一种新的去除混合噪声的变分模型及其应用

由于现有的某些去噪模型仅对某种噪声特别有效,而对其它类型噪声的效果却不够显著,因此提出一种能有效地去除多种噪声的变分模型,它融合了几种经典去噪模型的优点,并在数值求解时采用了高效且无条件稳定的AOS算法.数值实验表明,与现有的一些去噪方法相比,提出的去噪方法耗时少且效果更好.最后给出了解的存在性证明.     

扩展的Chan-Vese模型在噪声图像分割中的应用

针对带噪声图像分割结果不理想的现象,提出一种对带不同类型噪声的图像都能进行有效分割的变分模型。首先扩展了Chan-Vese(CV)模型的能量泛函,然后在数值求解过程中,引入一个辅助变量与水平集方法相结合,采用高效和无条件稳定的MOS算法,提高精度和计算效率。对带一定强度噪声的图像进行地分割实验,并与CV变分模型的分割结果进行比较。结果表明,该新变分模型较好地克服了噪声干扰的影响,对带噪图像的分割是有效的,迭代次数少,速度快且提高了目标分割的准确性。     

Total Generalized Variation Based Denoising Models for Ultrasound Images

In this paper, we introduce a class of variational models for the restoration of ultrasound images corrupted by noise. The proposed models involve the convex or nonconvex total generalized variation regularization. The total generalized variation regularization ameliorates the staircasing artifacts that appear in the restored images of total variation based models. Incorporating total generalized variation regularization with nonconvexity helps preserve edges in the restored images. To realize the proposed convex model, we adopt the alternating direction method of multipliers, and the iteratively reweighted \(\ell _1\) algorithm is employed to handle the nonconvex model. These methods result in fast and efficient optimization algorithms for solving our models. Numerical experiments demonstrate that the proposed models are superior to other state-of-the-art models.     

Invariant Kalman Filter for Correlated Wide Band Noises

Kalman filtering is a powerful estimation method. One of its weaknesses is related to the white or coloured nature of the disturbing noises in the Kalman filtering model. At the same time, real noises are rarely white or coloured. They are mostly wide band. In this regard, white or coloured noise Kalman filtering makes concessions on adequacy. This pushes system scientists to develop mathematical methods of estimation for systems corrupted by wide band noises. In applications, wide band noises are detected by their autocovariance and cross‐covariance functions, which do not allow to model them uniquely. Therefore, it becomes important to develop estimation methods which are independent of a class of wide band noises, but dependent on the unique autocovariance and cross‐covariance functions. Such results are called invariant results. In this paper, we prove a complete set of invariant equations for Kalman type filter for a linear signal‐observation system corrupted by correlated wide band noises. This filter has a ready form to be used in applications, just respective numerical methods must be developed.     

Restoration of binary images using stochastic relaxation with annealing

This paper investigates the application of variations of Stochastic Relaxation with Annealing (SRA) as proposed by Geman and Geman [1] to the Bayesian restoration of binary images corrupted by white noise. After a general review we present some specific prior models and show examples of their application. It appears that a proper selection of the prior model is critical for the success of the method. We obtained better results on artificial images which fitted the model closely than on real images for which there was no precise model.     

A well-balanced and adaptive variational model for the removal of mixed noise

Image denoising is one of the fundamental problems concerning image processing. Over the last decade mathematical models based on partial differential equations and variational techniques have led to superior results related to denoising problems. The additive noise models have been studied extensively, however, the reconstruction of images corrupted by nonadditive noise has not yet been thoroughly studied. In this paper, a novel variational method for the reconstruction of images corrupted by non-uniformly distributed noise is presented. The proposed model includes a balance between the data term and the regularization term in the energy functional, which takes into account the statistical control of the parameters and the position of the noisy points related to the edges presented in the image. The parameters are determined by the given initial noisy image. The obtained results have shown the effectiveness and robustness of the proposed model and in restoring images with multiplicative noise or mixed Gaussian noise, while preserving edges and small structures belonging to the image.     

