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Adaptive variational models for image decomposition combining staircase reduction and texture extraction

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Journal of Systems Engineering and Electronics 2009年第2期20卷 254-259页

作者： Jiang Lingling Yin Haiqing feng xiangchu School of Mathematics and Computational Science China Univ. of Petroleum Dongying 257061 P. R. China School of Science Xidian Univ. Xi'an 710071 P. R. China

New models for image decomposition are proposed which separate an image into a cartoon, consisting only of geometric objects, and an oscillatory component, consisting of textures or noise. The proposed models are given in a variational formulation with adaptive regularization norms for both the cartoon and texture parts. The adaptive behavior preserves key features such as object boundaries and textures while avoiding staircasing in what should be smooth regions. This decomposition is computed by minimizing a convex functional which depends on the two variables u and v, alternatively in each variable. Experimental results and comparisons to validate the proposed models are presented.

关键词： image decomposition total variation minimization bounded variation texture

Digital ridgelet reconstruction based on local dual frame

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Science in China(Series F) 2005年第6期48卷 782-794页

作者： BAI Jian feng xiangchu Department of Applied Mathematics Xidian University Xi'an 710071 China

A global dual frame （GDF） representation for the digital ridgelet reconstruction algorithm is discussed and a novel concept of local dual frame （LDF） is presented. Based on the properties of LDF, we propose a new digital ridgelet reconstruction algorithm. The method reduces the redundancy in the digital ridgelet reconstruction while keeping the characteristics of low computation cost. When applying it to the image compression and denoising, good results are obtained.

关键词： ridgelet fast Slant Stack digital ridgelet global dual frame local dual frame

Image decomposition and staircase effect reduction based on total generalized variation

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Journal of Systems Engineering and Electronics 2014年第1期25卷 168-174页

作者： Jianlou Xu xiangchu feng Yan Hao Yu Han School of Science Xidian University School of Mathematics and Statistics Henan University of Science and Technology College of Mathematic and Computational Science Shenzhen University

Total variation （TV） is widely applied in image process-ing. The assumption of TV is that an image consists of piecewise constants, however, it suffers from the so-cal ed staircase effect. In order to reduce the staircase effect and preserve the edges when textures of image are extracted, a new image decomposition model is proposed in this paper. The proposed model is based on the to-tal generalized variation method which involves and balances the higher order of the structure. We also derive a numerical algorithm based on a primal-dual formulation that can be effectively imple-mented. Numerical experiments show that the proposed method can achieve a better trade-off between noise removal and texture extraction, while avoiding the staircase effect efficiently.

关键词： total variation (TV) image decomposition staircaseeffect total generalized variation.

Adaptive variational models for image decomposition

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Science China(Information Sciences) 2014年第2期57卷 245-252页

作者： XU JianLou feng xiangchu HAO Yan HAN Yu School of Science Xidian University School of Mathematics and Statistics Henan University of Science and Technology

Image decomposition refers to the splitting of an image into two or more *** this paper,a clean image is separated into two parts:one is the cartoon component,consisting only of geometric structure,and the other is the oscillatory component,consisting of *** parts for noisy image are considered:cartoon,texture,and *** better decompose an image,we propose two new variational *** our models,two adaptive regularization terms are *** two regularization terms are determined by an adaptive function which can discriminate the cartoon and texture of an image *** results illustrate the efectiveness of the proposed models for image decomposition.

关键词： total variation image decomposition cartoon texture

Image restoration using total variation and anisotropic diffusion equation

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Frontiers of Electrical and Electronic Engineering in China 2007年第4期2卷 400-403页

作者： LI Min feng xiangchu School of Science Xidian UniversityXi’an 710071China

This paper proposes a new model for the image restoration which combines the total variation minimization with the“pure”anisotropic diffusion equation of Alvarez and *** to the introduction of new diffusion term,this model can not only remove noise but also enhance edges and keep their *** it can also keep textures and large-scale fine features that are not characterized by *** to these favorable characteristics,the processed images turn much clearer and smoother,meanwhile,their significant details are kept,which results in appealing vision.

关键词： total variation anisotropic diffusion equation noise removal detail subject classification

Two-direction nonlocal model for image interpolation

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Science China(Technological Sciences) 2013年第5期56卷 930-939页

作者： ZHANG XuanDe feng xiangchu WANG WeiWei LIU GuoJun Department of Applied Mathematics School of ScienceXidian University School of Mathematics and Computer Ningxia University

How to sufficiently exploit the self-similarity of natural images for image restoration has attracted extensive interest in the field of image processing in recent *** fact,the self-similarity implies two-direction similarity structures inherent in images,when a group of similar patches are rearranged to form a matrix,there exists similarity between both columns and rows of this *** this paper,we propose a two-direction nonlocal model (TDNL) to symmetrically exploit the two-direction similarity structures in images,the model directly takes the similar patches as local adaptive dictionary to represent each patch in the image and constrain the representation coefficients by Tikhonov *** can achieve the best results so far and obtain significant gains over the existing methods,in terms of both peak signal to noise ratio (PSNR) measure and the visual quality when it is applied to the problem of image interpolation.

