改进的二阶总广义变分图像去噪算法

为了有效地去除含噪图像中的噪声,克服总变分（TV）去噪易于导致阶梯效应的缺陷,提出了一种改进的二阶总广义变分（TGV）的图像去噪方法。介绍了二阶TGV的理论基础,在二阶TGV中引入了各向异性扩散张量,利用张量函数引导扩散,获得了新的去噪模型,最后提出了一种扩展了的原始-对偶算法对新模型进行数值求解。新模型充分结合了二阶TGV作为正则项自动平衡了一阶和二阶导数项,以及张量函数的各向异性扩散,有效突出边缘结构的特性。实验结果表明,该方法在有效地去除含噪图像中噪声的同时,避免了阶梯效应,增强了对原始图像中边缘结构的保持。     

Total variation and high-order total variation adaptive model for restoring blurred images with Cauchy noise

In this paper, we propose a novel model to restore an image corrupted by blur and Cauchy noise. The model is composed of a data fidelity term and two regularization terms including total variation and high-order total variation. Total variation provides well-preserved edge features, but suffers from staircase effects in smooth regions, whereas high-order total variation can alleviate staircase effects. Moreover, we introduce a strategy for adaptively selecting regularization parameters. We develop an efficient alternating minimization algorithm for solving the proposed model. Numerical examples suggest that the proposed method has the advantages of better preserving edges and reducing staircase effects.     

混合高阶全变差正则化的运动模糊图像盲复原

针对运动模糊图像的盲复原,提出一种基于混合高阶全变差正则化的盲复原方法。该方法首先采用shock滤波器从模糊图像中预测出清晰的图像边缘,并用多尺度策略实现对模糊核由粗到细的准确估计。然后根据自然图像边缘的稀疏特性,将全变差模型的保护边缘特性结合高阶全变差克服平滑区域阶梯效应的优势,对图像进行正则化约束,提出新的混合高阶全变差正则化模型。最后,利用分裂布雷格曼迭代策略对提出模型进行最优化求解。实验结果表明,提出的方法能够很好地保护图像边缘细节,同时有效地抑制平滑区域内振铃和阶梯效应的产生,获得高质量的复原图像。与近几年图像盲复原算法相比,不仅改进了复原图像的主观视觉效果,而且客观上提高了峰值信噪比。     

基于对数函数的非局部总变分图像修复模型

针对基于总变分最小化的图像修复模型容易造成阶梯效应及假边缘的问题,提出了基于对数函数的非局部总变分图像修复模型。新的总变分能量泛函的被积函数为一个关于梯度幅度的对数函数。在总变分模型与各向异性扩散模型的偏微分方程框架下,首先,从理论上证明了对数总变分模型满足良好扩散所需的所有性质,并对其局部扩散行为进行了理论分析,证明了其在等照度方向及梯度方向扩散的良好特性。其次,为考虑图像块的相似性及避免局部模糊,采用非局部对数总变分进行数值实现。实验结果表明,与经典的总变分修复模型相比,基于对数函数的非局部总变分模型对图像修复的效果良好,避免了局部模糊,且在图像平滑区域能较好地抑制阶梯效应;与基于样例的修复模型相比,所提模型对纹理图像能获得更为自然的修复效果。实验结果表明,与三类总变分模型和基于样例的修复模型相比,所提模型的性能最优,且与各对比模型的平均结果（图2、图3、图4）相比,其结构相似性指数（SSIM）分别提高了0.065、0.022和0.051,峰值信噪比（PSNR）分别提高了5.94 dB、4.00 dB和6.22 dB。含噪图像的修复结果表明所提模型具有较好的鲁棒性,对含噪声的图像也能获得良好的修复效果。     

基于非局部总广义变分的图像去噪

针对全变分(TV)模型在去除图像噪声时容易产生阶梯效应的缺点,将二阶总广义变分(TGV)作为正则项应用于全变分模型中可以有效地去除阶梯效应,并且还能够更好地保持图像边缘纹理结构;利用非局部均值滤波算法的思想来构造非局部微分算子,将非局部微分算子应用于总广义变分模型中,综合提出了一种基于非局部总广义变分的图像去噪新模型。新模型充分利用了图像的全局信息进行去噪。实验结果显示了该模型的有效性和优越性。     