Image denoising using 2-D FIR filters designed with DEPSO

Digital images are often corrupted by additive noises during transmission. Thus, how to alleviate noise as much as possible has received concerns for decades. In this paper, we present a simple denoising method based on two dimensional (2-D) finite impulse response (FIR) filtering, where by differential evolution particle swarm optimization (DEPSO) algorithm, five two dimensional finite impulse response filters are designed to filter different kinds of pixels. Comprised by differential evolution algorithm and particle swarm optimization algorithm, differential evolution particle swarm optimization algorithm is effective and robust, which helps to yield better denoise performance. And computer simulation demonstrates that the proposed method is superior to the conventional lowpass filtering method, as well as the modern bilateral filtering and stochastic denoising method.     

A two-stage filter for high density salt and pepper denoising

Image restoration is an important and interesting problem in the field of image processing because it improves the quality of input images, which facilitates postprocessing tasks. The salt-and-pepper noise has a simpler structure than other noises, such as Gaussian and Poisson noises, but is a very common type of noise caused by many electronic devices. In this article, we propose a two-stage filter to remove high-density salt-and-pepper noise on images. The range of application of the proposed denoising method goes from low-density to high-density corrupted images. In the experiments, we assessed the image quality after denoising using the peak signal-to-noise ratio and structural similarity metric. We also compared our method against other similar state-of-the-art denoising methods to prove its effectiveness for salt and pepper noise removal. From the findings, one can conclude that the proposed method can successfully remove super-high-density noise with noise level above 90%.

     

基于噪声检测的总变分去噪算法

对受高斯和脉冲混合噪声污染的数字图像去噪方法进行了研究,提出了一种基于噪声检测的自适应总变分(TV)去噪算法。提出的改进算法采用两步迭代框架实现:脉冲噪点检测和全变分图像恢复。第一步中,考虑到脉冲噪声污染的像素点不包含原图像有效信息,采用一种局部统计值,即邻域像素间的随机绝对差排序值(ROAD)估计出噪点的位置;第二步中,采用L2-TV方法进行去噪处理,并对上述过程进行迭代处理,得到去噪图像。在噪点估计过程中引入脉冲噪点水平参数,这样处理的优势在于可更准确地检测出脉冲噪点;而L2-TV去噪方法可很好地去除高斯噪声,两者结合有效地解决了TV算法存在误判图像脉冲噪声为边缘而产生假边缘的问题。与现有典型去噪方法的比较实验表明,该迭代去噪算法,即TV-ROAD算法,既能够去除混合噪声,又可以保留图像细节特征。     

Minimum entropy restoration of star field images

In this correspondence, we present an algorithm for restoration of star field images by incorporating both the minimum mean square error and the maximum varimax criteria. It is assumed that the point spread function of the distortion system can be well approximated by a Gaussian function. Simulated annealing (SA) is used to implement the optimization procedure. Simulation results for both Gaussian and square point spread functions with heavy additive independent white Gaussian noise are provided. Visual evaluation of the results indicate that the proposed algorithm performs better than the noncausal Wiener filtering method.     

On the Convergence of Primal–Dual Hybrid Gradient Algorithms for Total Variation Image Restoration

In this paper we establish the convergence of a general primal?Cdual method for nonsmooth convex optimization problems whose structure is typical in the imaging framework, as, for example, in the Total Variation image restoration problems. When the steplength parameters are a priori selected sequences, the convergence of the scheme is proved by showing that it can be considered as an ??-subgradient method on the primal formulation of the variational problem. Our scheme includes as special case the method recently proposed by Zhu and Chan for Total Variation image restoration from data degraded by Gaussian noise. Furthermore, the convergence hypotheses enable us to apply the same scheme also to other restoration problems, as the denoising and deblurring of images corrupted by Poisson noise, where the data fidelity function is defined as the generalized Kullback?CLeibler divergence or the edge preserving removal of impulse noise. The numerical experience shows that the proposed scheme with a suitable choice of the steplength sequences performs well with respect to state-of-the-art methods, especially for Poisson denoising problems, and it exhibits fast initial and asymptotic convergence.     

基于模糊推理的多窗口中央值滤波器设计方法

提出了一种基于模糊推理用于去除图像椒盐噪声的中央值滤波器的新型设计方法,在图像复原处理中,理想的期望是对图像被劣化的部分处理,没有被劣化的部分不作处理,但实际图像处理中处理点是否为噪声点具有模糊性.利用模糊推理对处理点像素多大程度上属于劣质像素进行推定,并且多个模糊滤波器联合使用,处理结果证明对广范围噪声发生率的各种被椒盐噪声劣化的图像复原处理都适用.     

