Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Noisy image decomposition: a new structure, texture and noise model based on local adaptivity

Jerome Gilles

TL;DR

A new model which decomposes an image into three parts (structures, textures and noise) based on a local regularization scheme is proposed, which is compared with the recent work of Aujol and Chambolle.

Abstract

These last few years, image decomposition algorithms have been proposed to split an image into two parts: the structures and the textures. These algorithms are not adapted to the case of noisy images because the textures are corrupted by noise. In this paper, we propose a new model which decomposes an image into three parts (structures, textures and noise) based on a local regularization scheme. We compare our results with the recent work of Aujol and Chambolle. We finish by giving another model which combines the advantages of the two previous ones.

Noisy image decomposition: a new structure, texture and noise model based on local adaptivity

TL;DR

A new model which decomposes an image into three parts (structures, textures and noise) based on a local regularization scheme is proposed, which is compared with the recent work of Aujol and Chambolle.

Abstract

These last few years, image decomposition algorithms have been proposed to split an image into two parts: the structures and the textures. These algorithms are not adapted to the case of noisy images because the textures are corrupted by noise. In this paper, we propose a new model which decomposes an image into three parts (structures, textures and noise) based on a local regularization scheme. We compare our results with the recent work of Aujol and Chambolle. We finish by giving another model which combines the advantages of the two previous ones.

Paper Structure

This paper contains 7 sections, 4 theorems, 62 equations, 12 figures.

Table of Contents

  1. Introduction
  2. Three part image decomposition: a local adaptative algorithm
  3. Aujol-Chambolle's algorithm
  4. Adaptative wavelet algorithm
  5. Conclusion
  6. Appendix A
  7. Appendix B

Key Result

Proposition 2.1

Let $u\in BV$, $v\in G_{\mu_1}$, $w\in G_{\mu_2}$ be the structures, textures and noise parts respectively and $f$ the original noisy image. Let the functions $(\nu_1(f)(.,.),\nu_2(f)(.,.))$ be defined on $\mathbb{R}^2\rightarrow ]0;1[$, and assume that these functions could be considered as locally is given by where $P_{G_{\mu}}$ is the Chambolle's non-linear projectors (see chambolle).

Figures (12)

  • Figure 1: Two part decomposition of noisy image, from left to right: noisy image, object part, texture part corrupted by noise.
  • Figure 2: On left we have the noisy image (Barbara$+$gaussian noise, $\sigma=20$); on right, texture partition $\nu_1$.
  • Figure 3: Results given by $F_{\lambda, \mu_1 ,\mu_2}^{JG}$ applied on the synthetic image.
  • Figure 4: Results given by $F_{\lambda, \mu_1 ,\mu_2}^{JG}$ applied on Barbara. First row gives the whole images and second row zooms on a section of the images.
  • Figure 5: Results given by $F_{\lambda, \mu_1 ,\mu_2}^{JG}$ applied on the real outdoor image.
  • ...and 7 more figures

Theorems & Definitions (5)

  • Definition 1
  • Proposition 2.1
  • Proposition 4.1
  • Lemma A.1
  • Lemma B.1