自适应二阶总广义变分图像恢复方法

针对经典的总变分(TV)去噪模型容易导致阶梯效应 的缺陷,提出了一种自适应的二阶总广义变分(TGV)图像恢 复模型。通过在二阶TGV正则项中引入边缘指示函数,并利用边缘指示函数在平滑区域,增强 扩散,去除噪声,在边缘处降低扩散,保护边缘等特征恢复图像,在新模型中,自适应二阶 总广义变分是正则项,它能自动的平衡一阶和二阶导数项。因此这些特征使得新 模型在去噪的同时不但能够自适应地保持图像的边缘信息,而且还能去除阶梯效应。为了有 效的计算该模型,本文采用原始一对偶算法仿真新模型,实验结果表明,与经 典的TV模型相比,改进的方法无论是在视觉效果还是信噪比(SNR)上都有 明显地提高。     

基于梯度保真项的低剂量CT统计迭代重建算法

针对低剂量计算机断层扫描(Computed Tomography,CT)重建图像时容易出现明显条形伪影这一现象,提出一种基于梯度保真项的低剂量CT统计迭代重建算法。该算法克服了原始全变分(Total Variation,TV)模型在抑制条形伪影和噪声的同时引入阶梯效应的缺点,首先把梯度保真约束项和能够区分图像平滑区和细节区的边缘指示函数应用到TV模型中得到基于梯度保真项的自适应全变分模型,然后再把新模型与惩罚加权最小二乘(Penalized Weighted Least Square,PWLS)重建算法相结合,使用交替方向迭代法得到最终的图像。采用Shepp-Logan模型来验证算法的有效性,实验结果表明,该算法不仅可以有效地去除条形伪影,还可以较好地保护图像的边缘和细节信息。     

结合全变分的双边滤波图像去噪方法研究

图像去噪是数字图像处理过程中的一个重要步骤,它将直接影响到图像处理的最终质量。针对传统的全变分(TV)正则化去噪算法容易产生阶梯效应的缺点,利用双边滤波去噪算法在空间域和值域两个方面进行滤波的特点,提出一种结合TV模型的双边滤波方法,该方法能在一定程度上有效地改善阶梯效应。仿真实验结果表明,提出的去噪方法不仅能够获得较好的去噪效果,还能有效地保持图像的边缘特征信息,降噪效果明显。在较高水平噪声情况下,与TV算法相比,该方法针对小尺寸灰度图片(256×256)图像的峰值信噪比(PSNR)提高1.45 d B左右,大尺寸灰度图片(512×512)图像的PSNR提高2.56 d B左右。     

SAR图像去噪的分数阶多尺度变分PDE模型及自适应算法

在合成孔径雷达(SAR)图像相干斑噪声抑制中,保持图像的边缘和纹理是非常重要的。该文首先利用分数阶导数和负指数Sobolev空间对图像进行建模,建立了分数阶多尺度变分偏微分方程(PDE)模型,然后给出了模型参数自适应选择方法,并在此基础上提出了区域、尺度自适应的去噪算法。数值实验表明,新方法能在去除噪声,抑制图像的 阶梯效应,保持图像的边缘、纹理细节几个方面取得较好的效果。     

基于结构相似度的图像去噪新方法

将结构相似度作为一种刻画忠诚项的度量用于图像去噪模型中。针对经典ROF模型忠诚项的约束项L2度量未考虑图像空间结构性而导致恢复图像视觉效果差的缺陷,引入结构相似度来改进模型的忠诚项,提出了一种新的去噪模型。为在去噪过程中,更好地保护图像的边缘,在此模型的基础上,文中还做了进一步改进,用非凸正则项代替TV正则项,得到推广模型。实验结果表明,相对于ROF模型,两个模型在有效去除噪声的同时,能更好地保持图像的结构信息,提高图像的视觉效果,且推广模型在图像边缘保护方面的性能更好。     

基于全变分理论的红外图像去噪

为了去除红外图像中的噪声,提出了一种基于全变分理论的去噪算法。该方法继承了经典全变分模型在去除噪声中保护边缘的优点,结合图像平滑扩散原理,得到了一个全新的扩散函数;同时引入了一个边缘检测算子,对正则项和忠诚项的相关参量进行了改进,使得修复后的图像大大避免了阶梯效应;最后对该算法的实现进行了推导。结果表明,该算法能够有效地去除噪声,并且避免了阶梯效应的产生。     

