Study On The Image Denoising Methods Based On Variation PDE And Nonlocal Means

During the acquisition, storage, or transmission, images are easily and inevitably corrupted by noise, which heavily affects the subsequent image processing. Therefore,image denoising is one of the foremost and widely studied tasks in image processing and computer vision. Image denoising aims to preserving important structure features including edges and corners while removing the noise in the image. Many algorithms have been proposed for removing noise from linear models to nonlinear models. This thesis mainly studies the removal of the Gaussian noise, salt-and-pepper noise, and random-valued impulse noise from digital images.The main contents are summarized as follows:1. In order to overcome the drawbacks of TV model and Tikhonov model, an adaptive image denoising model is proposed by the weighted combination of Tikhonov regularization and total variation regularization. In the proposed model, Tikhonov regularization and total variation regularization can be adaptively selected based on the gradient information of the image. When the pixels belong to the smooth regions,Tikhonov regularization is adopted, which can eliminate the staircase artifacts. The total variation regularization is selected when the pixels locate at the edges, which can preserve the edges. We employ the split Bregman method to solve our model.Experimental results demonstrate that our model can obtain better performance than those of other models.2. To eliminate the staircasing effect for TV filter and synchronously avoid the edges blurring for high-order PDE filter, a hybrid regularizers-based adaptive anisotropic diffusion is proposed for image denoising. In the proposed model, the H-1-norm is considered as the fidelity term and the regularization term is composed of TV filter and a fourth-order filter. The two filters can be adaptively selected according to the diffusion function. When the pixels locate at the edges, TV filter is selected to filter the image,which can preserve the edges. When the pixels belong to the flat regions, the fourth-order filter is adopted to smooth the image, which can eliminate the staircase artifacts. In addition,the split Bregman and relaxation approach are employed in our numerical algorithm to speed up the computation. Experimental results demonstrate that our proposed model outperforms the state-of-the-art models cited in the paper in both the qualitative and quantitative evaluations.3. Anisotropic diffusions based on gradient such as the Perona-Malik model indicate good performance in preserving the edges for image denoising. However, they often suffer from so-called staircase effects and the loss of fine details. To overcome these drawbacks, a novel anisotropic diffusion model is proposed, whose diffusion coefficients are defined by the functions of both the determinant and the trace of the structure tensor of the image. Since the determinant and the trace of the structure tensor can well distinguish the smooth regions from the edges and corners, our proposed model can diffuse isotropically in the smooth regions, diffuses anisotropicly along the edges and confines the diffusion process in the corners. Some qualitative and quantitative experimental results demonstrate better performance in comparison with the cases of other anisotropic diffusion models.4. The model with fidelity term based on diffusion tensor is proposed. Firstly, we reset the two eigenvalues of the diffusion tensor, and then reconstruct the new diffusion tensor by the resetted two eigenvalues, which is used as diffusion coefficient. The experimental results demonstrate that the proposed model can both preserve the structural details and avoid blurring the corners.5. A switching mean curvature motion model with data fidelity term is proposed for removing salt-and-pepper noise from digital images. The proposed model firstly detects noise pixels using the two-phase morphological noise detector. At the first phase noise detection, the initial morphological noise detection based on morphological gradients is used to identify the noise candidates. At the second phase, the refined noise detection based on conditional morphological operators is utilized to identify the true noise pixels from the noise candidates. For filtering, only the identified noise pixels are restored by mean curvature motion model while the noise-free pixels remain unchanged.Experimental results demonstrate that the proposed model outperforms the state-of-the-art models in both objective quantitative measures and subjective visual evaluation.6. A fuzzy weighted switching nonlocal means filter is proposed for the removal of random-valued impulse noise. Firstly, we introduce a novel fuzzy weighting function for each pixel to nonlocal means. The larger the value of the fuzzy weighting function is,the more the pixel is corrupted. Therefore, there is the less information to reconstruct image. Extensive simulations show that the proposed model is significantly superior to a number of existing methods with respect to visual effects and quantitative measures.