具有简单约束的图像恢复正则化方法

图像恢复就是对退化的图像进行处理、尽可能恢复原图像的本来面目的过程.注意到图像的像素值一般都限制在一定的范围内,如8bit的灰度图像,其像素值在0到255之间,如果在图像恢复过程中充分考虑图像的这种特性,那么对图像恢复的效果将是有益的,因此,考虑这种带有简单约束的图像恢复问题.在一类基于分割的正则化模型的基础上,提出了利用ASCBB算法求解这种具有简单约束的图像恢复问题.数值实验结果表明,该算法是有效的.     

脉冲噪声下图像去模糊非光滑非凸最小化问题的近端线性化最小化算法

去除脉冲噪声是图像复原中的重要任务之一.我们提出一类非光滑非凸模型来恢复模糊和脉冲噪声污染的图像,该模型具有灵活的先验信息引入机制,如盒子约束或低秩等.为了求解所提非凸问题,我们采用近端线性化最小化算法.对于算法中的子问题,我们运用交替方向乘子法.在目标函数满足Kurdyka-Lojasiewicz性质的假设下,我们证明所提算法的全局收敛性.数值实验表明,在主观和客观质量评价方面,我们的方法优于$\ell_{1}$TV和非凸TV模型.     

基于上下文光谱角映射的无监督图像变化检测方法

对传统遥感图像变化检测方法未充分利用像素上下文信息的问题,提出一种无需关于像素的概率分布假设、基于上下文光谱角映射的无监督图像变化检测方法.方法避免了在图像分析过程中将像素看作独立单元,通过引入图像的空间上下文信息特征,在对像素变化类别的判别测试阶段加以利用,从而达到提高变化检测精确度的效果.对卫星图像的实施过程首先利用上下文光谱角映射创建一幅相似图像,然后用K均值聚类算法将其分为有变化和无变化的两类来生成映射图像.实验从定量和定性的两方面与最大似然估计法(MLC)比较,结果显示所提方法比已有方法有所改进,对于二时刻图像和多光谱图像的变化检测问题有更好的适用性.     

基于卫星云图的风矢场度量模型与算法探讨

首先通过换算视场坐标确定灰度矩阵中每个元素对应的采样点在地球上的经纬度,从而将灰度矩阵转化为卫星云图,并添加海岸线.在此基础上,使用相关匹配法对具有一定时间间隔的两幅相关卫星云图进行模板匹配生成风矢场(云导风)矢量.然后,借助于近年来发展起来的数值微分方法,从图像灰度中提取出图像梯度信息,再利用正则化方法,实现了云导风的反演.对云图中加入灰度梯度信息和未加入灰度梯度信息的风场反演结果进行比较.结果表明,加入图像灰度梯度信息后所实施的新反演方法可有效减小图像干扰的影响,同时也大大提高了风矢量反演的精度,为卫星云图反演云导风探索出一条新路.     

Chan-Vese模型的共轭梯度算法

随着图像采集设备的发展和对图像分辨率要求的提高,人们对图像处理算法在收敛速度和鲁棒性方面提出了更高的要求.从优化的角度对Chan-Vese模型进行算法上的改进,即将共轭梯度法应用到该模型中,使得新算法有更快的收敛速度.首先,简单介绍了Chan-Vese模型的变分水平集方法的理论框架;其次,将共轭梯度算法引入到该模型的求解,得到了模型的新的数值解方法;最后,将得到的算法与传统求解Chan-Vese模型的最速下降法进行了比较.数值实验表明,提出的共轭梯度算法在保持精度的前提下有更快的收敛速度.     

基于元胞自动机模型的图像分割算法

针对图像处理中的图像分割任务,我们提出了一个基于模糊元胞自动机模型的图像分割算法.将元胞自动机原理中的演化规则换为模糊规则建立模糊元胞自动机模型,使图像中灰度水平介于目标和背景之间的像素得以更好地归类,从而得到较好的图像分割结果.     

基于分数阶微积分正则化的图像处理

全变分正则化方法已被广泛地应用于图像处理,利用此方法可以较好地去除噪声,并保持图像的边缘特征,但得到的优化解会产生"阶梯"效应.为了克服这一缺点,本文通过分数阶微积分正则化方法,建立了一个新的图像处理模型.为了克服此模型中非光滑项对求解带来的困难,本文研究了基于不动点方程的迫近梯度算法.最后,本文利用提出的模型与算法进行了图像去噪、图像去模糊与图像超分辨率实验,实验结果表明分数阶微积分正则化方法能较好的保留图像纹理等细节信息.     