一种改进的二阶偏微分去噪模型

分析了基于二阶偏微分的扩散方程模型的基本原理,针对该模型在去噪的同时会产生阶梯效应的缺点,提出了一种基于图像结构信息的二阶偏微分去噪模型。在该模型中,在二阶偏微分的全变分模型的正则化项加入图像的切矢量和法矢量信息,并由此推导出相应的扩散方程,再对扩散方程的扩散强度因子进行修改。在实验中,将模型分别与基于二阶偏微分、四阶偏微分的全变分模型进行对比分析表明,实验结果证明该模型能有效地去除图像噪声,克服阶梯效应的产生,主观性能最优。     

去除乘性噪声的二阶总广义变分模型及算法

针对总变分去噪模型容易导致阶梯效应的缺陷,提 出了一种新的乘性噪声去噪模型。在新模型中,二阶总广义变分(TGV)是正则项,它能自动平 衡一阶和二阶导数项,使得新模型在去除乘性噪声的同时不但能够保 持图像的边缘信息,而且还能去除阶梯效应。为了有效的计算该模型,设计了一个快速迭代算 法。在算法中,首先采用分裂方法和交替方向法将原问题变为两个相关的子问题,然后分别对 子问题利用牛顿法和原始-对偶算法。实验结果表明,与同类模型相比,本文方法无论是在视 觉效果还是定量指标,如峰值信噪比(PSNR)等都有明显地提高。     

基于图像分解的图像修复算法

针对传统变分模型在修复图像时易产生“阶梯效应”与细节模糊等问题,提出了一种基于图像分解的自适应二阶总广义变分和分数阶变分的图像修复算法。首先将待修复的目标图像分解为卡通部分与纹理部分,其中卡通对应目标图像的低、中频部分,因此利用抑制“阶梯效应”较好的二阶总广义变分模型对其进行修复;纹理对应其高频部分,因此利用对细节部分有增强效果的分数阶变分模型对其进行修复。由于文中所提到的修复模型均与线性鞍点结构下求取最优值的模型类似,因此在算法上均采用基于预解式的原始对偶算法对新模型进行求解。另外,为了取得更好的修复效果,文中设计了一个边缘指示算子来自适应地控制新模型的扩散,以更好地保护修复图像的边缘细节。实验结果表明:相比传统的TV、TGV修复模型,新模型的修复效果在主观视觉上显得更加自然,且在峰值信噪比与相关系数等客观评价指标上均有提高。     

图像方向纹理保持的方向全变差正则化去噪模型及其主优化算法

正则化方法是目前解决图像去噪不适定性的一条有效途径,但对于图像中纹理细节的保持仍是棘手的问题。本文针对图像方向纹理保持的去噪问题,给出了图像方向纹理保持的方向全变差正则化去噪模型。分析和证明了方向全变差的若干等价表示性质,并基于该性质迭代构造代理泛函和B样条离散差分逼近方法,给出了一种主优化去噪算法。数值实验表明,该方法在去除噪声、抑制图像的“阶梯效应”和保持图像方向纹理等方面取得较好的效果。     

Low-illumination image denoising method for wide-area search of nighttime sea surface

In order to suppress complex mixing noise in low-illumination images for wide-area search of nighttime sea surface, a model based on total variation (TV) and split Bregman is proposed in this paper. A fidelity term based on L1 norm and a fidelity term based on L2 norm are designed considering the difference between various noise types, and the regularization mixed first-order TV and second-order TV are designed to balance the influence of details information such as texture and edge for sea surface image. The final detection result is obtained by using the high-frequency component solved from L1 norm and the low-frequency component solved from L2 norm through wavelet transform. The experimental results show that the proposed denoising model has perfect denoising performance for artificially degraded and low-illumination images, and the result of image quality assessment index for the denoising image is superior to that of the contrastive models.     

