $G-$norm for cartoon + textures decomposition

TL;DR

A very simple algorithm based on Split Bregman iterations to numerically solve the cartoon + textures decomposition model of Meyer results in a significant gain in speed compared to Chambolle's nonlinear projectors.

Abstract

In this paper, we design a very simple algorithm based on Split Bregman iterations to numerically solve the cartoon + textures decomposition model of Meyer. This results in a significant gain in speed compared to Chambolle's nonlinear projectors.

Paper Structure

This paper contains 6 sections, 2 theorems, 9 equations, 4 figures, 3 algorithms.

Table of Contents

  1. Introduction
  2. Chambolle's projector and cartoon + textures decomposition
  3. Split Bregman iteration for $TV$ minimization
  4. Bregman Meyer's $G-$norm implementation
  5. Experiments
  6. Conclusion

Key Result

proposition thmcounterproposition

If $\tau<\frac{1}{8}$ then $\mu \textup{div\,}(p^n)$ converges to $P_{G_{\mu}}(f)$ when $n\rightarrow +\infty$ where

Figures (4)

  • Figure 1: Original images used as inputs of the decomposition algorithms.
  • Figure 2: Cartoon + textures parts obtained with $\lambda=\mu=1000$ for both images.
  • Figure 3: Cartoon + textures parts obtained with $\lambda=\mu=1000$.
  • Figure 4: Cartoon + textures parts obtained with $\lambda=\mu=1000$ from the nonlinear projectors.

Theorems & Definitions (3)

  • proposition thmcounterproposition
  • proposition thmcounterproposition
  • proof