Detecting Occlusions as an Inverse Problem

Occlusions generally become apparent when integrated over time because violations of the brightness-constancy constraint of optical flow accumulate in occluded areas. Based on this observation, we propose a variational model for occlusion detection that is formulated as an inverse problem. Our forward model adapts the brightness constraint of optical flow to emphasize occlusions by exploiting their temporal behavior, while spatio-temporal regularizers on the occlusion set make our model robust to noise and modeling errors. In terms of minimization, we approximate the resulting variational problem by a sequence of convex optimizations and develop efficient algorithms to solve them. Our experiments show the benefits of the proposed formulation, both forward model and regularizers, in comparison to the state-of-the-art techniques that detect occlusion as the residual of optical-flow estimation.     

基于稀疏表示与非局部相似的图像去噪算法

针对受加性高斯白噪声(AWGN)与椒盐噪声(SPIN)以及随机值冲击噪声(RVIN)组成的混合噪声污染的图像进行去噪的问题,提出一种在现有加权编码算法的基础上将图像稀疏表示和非局部相似先验融合的改进算法。首先,利用基于字典的图像稀疏表示构建去噪变分模型,对模型中的数据保真项设计一个权重因子来抑制冲击噪声的干扰;其次,利用非局部平均思想对混合噪声图像进行初始去噪,在得到的图像中构建掩膜矩阵将冲击噪声点排除进而求取非局部相似先验知识;最后,将非局部相似先验与稀疏先验融合进变分模型的正则项中,求解变分模型得到最终去噪图像。实验结果表明,在不同的噪声比率下,所提算法与模糊加权非局部平均算法相比,峰值信噪比(PSNR)提高了1.7 dB,特征相似性指数(FSIM)提高了0.06;与加权编码算法相比,PSNR提高了0.64 dB,FSIM提高了0.03。该算法对于纹理较强的图像可以显著提升去噪效果,能有效地保留图像的本真信息。     

局部均值噪声估计的盲3维滤波降噪算法

目的 图像在获取和传输的过程中很容易受到噪声的干扰,图像降噪作为众多图像处理系统的预处理模块在过去数十年中得到了广泛的研究。在已提出的降噪算法中,往往采用加性高斯白噪声模型AWGN（additive white Gaussian noise）为噪声建模,噪声水平（严重程度）由方差参数控制。经典的BM3D 3维滤波算法属于非盲降噪（non-blind denoising algorithm）算法,在实际使用中需要由人工评估图像噪声水平并设置参数,存在着噪声评估值随机性大而导致无法获得最佳降噪效果的问题。为此,提出了一种新的局部均值噪声估计（LME）算法并作为BM3D算法的前置预处理模块。方法 本文专注于利用基于自然统计规律（NSS）的图像质量感知特征和局部均值估计技术构建图像噪声水平预测器,并通过它高效地获得噪声图像中准确的噪声水平值。关于自然场景统计方面的研究表明,无失真的自然场景图像在空域或者频率域上具有显著的统计规律,一旦受到噪声干扰会产生规律性的偏移,可以提取这些特征值作为反映图像质量好坏的图像质量感知特征。另外,局部均值估计因其简单而高效率的预测特性被采用。具体实现上,在具有广泛代表性且未受噪声干扰图像集合上添加不同噪声水平的高斯噪声构建失真图像集合,然后利用小波变换对这些失真图像进行不同尺度和不同方向的分解,再用广义高斯分布模型（GGD）提取子带滤波系数的统计信息构成描述图像失真程度的特征矢量,最后用每幅失真图像上所提取的特征矢量及对其所施加的高斯噪声水平值构成了失真特征矢量库。在降噪阶段,用相同的特征提取方法提取待降噪的图像的特征矢量并在失真特征矢量库中检索出与之类似的若干特征矢量及它们所对应的噪声水平值,然后用局部均值法估计出待降噪图像中高斯噪声大小作为经典BM3D算法的输入参数。结果 改进后的BM3D算法转换为盲降噪算法,称为BM3D-LME（block-matching and 3D filtering based on local means estimation）算法。准确的噪声估计对于诸如图像降噪,图像超分辨率和图像分割等图像处理任务非常重要。已经验证了所提出噪声水平估计算法的准确性、鲁棒性和有效性。结论 相对人工进行噪声估计,LME算法能够准确、快速地估算出任意待降噪图像中的噪声大小。配合BM3D算法使用后,有效提高了它的实际降噪效果并扩大它的应用范围。     

