Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Color image restoration based on nonlocal saturation-value similarity

Wei Wang, Yakun Li

Abstract

In this paper, we propose and develop a novel nonlocal variational technique based on saturation-value similarity for color image restoration. In traditional nonlocal methods, image patches are extracted from red, green and blue channels of a color image directly, and the color information can not be described finely because the patch similarity is mainly based on the grayscale value of independent channel. The main aim of this paper is to propose and develop a novel nonlocal regularization method by considering the similarity of image patches in saturation-value channel of a color image. In particular, we first establish saturation-value similarity based nonlocal total variation by incorporating saturation-value similarity of color image patches into the proposed nonlocal gradients, which can describe the saturation and value similarity of two adjacent color image patches. The proposed nonlocal variational models are then formulated based on saturation-value similarity based nonlocal total variation. Moreover, we design an effective and efficient algorithm to solve the proposed optimization problem numerically by employing bregmanized operator splitting method, and we also study the convergence of the proposed algorithms. Numerical examples are presented to demonstrate that the performance of the proposed models is better than that of other testing methods in terms of visual quality and some quantitative metrics including peak signal-to-noise ratio (PSNR), structural similarity index (SSIM), quaternion structural similarity index (QSSIM) and S-CIELAB color error.

Color image restoration based on nonlocal saturation-value similarity

Abstract

In this paper, we propose and develop a novel nonlocal variational technique based on saturation-value similarity for color image restoration. In traditional nonlocal methods, image patches are extracted from red, green and blue channels of a color image directly, and the color information can not be described finely because the patch similarity is mainly based on the grayscale value of independent channel. The main aim of this paper is to propose and develop a novel nonlocal regularization method by considering the similarity of image patches in saturation-value channel of a color image. In particular, we first establish saturation-value similarity based nonlocal total variation by incorporating saturation-value similarity of color image patches into the proposed nonlocal gradients, which can describe the saturation and value similarity of two adjacent color image patches. The proposed nonlocal variational models are then formulated based on saturation-value similarity based nonlocal total variation. Moreover, we design an effective and efficient algorithm to solve the proposed optimization problem numerically by employing bregmanized operator splitting method, and we also study the convergence of the proposed algorithms. Numerical examples are presented to demonstrate that the performance of the proposed models is better than that of other testing methods in terms of visual quality and some quantitative metrics including peak signal-to-noise ratio (PSNR), structural similarity index (SSIM), quaternion structural similarity index (QSSIM) and S-CIELAB color error.
Paper Structure (22 sections, 9 theorems, 102 equations, 32 figures, 2 tables)

This paper contains 22 sections, 9 theorems, 102 equations, 32 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Saturation-value similarity and nonlocal saturation-value gradients
  3. Saturation-value similarity
  4. Nonlocal saturation-value gradients
  5. Saturation-value similarity based nonlocal bounded variation space
  6. SVS-NLTV and the proposed color image restoration models
  7. SVS-NLTV
  8. The proposed color image restoration models
  9. Numerical algorithm for $\operatorname{\rm SVS-NLTV}$ model
  10. The proposed algorithm for $\operatorname{\rm SVS-NLTV}$
  11. The proposed algorithm for $\operatorname{\rm SVS-NLTV-L1}$
  12. The proposed algorithm for $\mathbf{u}$-subproblem
  13. Convergence analysis
  14. Numerical experiments
  15. Image denoising I: Gaussian noise
  16. ...and 7 more sections

Key Result

Proposition 2.1

Assume $\mathbf{u}\in W^{1, 1}(\Omega)$, $p\in C^1(\Omega \times \Omega)$, $\mathbf{p} = (p_1, p_2)$, $p_1, p_2 \in C^1(\Omega \times \Omega)$, $\omega_v, \omega_s\in C^1(\Omega \times \Omega)$, then the following formulas hold in saturation-value space, \newlabelpro2.1

Figures (32)

  • Figure 5.1: First to third: The spatial distributions of PSNR values of the restored results by using different methods corresponding to d = 30/255, 50/255, 70/255 respectively; Fourth: the histogram of the average PSNR values of the restored results by using different methods.
  • Figure 5.2: First to third: The spatial distributions of SSIM values of the restored results by using different methods corresponding to d = 30/255, 50/255, 70/255 respectively; Fourth: the histogram of the average SSIM values of the restored results by using different methods.
  • Figure 5.3: First to third: The spatial distributions of QSSIM values of the restored results by using different methods corresponding to d = 30/255, 50/255, 70/255 respectively; Fourth: the histogram of the average QSSIM values of the restored results by using different methods.
  • Figure 5.4: The first three rows: top to bottom: degraded and restored images with noise level d = 30/255, 50/255, 70/255 respectively; left to right: the restored results by using CTV, GVTV, NLTV, SVTV, and SVS-NLTV respectively. The fourth row: the histograms of measure values by using different methods.
  • Figure 5.5: Top to bottom: the corresponding results with noise level d = 30/255, 50/255, 70/255 respectively. The results include the noisy image (left large picture), the corresponding zoom-in parts of the noise image, the restored results by using CTV, HTV, NLTV, SVTV, SVS-NLTV, the ground-truth image respectively. The spatial distributions of S-CIELAB error (larger than 15 units) are also shown.
  • ...and 27 more figures

Theorems & Definitions (17)

  • Proposition 2.1
  • proof
  • Proposition 2.2: Lower semicontinuity
  • Proposition 2.3: Approximation
  • Proposition 2.4: Compactness
  • Proposition 3.1
  • proof
  • Proposition 3.2
  • proof
  • Theorem 3.3: Existence and Uniqueness
  • ...and 7 more