Non-convex hybrid total variation for image denoising

Image restoration problems, such as image denoising, are important steps in various image processing method, such as image segmentation and object recognition. Due to the edge preserving property of the convex total variation (TV), variational model with TV is commonly used in image restoration. However, staircase artifacts are frequently observed in restored smoothed region. To remove the staircase artifacts in smoothed region, convex higher-order TV (HOTV) regularization methods are introduced. But the valuable edge information of the image is also attenuated. In this paper, we propose non-convex hybrid TV regularization method to significantly reduce staircase artifacts while well preserving the valuable edge information of the image. To efficiently find a solution of the variation model with the proposed regularizer, we use the iterative reweighted method with the augmented Lagrangian based algorithm. The proposed model shows the best performance in terms of the signal-to-noise ratio (SNR) and the structure similarity index measure (SSIM) with comparable computational complexity.     

基于广义变分正则化的红外图像噪声抑制方法

文中提出了一种广义变分正则化的红外图像噪声抑制方法,该方法采用p-范数代替目前广泛被采用的全变分范数作为正则项,构造了用于抑制图像噪声的展平泛函,从而将图像噪声抑制问题转化为能量泛函优化问题。通过推导,得到了相应的用于图像噪声抑制的非线性偏微分方程,并采用固定点迭代算法进行线性化求解,使得迭代解稳定收敛。数值试验结果表明,该方法能够有效地去除图像噪声,较之全变分图像噪声抑制方法,新方法进一步提高了对小宽度图像边缘的保持能力,是一种有效且性能优良的红外图像噪声抑制方法。     

Total Variation for Image Restoration with Smooth Area Protection

The problem for image restoration is usually reduced to a constraint optimization problem. Different choice of optimization operator leads to various restoration models, e.g. least squares model and original total variation (TV) model. The TV model and its modified version can efficiently preserve the edge of the restored image well, but there exist obvious staircases in smooth area of the restored image. To reduce those staircases, we propose a new modified TV model, by adding a constraint term for smooth area protection as a penalty function. The numerical experiment shows our model can not only preserve the edge as well as TV model, but also efficiently reduce the staircase appearing in the smooth areas. Furthermore, It is shown that the restored image by our model has higher signal-to-noise ratio, less mean square error and better visual effect than those by the least squares model and by the TV models.     

Total generalized variation restoration with non-quadratic fidelity

Total variation (TV) based Models have been widely used in image restoration problems. However, these models are always accompanied by staircase effect due to the property of bounded variation (BV) space. In this paper, we present two high order variational models based on total generalized variation (TGV) with two common and important non-quadratic fidelity data terms for blurred images corrupted by impulsive and Poisson noises. Since the direct extension of alternative direction method of multipliers (ADMM) to solve three-block convex minimization problems is not necessarily convergent, we develop an efficient algorithm called Prediction–Correction ADMM to solve our models and also show the convergence of the proposed method. Moreover, we extend our models to deal with color images restoration. Numerical experiments demonstrate that the proposed high order models can reduce staircase effect while preserving edges and outperform classical TV based models in SNR and SSIM values.     

一种基于图割的全变差图像去噪算法

本文提出一种基于图割的全变差(TV)图像去噪算法.该算法将全变差去噪模型的能量函数最小化问题转化为图的最小割问题,然后采用图割技术(最大流/最小割算法)求得能量函数的全局最优解.并给出了去噪模型中,均衡系数的自适应设定方案.实验结果及分析表明,该算法能有效抑制以往最小化方法产生的阶梯效应,具有较优的复原效果.     

A Variational Model for Staircase Reduction in Image Denoising

We propose a new variational model to reduce the staircase that often appears in Total variation (TV) based models in image denoising. The model uses BV-seminorm and Besov-seminorm to measure the piece-wise constant component and piecewise smooth component of the image, respectively. We discuss the nontrivial prop-erty of the proposed model and introduce an alternating iteration algorithm that combines the dual projection al-gorithm with Wavelet soft thresholding (WST) algorithm to solve the model numerically. The experimental results show that the proposed model is effective for noise removal and staircase reduction, while the contour can be preserved in the denoised images. Furthermore, compared with two classical staircase reduction models, CEP2 and TGV, the proposed model is much faster than these two models.