scholarly journals Local and Nonlocal Regularization to Image Interpolation

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Yi Zhan ◽  
Sheng Jie Li ◽  
Meng Li
Keyword(s):  
Anisotropic Diffusion ◽  
Image Interpolation ◽  
Real Image ◽  
Interpolation Model ◽  
Orthogonal Direction ◽  
Nonlocal Functional ◽  
Image Edges ◽  
Anisotropic Diffusion Equation ◽  
Nonlocal Regularization ◽  
Staircase Artifacts

This paper presents an image interpolation model with local and nonlocal regularization. A nonlocal bounded variation (BV) regularizer is formulated by an exponential function including gradient. It acts as the Perona-Malik equation. Thus our nonlocal BV regularizer possesses the properties of the anisotropic diffusion equation and nonlocal functional. The local total variation (TV) regularizer dissipates image energy along the orthogonal direction to the gradient to avoid blurring image edges. The derived model efficiently reconstructs the real image, leading to a natural interpolation which reduces blurring and staircase artifacts. We present experimental results that prove the potential and efficacy of the method.

scholarly journals The Nonlocalp-Laplacian Evolution for Image Interpolation

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
Yi Zhan
Keyword(s):  
Image Interpolation ◽  
Image Features ◽  
Image Feature ◽  
Real Image ◽  
Interpolation Model ◽  
Tv Regularization ◽  
Proposed Model ◽  
Image Density ◽  
Laplacian Regularization ◽  
Staircase Artifacts

This paper presents an image interpolation model with nonlocalp-Laplacian regularization. The nonlocalp-Laplacian regularization overcomes the drawback of the partial differential equation (PDE) proposed by Belahmidi and Guichard (2004) that image density diffuses in the directions pointed bylocalgradient. The grey values of images diffuse along image feature direction not gradient direction under the control of the proposed model, that is, minimal smoothing in the directions across the image features and maximal smoothing in the directions along the image features. The total regularizer combines the advantages of nonlocalp-Laplacian regularization and total variation (TV) regularization (preserving discontinuities and 1D image structures). The derived model efficiently reconstructs the real image, leading to a natural interpolation, with reduced blurring and staircase artifacts. We present experimental results that prove the potential and efficacy of the method.

scholarly journals Experimental Investigation of Anisotropic Diffusion Applied in Ghost Imaging Reconstruction

2020 ◽  
Vol 10 (18) ◽  
pp. 6437
Author(s):  
Xiaobin Gong ◽  
Min Tao ◽  
Gang Su ◽  
Baohua Li ◽  
Jian Guan ◽  
...  
Keyword(s):  
Anisotropic Diffusion ◽  
Noise Removal ◽  
Interference Term ◽  
Ghost Imaging ◽  
Initial Image ◽  
Noise Interference ◽  
Imaging Reconstruction ◽  
Image Edges ◽  
Anisotropic Diffusion Equation ◽  
Pseudo Inverse

In iterative pseudo-inverse ghost imaging (IPGI), how much the noise interference item of the current iteration approximates the real noise greatly depends on the clarity of initial image. In order to improve IPGI, we propose a method that introduces anisotropic diffusion to construct a more accurate noise interference term, where anisotropic diffusion adapts to both the image and the noise, so that it balances the tradeoff between noise removal and preservation of image details. In our algorithm, the anisotropic diffusion equation is used to denoise the result of each iteration, then the denoised image is used to construct the noise interference term for the next iteration. Compared to IPGI, our method has better performance in visual effects and imaging quality, as the image edges and details are better preserved according to the experimental results.

A nonlinear anisotropic diffusion equation for image restoration with forward-backward diffusivities

2021 ◽  
Vol 14 ◽  
Author(s):  
Santosh Kumar ◽  
Nitendra Kumar ◽  
Khursheed Alam
Keyword(s):  
Image Processing ◽  
Anisotropic Diffusion ◽  
Diffusion Models ◽  
Smoothing Kernel ◽  
Proposed Model ◽  
Invariant Kernel ◽  
Nonlinear Anisotropic Diffusion ◽  
Anisotropic Diffusion Equation ◽  
Frequent Problem ◽  
Deblurring And Denoising

Background: In the image processing area, deblurring and denoising are the most challenging hurdles. The deblurring image by a spatially invariant kernel is a frequent problem in the field of image processing. Methods: For deblurring and denoising, the total variation (TV norm) and nonlinear anisotropic diffusion models are powerful tools. In this paper, nonlinear anisotropic diffusion models for image denoising and deblurring are proposed. The models are developed in the following manner: first multiplying the magnitude of the gradient in the anisotropic diffusion model, and then apply priori smoothness on the solution image by Gaussian smoothing kernel. Results: The finite difference method is used to discretize anisotropic diffusion models with forward-backward diffusivities. Conclusion: The results of the proposed model are given in terms of the improvement.

Multi-Frame Super-Resolution Reconstruction Algorithm Based on Diffusion Tensor Regularization Term

2014 ◽  
Vol 543-547 ◽  
pp. 2828-2832 ◽  
Author(s):  
Xiao Dong Zhao ◽  
Zuo Feng Zhou ◽  
Jian Zhong Cao ◽  
Long Ren ◽  
Guang Sen Liu ◽  
...  
Keyword(s):  
Diffusion Tensor ◽  
Lagrange Equation ◽  
Super Resolution ◽  
Reconstruction Algorithm ◽  
Energy Functional ◽  
L1 Norm ◽  
Regularization Term ◽  
Sr Reconstruction ◽  
Image Edges ◽  
Anisotropic Diffusion Equation

This paper presents a multi-frame super-resolution (SR) reconstruction algorithm based on diffusion tensor regularization term. Firstly, L1-norm structure is used as data fidelity term, anisotropic diffusion equation with directional smooth characteristics is introduced as a prior knowledge to optimize reconstruction result. Secondly, combined with shock filter, SR reconstruction energy functional is established. Finally, Euler-Lagrange equation based on nonlinear diffusion model is exported. Simulation results validate that the proposed algorithm enhances image edges and suppresses noise effectively, which proves better robustness.

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