基于自适应正则化的全变分去噪算法

Stanley Osher和Martin Burger提出的基于Bregman距离的迭代正则化全变分去噪算法运算速度较快,但是应用于图像去噪时,没有考虑不同区域的灰度分布特性,从而容易导致纹理等重要信息丢失或模糊的缺陷.针对这一现象,提出了一种基于自适应正则化的全变分去噪算法.论文对Osher的去噪模型中的全局正则化参数进行改进,给出了一种根据图像中不同区域的灰度分布特性,自适应选取正则化参数的方法.该算法可以保留图像的边缘和纹理细节信息.实验结果证实了所提算法的有效性,其信噪比较原有方法至少提高1.0 dB以上.     

自适应非局部数据保真项和双边总变分的图像去噪模型

针对常见去噪方法容易造成特定区域过度平滑、奇异结构残余噪声以及产生阶梯效应和对比度损失等问题,提出一种自适应非局部数据保真项和双边总变分的图像去噪模型,建立了自适应非局部正则化能量泛函和相应的变分框架。首先,对噪声图像利用自适应权值的非局部均值求得数据拟合项;其次,引入双边总变分正则化项,利用正则化系数来适度平衡数据拟合项和正则化项的影响;最后,通过能量函数最小化对不同的噪声统计快速求得最优解,从而达到降低残余噪声并纠正过度平滑的目的。通过理论分析和针对模拟噪声图像与真实噪声图像的实验结果表明,所提出的图像去噪模型能够较好地处理具有不同统计特性的图像噪声,与自适应非局部均值滤波去噪相比,所提算法的峰值信噪比（PSNR）值最多可以得到0.6 dB的改善;与全变分正则化图像去噪算法比较,所提算法的主观视觉效果明显更好,在去噪的同时图像纹理和边缘等细节信息保护得更好,PSNR值最多可以提高10 dB,而多尺度结构相似性度（MS-SSIM）指标可以提升0.3。因此,所提出的图像去噪模型可以在理论上更好地探讨如何合理处理噪声和图像内容本身的高频细节信息,在视频和图像分辨率提升等领域也具有良好的实际应用价值。     

基于图像局部梯度L0范数正规化的图像分解算法

针对基于梯度L0范数正规化的变分泛函最优化分解图像时误判噪声梯度为边缘梯度的问题,提出一种基于图像局部梯度的L0范数正规化的图像分解算法。该算法构造了一个由保真函数和正则项构成的适用于图像分解的变分泛函,其中正则项用图像的局部梯度的L0范数进行估计,进而通过求解泛函的最小值,以分解出图像的结构信息(即图像的边缘)。与直接基于图像一阶梯度的L0范数的分解算法相比,该算法可以去除噪声梯度的干扰,从而使分解出的图像边缘中不含有噪声。实验结果表明,该算法在分解图像结构和纹理时,既能很好地把边缘保留在图像结构层中,也可把噪声分解到图像结构层外。     

基于前向后向算子分裂的稀疏性正则化图像超分辨率算法

提出了一种新的基于稀疏表示正则化的多帧图像超分辨凸变分模型, 模型中的正则项刻画了理想图 像在框架系统下的稀疏性先验, 保真项度量其在退化模型下与观测信号的一致性, 同时分析了最优解条件. 进一步, 基于前向后向算子分裂法提出了求解该模型的不动点迭代数值算法, 每一次迭代分解为仅对保真项的前向(显式)步与仅对正则项的后向(隐式)步, 从而大幅度降低了计算复杂性; 分析了算法的收敛性, 并采取序贯策略提高收敛速度. 针对可见光与红外图像序列进行了数值仿真, 实验结果验证了本文模型与数值算法的有效性.     

Joint sparsity and fidelity regularization for segmentation-driven CT image preprocessing基于稀疏性和保真性正则化模型的分割驱动的CT图像预处理研究

In this paper, we propose a novel segmentation-driven computed tomography (CT) image preprocessing approach. The proposed approach, namely, joint sparsity and fidelity regularization (JSFR) model can be regarded as a generalized total variation (TV) denoising model or a generalized sparse representation denoising model by adding an additional gradient fidelity regularizer and a stronger gradient sparsity regularizer. Thus, JSFR model consists of three terms: intensity fidelity term, gradient fidelity term, and gradient sparsity term. The interactions and counterbalance of these terms make JSFR model has the ability to reduce intensity inhomogeneities and improve edge ambiguities of a given image. Experimental results carried out on the real dental cone-beam CT data demonstrate the effectiveness and usefulness of JSFR model for CT image intensity homogenization, edge enhancement, as well as tissue segmentation.     