一种新型的四相水平集图像分割方法

水平集方法在图像分割和计算机视觉领域有很广泛的应用,在传统的水平集方法中,水平集函数需要保持符号距离函数.现有的活动轮廓模型、GAC模型、M-S模型、C-V模型等在演化过程中均需要对水平集函数进行重新初始化,使其保持符号距离函数,然而这样会引起数值计算的错误,最终破坏演化的稳定性,另外这些模型只适用于灰度值较为均匀的图像,对灰度值不均匀的图像不能进行理想的分割·针对这些问题,结合C-V模型的思想,提出了一种带有正则项的四相水平集分割模型,其中正则项被定义为一个势函数,具有向前向后扩散的作用,使水平集函数在演化过程中保持为符号距离函数,避免了水平集函数重新初始化的过程.最后对该模型进行数值实现,实验表明了新模型的可行性和有效性.     

列正交约束下广义Sylvester方程极小化问题的有效算法

研究列正交约束下广义Sylvester方程极小化问题的有效算法.基于Stiefel流形的几何性质和欧氏空间中的MPRP共轭梯度法,构造一类黎曼MPRP共轭梯度迭代求解算法,给出算法全局收敛性.该迭代格式得到的搜索方向总能保证该目标函数下降.数值实验和数值比较验证所提出算法对于问题模型是高效可行的.     

一般线性或非线性约束下的共轭投影变尺度方法

梯度投影法是一类有效的约束最优化算法，在最优化领域中占有重要的地位．但是，梯度投影法所采用的投影是正交投影，不包含目标函数和约束函数的二阶导数信息·因而；收敛速度不太令人满意．本文介绍一种共轭投影概念，利用共轭投影构造了一般线性或非线性约束下的共轭投影变尺度算法，并证明了算法在一定条件下具有全局收敛性．由于算法中的共轭投影恰当地包含了目标函数和约束函数的二阶导数信息，因而收敛速度有希望加快．数值试验的结果表明算法是有效的．     

A Nonlinear Diffusion Equation-Based Model for Ultrasound Speckle Noise Removal

Ultrasound images are contaminated by speckle noise, which brings difficulties in further image analysis and clinical diagnosis. In this paper, we address this problem in the view of nonlinear diffusion equation theories. We develop a nonlinear diffusion equation-based model by taking into account not only the gradient information of the image, but also the information of the gray levels of the image. By utilizing the region indicator as the variable exponent, we can adaptively control the diffusion type which alternates between the Perona–Malik diffusion and the Charbonnier diffusion according to the image gray levels. Furthermore, we analyze the proposed model with respect to the theoretical and numerical properties. Experiments show that the proposed method achieves much better speckle suppression and edge preservation when compared with the traditional despeckling methods, especially in the low gray level and low-contrast regions.     

Adaptive Segmentation Model for Images with Intensity Inhomogeneity based on Local Neighborhood Contrast

Segmentation of images with intensity inhomogeneity is a significant task in the field of image processing, especially in medical image processing and analysis. Some local region-based models work well on handling intensity inhomogeneity, but they are always sensitive to contour initialization and high noise. In this paper, we present an adaptive segmentation model for images with intensity inhomogeneity in the form of partial differential equation. Firstly, a global intensity fitting term and a local intensity fitting term are constructed by employing the global and local image information, respectively. Secondly, a tradeoff function is defined to adjust adaptively the weight between two fitting terms, which is based on the neighborhood contrast of image pixel. Finally, a weighted regularization term related to local entropy is used to ensure the smoothness of evolution curve. Meanwhile, a distance regularization term is added for stable level set evolution. Experimental results show that the proposed model without initial contour can segment inhomogeneous images stably and effectively, which thereby avoiding the influence of contour initialization on segmentation results. Besides, the proposed model works better on noise images comparing with two relevant segmentation models.     

Constraining by a family of strictly nonexpansive idempotent functions with applications in image reconstruction

When solving an image reconstruction problem a previous knowledge concerning the original image may lead to various constraining strategies. A convergence result has been previously proved for a constrained version of the Kaczmarz projection algorithm with a single strictly nonexpansive idempotent function with a closed image. In this paper we consider a more general projection based iterative method and a family of such constraining functions with some additional hypotheses in order to better use the a priori information for every approximation calculated. We present a particular family of box-constraining functions which satisfies our assumptions and we design an adaptive algorithm that uses an iteration-dependent family of constraining functions for some numerical experiments of image reconstruction on Tomographic Particle Image Velocimetry.     