改进的二阶总广义变分图像前后景分割模型

针对总变分TV图像前后景分割模型易导致阶梯效应的缺陷,提出了二阶总广义变分TGV图像前后景分割模型。为进一步提升图像分割质量,在TGV前后景分割模型的正则项中引入边缘指示函数,使其在图像边缘区域减弱扩散,较好地保护边缘;在图像平滑区域增强扩散,有效地消除噪声。为突出前景信息,用矩形框标出图像的前景信息,对框内部、外部和边缘的像素做距离映射,并根据能量最小化原则,在二阶TGV模型的数据项中引入此距离映射函数,使模型总能量更小。最后,提出了一种有效的原始对偶分割算法来求解模型。实验表明,新模型不但能够去除阶梯效应现象,保持图像的边缘信息,还使得模型总能量更小,分割得到的图像视觉效果更好。     

基于张量奇异值分解的动态核磁共振图像重建

本文为了改善动态MR图像重建质量,提出了一种结合张量奇异值分解和全变分稀疏模型(TV)的动态核磁共振图像重建算法。算法对动态MR图像进行了低秩约束规范和稀疏约束规范,分别使用了张量奇异值分解阈值方法和全变分稀疏变化基方法求解。实验结果和重建视觉效果表明,在相同采样率下本文算法与单独使用全变分方法,k-t SLR方法,单独使用张量奇异值分解方法相比重建质量更优,在峰值信噪比(PSNR),均方差(MSE)和结构相似性度量(SSIM)的评价指标上有所提高,对图像去噪去模糊重建有具体的应用价值。     

基于混合变分模型的图像去噪

为了有效抑制噪声,获得更好的视觉效果,提出了一种基于混合变分模型的图像去噪方法。将调和模型和全变分模型进行融合,增强模型的去噪性能,根据自适应选取组合系数,组合系数较大时偏向于全变分模型,较小时偏向于调和模型,这样不仅可以有效去除阶梯效应,同时保护边缘细节,采用仿真对比实验以测试模型性能。结果表明,相对其他去噪模型,相同条件下,该模型取得更优的去噪声效果,提高了图像的质量。     

基于分数阶全变分正则化的超分辨率图像重建

从退化的低分辨率图像重建得到高分辨率图像的本质是一病态逆问题,针对该问题,通过添加正则项进行处理。在使用传统的全变分(TV)的基础上,添加了分数阶全变分(FOTV)作为另一正则项来约束解空间。分数阶全变分正则项的使用可以更好地重建图像的细节纹理信息,弥补了全变分算子在平滑区域易出现阶梯效应的缺陷。利用交替方向乘子(ADMM)算法将问题划分为子问题,将全变分和分数阶全变分算子作为循环矩阵,通过傅里叶变换将其对角化,降低了计算的复杂程度。实验结果表明,与已有的方法相比,所提方法有效地避免了阶梯效应的产生,较好地保持了细节信息,并且具有更好的峰值信噪比(PSNR)和结构相似度(SSIM)。     

彩色纹理图像恢复的非局部TV模型

基于局部算子不同形式的TV(total variation)模型用于彩色图像的噪声去除时往往存在边缘模糊、纹理模糊、阶梯效应、Mosaic效应等问题.因此,将传统局部的Tikhonov模型、TV模型、MTV(multi-channel total variation)模型、CTV(color total variation)模型推广到基于非局部算子概念的NL-CT(non-local color Tikhonov)模型、NL-LTV(non-local layered total variation)模型、NL-MTV(non-local multi-channel total variation)模型、NL-CTV(non-local color total variation)模型,并通过引入辅助变量和Bregman迭代参数设计了相应的快速Split Bregman算法.实验结果表明,所提出的非局部TV模型都很好地解决了局部模型中出现的问题,在纹理、边缘、光滑度等特征保持方面取得了良好特性,其中NL-CTV处理效果最好,但是计算效率较低.     

