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Weighted structure tensor total variation for image denoising

Xiuhan Sheng, Lijuan Yang, Jingya Chang

TL;DR

The proposed weighted STV (WSTV) model can effectively capture local information from images and maintain their details during the denoising process and can effectively improve the quality of restored images compared to other TV and STV-based models.

Abstract

For image denoising problems, the structure tensor total variation (STV)-based models show good performances when compared with other competing regularization approaches. However, the STV regularizer does not couple the local information of the image and may not maintain the image details. Therefore, we employ the anisotropic weighted matrix introduced in the anisotropic total variation (ATV) model to improve the STV model. By applying the weighted matrix to the discrete gradient of the patch-based Jacobian operator in STV, our proposed weighted STV (WSTV) model can effectively capture local information from images and maintain their details during the denoising process. The optimization problem in the model is solved by a fast first-order gradient projection algorithm with a complexity result of $O(1 / i^2)$. For images with different Gaussian noise levels, the experimental results demonstrate that the WSTV model can effectively improve the quality of restored images compared to other TV and STV-based models.

Weighted structure tensor total variation for image denoising

TL;DR

The proposed weighted STV (WSTV) model can effectively capture local information from images and maintain their details during the denoising process and can effectively improve the quality of restored images compared to other TV and STV-based models.

Abstract

For image denoising problems, the structure tensor total variation (STV)-based models show good performances when compared with other competing regularization approaches. However, the STV regularizer does not couple the local information of the image and may not maintain the image details. Therefore, we employ the anisotropic weighted matrix introduced in the anisotropic total variation (ATV) model to improve the STV model. By applying the weighted matrix to the discrete gradient of the patch-based Jacobian operator in STV, our proposed weighted STV (WSTV) model can effectively capture local information from images and maintain their details during the denoising process. The optimization problem in the model is solved by a fast first-order gradient projection algorithm with a complexity result of . For images with different Gaussian noise levels, the experimental results demonstrate that the WSTV model can effectively improve the quality of restored images compared to other TV and STV-based models.
Paper Structure (12 sections, 34 equations, 4 figures, 2 tables, 1 algorithm)

This paper contains 12 sections, 34 equations, 4 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Contributions
  3. Preliminaries
  4. Notations
  5. Image restoration model
  6. Anisotropic total variation (ATV)
  7. Structure tensor total variation (STV)
  8. The proposed model and algorithm
  9. The weighted structure tensor total variation (WSTV) model
  10. Algorithm for WSTV
  11. Numerical experiment
  12. Conclusion

Figures (4)

  • Figure 1: Twelve 256 $\times$ 256 test images. From left to right and top to bottom: Cameraman, House, Peppers, Starfish, Butterfly, Parrot, Baboon, Boats, Colored butterfly, Babara, Colored peppers and Airplane.
  • Figure 2: Compare the denoising effects of various models on grayscale images at the Gaussian noise level $\sigma=0.05$. From left to right are the image restoration results obtained using TV, ATV, STV, and the proposed model (WSTV). The first row of each image represents the complete restored image. The second row of each image is a part of the restored image.
  • Figure 3: Compare the denoising effects of various models on grayscale images at the Gaussian noise level $\sigma=0.1$. From left to right are the image restoration results obtained using TV, ATV, STV, and the proposed model (WSTV). The first row of each image represents the complete restored image. The second row of each image is the difference between the restored image and the original image. The colorbar displays more efficient restorations if the color is more shaded.
  • Figure 4: Compare the denoising effects of three models under various noise levels. The Gaussian noise levels from top to bottom are $\sigma=\{0.05, 0.1, 0.15\}$. The restoration results using VTV, STV, and WSTV are shown from the second column on the left to the last column on the right. The first column is the initial noise image.