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BMO-type functionals related to the total variation and connection to denoising models

Serena Guarino Lo Bianco, Roberta Schiattarella

TL;DR

The asymptotic behaviour in the spirit of $\Gamma$-convergence of BMO-type functionals related to the total variation of a function $u$ is analyzed and a minimization problem coming from applications in image processing is dealt with.

Abstract

The purpose of this paper is to analyze the asymptotic behaviour in the spirit of $Γ$-convergence of BMO-type functionals related to the total variation of a function $u$. Moreover, we deal with a minimization problem coming from applications in image processing.

BMO-type functionals related to the total variation and connection to denoising models

TL;DR

The asymptotic behaviour in the spirit of -convergence of BMO-type functionals related to the total variation of a function is analyzed and a minimization problem coming from applications in image processing is dealt with.

Abstract

The purpose of this paper is to analyze the asymptotic behaviour in the spirit of -convergence of BMO-type functionals related to the total variation of a function . Moreover, we deal with a minimization problem coming from applications in image processing.
Paper Structure (6 sections, 10 theorems, 104 equations)

This paper contains 6 sections, 10 theorems, 104 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Properties of the functional $H_\varepsilon$
  4. Properties of the functional $K_\varepsilon$
  5. $\Gamma-$convergence for $H_\varepsilon$ and $K_\varepsilon$
  6. Application to image processing

Key Result

Theorem 1.1

The family of functionals $(H_\varepsilon)$ defined in Hfunct for $\varepsilon>0$, $\Gamma$-converges in $L^1$ to the functional $H$ defined for any $u\in L^1(\Omega)$ by

Theorems & Definitions (19)

  • Theorem 1.1
  • Theorem 1.2
  • Theorem 1.3
  • Lemma 2.1
  • proof
  • Theorem 2.2
  • Theorem 2.3: Poincarè inequality in $BV^m$ FM
  • Theorem 2.4
  • Remark 2.5
  • Proposition 2.6
  • ...and 9 more