梯度引导的高阶几何彩色图像去噪模型

目的 为了消除低阶彩色图像去噪模型产生视觉上不希望得到的"阶梯效应"并提高去噪过程中的边缘保持效果,提出一种黎曼几何驱动的高阶彩色图像去噪模型,并在扩散中使用一阶梯度信息引导高阶信息驱动的扩散,以改善去噪过程中的边界探测和保持能力。方法 在黎曼几何框架下,对低阶彩色图像去噪模型进行分析,并由面积微元出发得到对应的二阶微分形式,利用二阶导数矩阵的Frobenius范数构造高阶彩色图像变分能量泛函,由此得到一个彩色图像去噪的高阶扩散模型。为在扩散中保持边界,使用高斯卷积后的一阶梯度信息引导高阶扩散,得到一个多通道耦合的高阶非线性彩色图像去噪模型。分析表明,该模型在扩散时兼顾了单通道和多通道、低阶和高阶等多种信息之间的关系进行耦合去噪。结果 在实验中对不同噪声水平下的1维彩色信号、合成彩色图像和标准彩色测试图像进行去噪,并使用峰值信噪比（PSNR）与结构相似性（SSIM）作为客观评价指标,将本文结果与相关彩色图像去噪扩散模型的结果进行对比。在不同噪声水平下本文模型去噪结果的平均PSNR与相关模型相比提高了2.33%,平均SSIM提高了0.4%。结论 本文模型能够有效去除彩色图像中不同噪声水平的高斯白噪声,能较好消除视觉上的"阶梯效应",得到分片线性光滑的彩色图像,同时还能够较好保持图像边界信息。     

一种低信噪比图像的模拟退火恢复算法

本文根据马尔可夫(Markov)随机场模型和全局最大后验概率估计技术提出了一种模拟退火图像恢复算法.应用这种算法对混入可加性独立高斯噪声的试验图像进行恢复的实验结果表明,该算法对低信噪比图像数据的恢复处理非常有效.     

A Variational Framework for Region-Based Segmentation Incorporating Physical Noise Models

Image segmentation is one of the fundamental problems in computer vision and image processing. In the recent years mathematical models based on partial differential equations and variational methods have led to superior results in many applications, e.g., medical imaging. A majority of works on image segmentation implicitly assume the given image to be biased by additive Gaussian noise, for instance the popular Mumford-Shah model. Since this assumption is not suitable for a variety of problems, we propose a region-based variational segmentation framework to segment also images with non-Gaussian noise models. Motivated by applications in biomedical imaging, we discuss the cases of Poisson and multiplicative speckle noise intensively. Analytical results such as the existence of a solution are verified and we investigate the use of different regularization functionals to provide a-priori information regarding the expected solution. The performance of the proposed framework is illustrated by experimental results on synthetic and real data.     

流线网络的物流组织优化模型研究

通过分析流线网络建设与运营的基本特征,构建了流线网络的抽象成本函数,为了降低物流成本和提高物流效率,建立以能力供给为约束,以网络建设和运营成本最小为目标的优化模型。将模型转化为相应的变分不等式,证明变分不等式与优化模型解的等价性,通过解变分不等式得到最优物流组织方案,算例验证了模型合理性和可行性,为企业对物流网络的经营提供理论支持。     

Iterative Constrained Minimization for Vectorial TV Image Deblurring

In this paper, we consider the problem of restoring blurred noisy vectorial images where the blurring model involves contributions from the different image channels (cross-channel blur). The proposed method restores the images by solving a sequence of quadratic constrained minimization problems where the constraint is automatically adapted to improve the quality of the restored images. In the present case, the constraint is the Total Variation extended to vectorial images, and the objective function is the \(\ell _2\) norm of the residual. After proving the convergence of the iterative method, we report the results obtained on a wide set of test images, showing that this approach is efficient for recovering nearly optimal results.