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Nonconvex models for recovering images corrupted by salt-and-pepper noise on surfaces

Yuan Liu, Peiqi Yu, Chao Zeng

TL;DR

A lower bound for data fitting term of the recovered image is established for the proximal linearization method with the support shrinking strategy to recover images corrupted by salt-and-pepper noise on surfaces.

Abstract

Image processing on surfaces has drawn significant interest in recent years, particularly in the context of denoising. Salt-and-pepper noise is a special type of noise which randomly sets a portion of the image pixels to the minimum or maximum intensity while keeping the others unaffected. In this paper, We propose the L$_p$TV models on triangle meshes to recover images corrupted by salt-and-pepper noise on surfaces. We establish a lower bound for data fitting term of the recovered image. Motivated by the lower bound property, we propose the corresponding algorithm based on the proximal linearization method with the support shrinking strategy. The global convergence of the proposed algorithm is demonstrated. Numerical examples are given to show good performance of the algorithm.

Nonconvex models for recovering images corrupted by salt-and-pepper noise on surfaces

TL;DR

A lower bound for data fitting term of the recovered image is established for the proximal linearization method with the support shrinking strategy to recover images corrupted by salt-and-pepper noise on surfaces.

Abstract

Image processing on surfaces has drawn significant interest in recent years, particularly in the context of denoising. Salt-and-pepper noise is a special type of noise which randomly sets a portion of the image pixels to the minimum or maximum intensity while keeping the others unaffected. In this paper, We propose the LTV models on triangle meshes to recover images corrupted by salt-and-pepper noise on surfaces. We establish a lower bound for data fitting term of the recovered image. Motivated by the lower bound property, we propose the corresponding algorithm based on the proximal linearization method with the support shrinking strategy. The global convergence of the proposed algorithm is demonstrated. Numerical examples are given to show good performance of the algorithm.
Paper Structure (14 sections, 5 theorems, 70 equations, 5 figures, 2 tables, 2 algorithms)

This paper contains 14 sections, 5 theorems, 70 equations, 5 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Triangulated surfaces
  4. Discretization of images on surfaces
  5. Models and algorithm
  6. Lower bound theory
  7. Algorithm
  8. Algorithm implementation
  9. Convergence analysis
  10. Experiments
  11. Performance of PLM
  12. Conclusions
  13. The subdifferential
  14. KL functions

Key Result

Theorem 3.2

For any local minimizer $u^{*}$ of $\mathcal{F}(u)$ in (tvp), there exists a constant $\theta > 0$ such that for all $j \in I_v$, if $|u_j-f_j|\neq 0$, then

Figures (5)

  • Figure 1: Triangle meshes and images on triangle meshes.
  • Figure 2: Dual mesh and control cells.
  • Figure 3: The gradient of the basis $\phi_i$ restricted on $[v_i,v_j,v_k]$: the red vector.
  • Figure 4: Test images. From top left to bottom right: Ball, Bottle, Bunny, Horse, Mug and Flag.
  • Figure 5: Noisy images with zoomed regions, where the noise level is $\rho=0.10$. The second (resp., fourth) column is the corresponding zoomed regions of the first (resp., third) column.

Theorems & Definitions (15)

  • Definition 3.1
  • Theorem 3.2
  • proof
  • Corollary 3.3
  • proof
  • Lemma 4.1
  • proof
  • Lemma 4.2
  • proof
  • Theorem 4.3
  • ...and 5 more