Shrinking gradient descent algorithms for total variation regularized image denoising

Total variation regularization introduced by Rudin, Osher, and Fatemi (ROF) is widely used in image denoising problems for its capability to preserve repetitive textures and details of images. Many efforts have been devoted to obtain efficient gradient descent schemes for dual minimization of ROF model, such as Chambolle’s algorithm or gradient projection (GP) algorithm. In this paper, we propose a general gradient descent algorithm with a shrinking factor. Both Chambolle’s and GP algorithm can be regarded as the special cases of the proposed methods with special parameters. Global convergence analysis of the new algorithms with various step lengths and shrinking factors are present. Numerical results demonstrate their competitiveness in computational efficiency and reconstruction quality with some existing classic algorithms on a set of gray scale images.     

A Recursive Algorithm to Restore Images Based on Robust Estimation of NSHP Autoregressive Models

The objective of this article is to present a new image restoration algorithm. First, each pixel in the image is classified into k categories. Then we assume that the gray levels in each category follow a nonsymmetric half-plane (NSHP) autoregressive model. Robust estimation of the parameters of the model is considered to attenuate the effect of the image contamination on the parameters. In each iteration we will construct a new image using a robustified version of the residuals. The introduction of the classification techniques as a first step of the algorithm reduces considerably the number of parameters to estimate. Hence, the computational time is also reduced because the robust estimations of the parameters are solutions of nonlinear system of equations. Some applications are presented to real synthetic aperture radar (SAR) images to illustrate how our algorithm restores an image in practice.     

A Nash-game approach to joint image restoration and segmentation

We propose a game-theoretic approach to simultaneously restore and segment noisy images. We define two players: one is restoration, with the image intensity as strategy, and the other is segmentation with contours as strategy. Cost functions are the classical relevant ones for restoration and segmentation, respectively. The two players play a static game with complete information, and we consider as solution to the game the so-called Nash equilibrium. For the computation of this equilibrium we present an iterative method with relaxation. The results of numerical experiments performed on some real images show the relevance and efficiency of the proposed algorithm.     

A New Implicit Method for Surface Segmentation by Minimal Paths in 3D Images

We introduce a novel implicit approach for single-object segmentation in 3D images. The boundary surface of this object is assumed to contain two known curves (the constraining curves), given by an expert. The aim of our method is to find the wanted surface by exploiting as much as possible the information given in the supplied curves and in the image. As for active surfaces, we use a cost potential that penalizes image regions of low interest (most likely areas of low gradient or too far from the surface to be extracted). In order to avoid local minima, we introduce a new partial differential equation and use its solution for segmentation. We show that the zero level set of this solution contains the constraining curves as well as a set of paths joining them. We present a fast implementation that has been successfully applied to 3D medical and synthetic images.     

A Compound Algorithm of Denoising Using Second-Order and Fourth-Order Partial Differential Equations

In this paper, we propose a compound algorithm for the image restoration. The algorithm is a convex combination of the ROF model and the LLT model with a parameter function 6. The numerical experiments demonstrate that our compound algorithm is efficient and preserves the main advantages of the two models. In particular, the errors of the compound algorithm in L2 norm between the exact images and corresponding restored images are the smallest among the three models. For images with strong noises, the restored images of the compound algorithm are the best in the corresponding restored images. The proposed algorithm combines the fixed point method, an improved AMG method and the Krylov acceleration. It is found that the combination of these methods is efficient and robust in the image restoration.     

基于小波多分辨率分析和改进窄带法的C-V水平集图像分割模型

本文研究了基于小波分析改进的C-V模型图像分割问题.利用小波多分辨率分析和改进的窄带水平集方法,获得了比传统C-V模型分割速度更快、准确度更高、算法复杂度更低的分割结果.推广了C-V水平集模型如何快速准确地分割灰度不均匀的图像和窄带水平集法等结果.     

A Retinex modulated piecewise constant variational model for image segmentation and bias correction

In this paper, we propose a novel Retinex induced piecewise constant variational model for simultaneous segmentation of images with intensity inhomogeneity and bias correction. Firstly, we obtain an additive model by decomposing the original image into a smooth bias component and a structure part based on the Retinex theory. Secondly, the structure part can be modeled by the piecewise constant variational model and thus deduced a new data fidelity term. Finally, we formulate a new energy functional by incorporating the data fidelity term into the level set framework and introducing a GL-regularizer to the level set function and a smooth regularizer to model the bias component. Based on the alternating minimization algorithm and the operator splitting method, we present a numerical scheme to solve the minimization problem efficiently. Experimental results on images from diverse modalities demonstrate the competitive performances of the proposed model and algorithm over other representative methods in term of efficiency and robustness.