基于Lp伪范数和高阶OGS全变分的椒盐噪声去除

全变分(TV)模型广泛应用于椒盐噪声的去除。然而,TV 模型中存在着严重的阶梯效应。近年 来,由于低阶交叠组稀疏(LOGS)全变分能够很好地抑制阶梯效应,受到了越来越多的关注,但仍有改进空间。 实际上,其只考虑一阶图像梯度的先验信息,而忽略了高阶图像梯度的先验信息。为了进一步提高恢复图像的 质量,提出了一种结合 Lp 伪范数的高阶 OGS 全变分,在利用高阶梯度的 OGS 约束更好地描述图像梯度稀疏 先验的同时,还利用 Lp 伪范数的强稀疏诱导能力更好地描述椒盐噪声的稀疏性。该模型采用交替方向乘子法 求解,并将模型分解为若干个子问题求解。最后,通过实验验证了该模型的正确性,并结合峰值信噪比、结构 相似性度和梯度幅值相似性偏差对模型的恢复性能进行了评价。实验结果表明,该方法相比一些先进的去噪模 型具有很强的竞争力。     

空间移不变系统图像超分辨复原的快速解耦算法

超分辨率图像复原是当今一个重要的热门研究课题. 本文提出了一种基于全变差模型的超分辨率复原快速解耦算法. 利用半二次正则化思想, 提出了一个新的解耦TV (Total variation)模型. 利用交替最小化方法和线性空间不变模糊的性质将上采样融合、去模糊和去噪分步进行. 算法中对上采样融合采用非迭代的直接计算方法; 去模糊过程采用基于变换的预处理共轭梯度迭代算法, 而去噪过程采用了子空间投影方法. 本文算法降低了算法复杂度; 超分辨率重建图像在去除噪声的同时, 不仅能够保证图像平坦区域的保真度, 较好地抑制阶梯效应的产生, 而且能够保持图像中边缘等重要几何结构的清晰度.     

An edge-weighted second order variational model for image decomposition

Decomposing an image into structure and texture is an important procedure for image understanding and analysis. Structure retains object hues and sharp edges whilst texture contains oscillating patterns of an observed image. The classical Vese–Osher model has been used for image decomposition, but its resulting structure image tends to show the undesirable staircase effect. Second order variational models that use a bounded Hessian regulariser have been proposed to remedy this side effect, but they tend to blur edges of objects in structure components. In this paper, we propose an edge-weighted second order variational model for image decomposition, which is able to eliminate staircase effects and preserve object edges. To avoid directly calculating the high order nonlinear partial differential equations of the proposed model, a fast split Bregman algorithm is developed, which uses the fast Fourier transform and analytical generalised soft thresholding equations. Extensive experiments demonstrate that the proposed variational image decomposition model outperforms state-of-the-art first and second order image decomposition models. By removing the texture component from the original noisy image, the effectiveness of the proposed model for image denoising has also been validated.     

图像引导的二阶总广义变分稀疏深度图的稠密重构

利用图像颜色信息进行深度图重构,可以恢复对象边界处的深度不连续性,但无法保证对象内部的深度均匀性。为解决该问题,提出图像引导下总广义变分正则化的深度图重构模型。该模型利用扩散张量将图像提供的边缘信息引入二阶总广义变分正则项,使得重构深度在保持对象边缘的同时逼近分段仿射平面,从而保证恢复深度既保持对象边界处的不连续性,又具有对象内部的均匀性。通过Legendre-Fenchel变换将模型转换成等效的凸凹鞍点问题,从而得到高效的一阶原始对偶求解算法。实验结果表明,该方法能够恢复尖锐的对象边缘,同时保持对象内部的深度均匀性。与现有算法相比,所提方法具有更高的峰值信噪比、归一化互协方差和更低的平均绝对误差。     

隐式曲面上图像扩散的高阶模型

用零水平集函数表达3维曲面,应用曲面上图像梯度的切投影表达其内蕴梯度,把基于梯度的图像扩散变分模型从平面图像拓展到了隐式曲面上的图像处理。基于内蕴梯度的变分模型对曲面上的图像进行扩散的同时可有效地保持其边缘,但像平面图像扩散的变分模型一样会在本该光滑的区域产生明显的阶梯效应。为消除阶梯效应,引入内蕴散度建立了基于内蕴梯度和内蕴散度的隐式曲面上图像扩散的变分模型,并以TV (total variation) 模型、PM(peronamalik)模型为例对所提出的模型的有效性进行了数值验证,实验结果表明该类模型在保持图像边缘的同时可以有效地抑制阶梯效应。     

