| Citation: |
Fahd Karami, Dris Meskine, Khadija Sadik. A NEW NONLOCAL MODEL FOR THE RESTORATION OF TEXTURED IMAGES[J]. Journal of Applied Analysis & Computation, 2019, 9(6): 2070-2095. doi: 10.11948/20170189
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A NEW NONLOCAL MODEL FOR THE RESTORATION OF TEXTURED IMAGES
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Abstract
In this paper, we focus on the mathematical and numerical study of a new nonlocal reaction-diffusion system for image denoising. This model is motivated by involving the decomposition approach of $H^{-1}$ norm suggested by Meyer [25] which is more appropriate to represent the oscillatory patterns and small details in the textured image. Based on Schaeffer's fixed point theorem, we prove the existence and uniqueness of solution of the proposed model. To illustrate the efficiency and effectiveness of our model, we test the denoising experimental results as well we compare with some existing models in the literature. -
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References
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Fahd Karami, Dris Meskine, Khadija Sadik. A NEW NONLOCAL MODEL FOR THE RESTORATION OF TEXTURED IMAGES[J]. Journal of Applied Analysis & Computation, 2019, 9(6): 2070-2095. doi: 10.11948/20170189
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Figure 1. Images corrupted by Gaussian noise with zero mean and variance
$ \sigma^2 = 0.025 $ - Figure 2. Restored images with the proposed model.
- Figure 3. First row : Noisy Lena images with noise at zero mean and different variances. Second row : Restored images using the proposed algorithm.
- Figure 4. First row : Noisy House images with noise at zero mean and different variances. Second row : Restored images using the proposed algorithm.
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Figure 5. Left : Noisy Barbara image with
$ PSNR = 26.5544 $ , middle : Restored image by TVH with$ PSNR = 29.0488 $ and Right : Restored image by our model (NLH) with$ PSNR = 32.5609 $ . - Figure 6. Left column : Zoom of the results of TVH and right column : Zoom of the images restored using NLH.
- Figure 7. Here, we compare the texture of restored images between our model and TVH model.
- Figure 8. Left column: Top to Bottom: Noisy image A, Noisy image B, Noisy Barbara image and Noisy image C. Middle column: Restored images by NLPL and Right column: Restored images by our proposed model.
- Figure 9. Left column : Zoom of the result of NLPL and Right column : Zoom of the image restored by our model.
- Figure 10. Left column: original image (top) and noisy image (bottom). Middle column: NLPL denoising result and error (PSNR = 27.6702). Right column: our model denoising result and error (PSNR = 28.3045).
- Figure 11. Left column: Top to Bottom: Noisy image C, Noisy Lena image, and Noisy image D. Middle column: Restored images by NLmeans and Right column: Restored images by our proposed model.