关键词： solar energy image interpolation image priors two-direction similarity structure two-direction nonlocal model

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双层优化估计图像去噪问题的退火参数

西安电子科技大学学报 2022年第6期49卷 86-94页

作者：冯象初卫丽丽西安电子科技大学数学与统计学院陕西西安710126

正则化参数的合理选取和有效利用是变分图像去噪问题中一个重要的问题。模拟退火算法利用迭代法逐步逼近能量泛函的最小解,并在迭代过程中单调地增加正则化参数。在一般情况下,模拟退火模型中的正则化参数/退火参数的确定和单调增加模... 详细信息

正则化参数的合理选取和有效利用是变分图像去噪问题中一个重要的问题。模拟退火算法利用迭代法逐步逼近能量泛函的最小解,并在迭代过程中单调地增加正则化参数。在一般情况下,模拟退火模型中的正则化参数/退火参数的确定和单调增加模式是基于经验的。希望通过数据自适应地学习最优的退火参数,文中将双层优化结构与模拟退火算法相结合,提出了一种新的估计退火参数的双层模型。下层是含有退火参数的迭代法,增加了Laplace附加正则项,以保证下层问题的良好性质;上层是基于L2范数度量的损失函数。同时,利用反向传播算法,提出了一种有效的估计退火参数的求解算法。并给出了一种简单的插值泛化方法,使提出的模型可以适应不同强度的噪声去除问题。实验结果表明,文中所提算法从数据中自适应学习的退火参数,满足模拟退火算法的先验性单增假定;对比常用正则化参数选取方法,所提算法在保证计算效率的同时提升了去噪效果;同时验证了所提算法具有很好的泛化能力。文中从数据学习的角度表明了迭代过程中正则化参数单调增加的合理性。进一步,说明了所提算法能够得到数值最优的退火参数和变化模式。

关键词：图像去噪模拟退火双层优化退火参数

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去除乘性噪声的积分微分方程模型

西安电子科技大学学报 2013年第3期40卷 132-138页

作者：白键冯象初西安电子科技大学理学院陕西西安710071

恢复含乘性噪声的图像是当前图像处理的重要研究课题.提出基于积分微分方程的乘性噪声去除模型.新模型中假定乘性噪声服从伽马分布.讨论了经典的去除乘性噪声的AA模型,在此基础上通过在逆尺度空间积分"尺度"图像,从而得到了新的积分微... 详细信息

恢复含乘性噪声的图像是当前图像处理的重要研究课题.提出基于积分微分方程的乘性噪声去除模型.新模型中假定乘性噪声服从伽马分布.讨论了经典的去除乘性噪声的AA模型,在此基础上通过在逆尺度空间积分"尺度"图像,从而得到了新的积分微分方程.这种新的积分微分方程含有一个单调增加的尺度函数.通过选取适当的尺度函数,该方程可以有效地去除乘性噪声.

关键词：图像去噪总变差最小乘性噪声积分微分方程

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非凸泛函的图像分解

西安电子科技大学学报 2013年第2期40卷 67-71,137页

作者：白键冯象初西安电子科技大学理学院陕西西安710071

提出了一种新的基于非凸泛函的图像分解模型.与经典的用Banach范数作为忠诚项的凸泛函模型相比,本文用残差图像的平方的积分除以它的梯度作为忠诚项.这种新的忠诚项对于纹理图像具有非常小的值,然而,对于几何图像有非常大的值,所以它很... 详细信息

提出了一种新的基于非凸泛函的图像分解模型.与经典的用Banach范数作为忠诚项的凸泛函模型相比,本文用残差图像的平方的积分除以它的梯度作为忠诚项.这种新的忠诚项对于纹理图像具有非常小的值,然而,对于几何图像有非常大的值,所以它很适合图像分解.应用梯度下降法求非凸泛函的极小值,这导致将一个新的非线性二阶偏微分方程演化到稳定的状态.与经典的总变差最小模型(TV)和四阶偏微分方程模型(OSV)相比,提出的模型可以更好地保持图像的边缘,所以纹理部分有更少的卡通信息.数值实验也证明了本文的模型比标准的TV和OSV模型具有更好的图像分解效果.

关键词：图像分解总变差最小泛函极小非凸泛函