Kullback–Leibler Divergence Based Composite Prior Modeling for Bayesian Super-Resolution

This paper proposes to adaptively combine the known total variation model and more recent Frobenius norm regularization for multi-frame image super-resolution (SR). In contrast to existing literature, in this paper both the composite prior modeling and posterior variational optimization are achieved in the Bayesian framework by utilizing the Kullback–Leibler divergence, and hyper-parameters related to the composite prior and noise statistics are all determined automatically, resulting in a spatially adaptive SR reconstruction method. Experimental results demonstrate that the new approach can generate a super-resolved image with higher signal-to-noise ratio and better visual perception, not only image details better preserved but also staircase effects better suppressed.     

A grid generator for 3-D explosion simulations using the staircase boundary approach in Cartesian coordinates based on STL models

In this paper, an automatic grid generator based on STL models is proposed. The staircase boundary treatment is implemented to handle irregular geometries and the computation domain is discretized using a regular Cartesian grid. Using the grid generator, staircase grids that are suitable for fast and accurate finite difference analysis could be generated. Employing the slicing algorithm in RP technologies [1], the STL models are sliced with a set of parallel planes to generate 2D slices after the STL files obtained from a CAD system undergo topology reconstruction. To decrease the staircase error (increase accuracy) and enhance working efficiency, the cross-section at the middle of the layer is taken to represent the cross-section of whole layer. The scan line filling technique of computer graphics [2] is used to achieve grid generation after slicing. Finally, we demonstrate an application of the introduced method to generate staircase grids, which allows successful FDM simulation in the field of explosion. The example shows that the automatic grid generator based on STL models is fast and gives simulation results that are in agreement with practical observations.     

Craniofacial reconstruction based on multi-linear subspace analysis

Craniofacial reconstruction aims to estimate an individual’s facial appearance from its skull. It can be applied in many multimedia services such as forensic medicine, archaeology, face animation etc. In this paper, a statistical learning based method is proposed for 3D craniofacial reconstruction. In order to well represent the craniofacial shape variation and better utilize the relevance between different local regions, two tensor models are constructed for the skull and the face skin respectively, and multi-linear subspace analysis is used to extract the craniofacial subspace features. A partial least squares regression (PLSR) based mapping from skull subspace to skin subspace is established with the attributes such as age and BMI being considered. For an unknown skull, the 3D face skin is reconstructed using the learned mapping with the help of the skin tensor model. Compared with some other statistical learning based method in literature, the proposed method more directly and properly reflects the shape relationship between the skull and the face. In addition, the proposed method has little manual intervention. Experimental results show that the proposed method is valid.     

基于复合正则化的荧光显微图像三维重建

针对荧光显微图像三维重建问题,采用广义全变差和剪切波变换作为重建图像的正则项,并构建重建模型,针对重建模型的高阶与非光滑特性,提出了基于变量分离理论和分裂Bregman迭代的快速重建算法,该算法不仅能够实现边缘保存,避免阶梯效应,还可以通过合理选择参数,获得很好的重建效果,在模拟图像栈和真实荧光显微图像栈的实验结果验证了该算法的有效性和可行性。     

A modified LOT model for image denoising

In image processing, it is often desirable to remove the noise and preserve image features. Due to the strong edge preserving ability, the total variation (TV) based regularization has been widely studied. However, it produces undesirable staircase effect. To alleviate the staircase effect, the LOT model proposed by Lysaker et al. (IEEE Trans Image Process 13(10): 1345–1357, 2004) has been studied, which is called the two-step method. After that, this method has started to appear as one of the more effective methods for image denoising, which includes two energy functions: one is about the normal field, the other is about the reconstruction image using the normal field obtained in the first step. However, the smoothed normal field is only related to the original noisy image in the first step, which is not enough. In this paper, we proposed a modified LOT model for image denoising, which lets the reconstruction vector field be related to the restored image. In addition, to compute the new model, we design a relaxed alternative direction method. The numerical experiments show that the new model can obtain the better results compared with some state-of-the art methods.