基于梯度曲面面积与稀疏约束的图像平滑方法

针对纹理图像在平滑过程中低对比度边缘易丢失和纹理细节抑制不彻底等问题,提出基于梯度曲面面积与稀疏约束的图像平滑方法。首先,将图像视作三维空间中的二维嵌入曲面,再在此基础上分析图像的几何特征并提出梯度曲面面积约束正则化项,以提高纹理抑制性能;其次,根据图像的统计特性,建立L₀梯度稀疏与自适应梯度曲面面积约束的混合正则化约束图像平滑模型;最后,采用交替方向乘子法对非凸非光滑的优化模型进行高效求解。通过纹理抑制、边缘检测、纹理增强和图像融合等方面的实验结果可知,所提出的图像平滑算法克服了L₀梯度最小化平滑方法易造成的阶梯效应和欠滤波等缺陷,能够在去除大量纹理信息的同时保持并锐化图像显著的边缘轮廓。     

基于广义变分模型的自适应图像去噪算法

通过分析全变分(TV)去噪模型的优缺点,提出了一种新的改进算法。该算法根据最大后验概率(MAP)和马尔可夫随机场(MRF)的理论,推导出一个广义变分的图像去噪模型,并对平衡正则化项和数据保真项的Lagrange乘子λ进行了自适应改进,最后采用了一种鲁棒性好和边缘保持能力强的势函数,结合梯度加权最速下降法和半点格式的数值迭代算法对自适应的广义变分去噪模型寻优求解。实验结果表明,新模型能很好地应用于图像去噪,与现有的算法相比,在峰值信噪比有所提高的同时,图像的主观视觉效果也更好。     

基于变分的CT图像环形伪影校正

有效去除CT图像中环形伪影是医学图像处理领域的一个重要研究方向,现有的方法在去除环形伪影的同时,对CT图像的边缘及细节保留存在困难和挑战.本文采用变分优化的思想,将环形伪影的去除问题建模为一个能量最小化问题,来缓解保持图像信息和去除伪影之间的矛盾,提出了一种后处理的伪影校正算法.根据环形伪影产生机理和特性表现构造有针对性的变分模型,一是从环形伪影的几何特性入手,设计更为合理的梯度保真形式,增强模型对图像细节信息的保护;二是从环形伪影的边缘特性入手,构建具有伪影辨识能力的相对全变分正则项,降低模型对图像结构性信息的影响.基于构造的变分模型,采用高效的优化求解算法,实现环形伪影的有效去除.对比实验表明,无论在视觉观察还是定量分析方面,本文算法均体现出了较好的性能.     

混合非凸非光滑正则化约束的模糊图像盲复原

为能够复原出高质量的清晰图像,提出一种混合正则化约束的模糊图像盲复原方法。首先,根据模糊核的稀疏性,采用L₀范数的正则项对模糊核进行稀疏约束,以提高模糊核估计的准确性;然后,根据图像梯度的稀疏性,采用混合一阶和二阶图像梯度的L₀范数对图像梯度进行正则化约束,以保留图像边缘信息;最后,由于所提出的混合正则化约束模型本质上是非凸非光滑优化问题,通过交替方向乘子法对模型进行求解,并在非盲反卷积阶段采用L₁范数数据拟合项和全变分的方法复原清晰图像。实验结果表明,所提方法能够复原出更加清晰的细节和边缘信息,复原结果的质量更高。     

基于PM模型的曲面去噪变分水平集方法

PM（perona-malik）模型是一种经典的非线性图像扩散模型,该模型能根据设定的阈值对图像光滑区域进行扩散,并能自适应地保持图像边缘。本文将曲面法矢量与一般灰度图像的强度进行类比,将经典的图像扩散的PM模型转化为曲面几何噪声处理的自适应扩散变分模型,在使曲面光滑的同时,能够保持曲面边缘。曲面采用隐函数的零水平集表达,能量泛函中的数据项用初始水平集函数的Heaviside函数与演化后水平集函数的Heaviside函数差的平方表达,能量泛函中的光滑项基于几何曲率定义。此外,在能量泛函中增加了水平集函数为符号距离函数的惩罚项,避免了水平集函数需要不断重新初始化的问题。数值实验验证了所提出模型的曲面噪声去除及曲面边缘保持效果。     

基于正则化的多光谱图像二值化处理

为了进一步提升传统多光谱图像二值化处理方法的处理速度和抗噪性能,提出基于正则化的多光谱图像二值化处理方法。将正则化约束引入到多光谱图像去噪模型中,对现有的多光谱去噪模型进行改进。并利用正则化框架中的数据正则项对图像的噪声机制以及图像的先验信息进行建模,以实现多光谱图像去噪处理。根据去噪结果采用约束能量最小化方法获取多光谱图像的边缘信息,将最佳全局阈值法和局部阈值自适应方法在边缘信息的基础上相结合,实现对多光谱图像的二值化处理。仿真结果表明,所设计方法具有较强的抗噪能力和较快的处理速度,并且经处理后的图像分辨率较高,充分验证了上述方法的有效性。     

一种自适应正则化的图像超分辨率算法

提出一种自适应正则化的图像超分辨率重建算法. 首先, 利用局部残差均值自适应地计算各低分辨率图像通道的权值参数矩阵, 可有效地利用各通道对应区域间的交叉信息; 其次, 利用正则项局部误差均值自适应地计算平衡正则项和保真项的正则化参数矩阵, 能较好地保持图像边缘纹理等信息.实验结果表明本文算法不但具有较高峰值信噪比(Peak signal to noise ratio, PSNR) 和结构相似度(Structural similarity, SSIM), 而且在边缘、纹理等细节区域具有更好的重建效果.     

Adaptive contourlet-wavelet iterative shrinkage/thresholding for remote sensing image restoration

In this paper, we present an adaptive two-step contourlet-wavelet iterative shrinkage/thresholding （TcwlST） algorithm for remote sensing image restoration. This algorithm can be used to deal with various linear inverse problems （LIPs）, including image deconvolution and reconstruction. This algorithm is a new version of the famous two-step iterative shrinkage/thresholding （TWIST） algorithm. First, we use the split Bregrnan Rudin-Osher-Fatemi （ROF） model, based on a sparse dictionary, to decompose the image into cartoon and texture parts, which are represented by wavelet and contourlet, respectively. Second, we use an adaptive method to estimate the regularization parameter and the shrinkage threshold. Finally, we use a linear search method to find a step length and a fast method to accelerate convergence. Results show that our method can achieve a signal-to-noise ratio improvement （ISNR） for image restoration and high convergence speed.     

基于大气物理模型的快速视觉优化去雾算法

针对雾霾天气条件下单幅图像降质以及现有去雾方法时间复杂度高的问题,以环境光物理模型为基础,引出快速视觉优化去雾算法.首先对单幅图像阈值分割找到天空区域,并结合二叉树模型定位精确的天空光矢量,进而采用改进的约束最小二乘法滤波细化粗略透射比率,保证其边缘细节较完整且受噪声影响小,最后利用环境光物理模型实现无雾图像的还原,并采用平均梯度、信息熵和视觉保真度等指标对图像进行评价.实验结果表明,所提算法与基于多尺度Retinex的自适应图像增强方法、基于独立分量的复原方法、快速可视化复原方法和暗原色先验复原方法对比,指标值较好且实时性强.     

Unsupervised change detection in SAR images using curvelet and L1-norm based soft segmentation

In this article, we propose a novel unsupervised change detection method for synthetic aperture radar (SAR) images. First, we generate a difference image as a weighted average of a log-ratio image and a mean-ratio image, which has the advantage of enhancing the information of changed regions and restraining the information of unchanged background regions simultaneously. Second, we propose a variational soft segmentation model based on non-differentiable curvelet regularization and L1-norm fidelity. Numerically, by using the split Bregman technique for curvelet regularization term and reformulating the L1-norm fidelity as weighted L2-norm fidelity, we get an effective algorithm in which each sub-problem has a closed-form solution. The numerical experiments and comparisons with several existing methods show that the proposed method is promising, with not only high robustness to non-Gaussian noise or outliers but also high change detection accuracy. Moreover, the proposed method is good at detecting fine-structured change areas. Especially, it outperforms other methods in preserving edge continuity and detecting curve-shaped changed areas.     

基于定向双边全变差正则化的文档图像超分辨率算法研究

针对文档图像超分辨率重建问题,在传统双边全变差(Bilateral Total Variation,BTV)正则化超分辨率算法的基础上,提出了一种基于改进BTV的文档图像超分辨率算法。该算法引入一个新的正则项,即笔画宽度的方向,并根据字符笔画的局部宽度和局部方向自适应地进行平滑处理;然后通过分析输入的低分辨率图像及其插值,使输出图像的局部笔画宽度接近于局部的笔画方向。这种信息被压缩到基于笔画宽度的方向全变分正则项中。通过最小化正则项和数据保真项的线性组合,重建了高分辨率的图像。与相关的文档图像超分辨率方法相比,所提方法在视觉图像质量和字符识别精度方面得到了显著的改善。     

基于改进布谷鸟搜索算法的图像边缘检测

针对传统边缘检测算法自适应能力差、固定阈值、背景噪声抑制的问题, 为了获得更理想的图像边缘检测结果, 提出了一种基于改进布谷鸟搜索算法的图像边缘测算法. 首先通过灰度图像矩阵的一阶导数得到灰度图像的梯度值矩阵, 然后用改进布谷鸟搜索算法根据布谷鸟繁殖行为找到搜索图像的梯度最大值, 检测出图像的边缘, 最后采用仿真实验对算法的性能进行检测. 仿真实验结果表明, 本文算法能快速、准确地检测出图像的边缘, 且优于其他传统边缘检测算法.     

Adaptive active contour model driven by image data field for image segmentation with flexible initialization

In this paper, a novel adaptive active contour model based on image data field for image segmentation with robust and flexible initializations is proposed. We firstly construct a new external energy term deduced from the image data field that drives the level set function to move in the opposite direction along the boundaries of object and an adaptive length regularization term based on the image local entropy. The designed external energy and length regularization term are then incorporated into a variationlevel set framework with an additional penalizing energy term. Due to the adaptive sign–changing property of the external energy and the adaptive length regularization term, the proposed model can tackle images with clutter background and noise, the level set function can be initialized as any bounded functions (e.g., constant function), which implies the proposed model is robust to initialization of contours. Experimental results on both synthetic and real images from different modalities confirm the effectiveness and competivive performance of the proposed method compared with other representative models.

     

Adaptive total variation denoising based on difference curvature

Image denoising methods based on gradient dependent regularizers such as Rudin et al.’s total variation (TV) model often suffer the staircase effect and the loss of fine details. In order to overcome such drawbacks, this paper presents an adaptive total variation method based on a new edge indicator, named difference curvature, which can effectively distinguish between edges and ramps. With adaptive regularization and fidelity terms, the new model has the following properties: at object edges, the regularization term is approximate to the TV norm in order to preserve the edges, and the weight of the fidelity term is large in order to preserve details; in flat and ramp regions, the regularization term is approximate to the L2 norm in order to avoid the staircase effect, and the weight of the fidelity term is small in order to strongly remove the noise. Comparative results on both synthetic and natural images demonstrate that the new method can avoid the staircase effect and better preserve fine details.     

Gaussian mixture model learning based image denoising method with adaptive regularization parameters

Gaussian mixture model learning based image denoising as a kind of structured sparse representation method has received much attention in recent years. In this paper, for further enhancing the denoised performance, we attempt to incorporate the gradient fidelity term with the Gaussian mixture model learning based image denoising method to preserve more fine structures of images. Moreover, we construct an adaptive regularization parameter selection scheme by combing the image gradient with the local entropy of the image. Experiment results show that our proposed method performs an improvement both in visual effects and peak signal to noise values.