基于卷积神经网络的正则化方法

正则化方法是逆问题求解中经常使用的方法.准确的正则化模型在逆问题求解中具有重要作用.对于不同类型的图像和图像的不同区域,正则化方法的能量约束形式应当不同,但传统的L1,L2正则化方法均基于单一先验假设,对所有图像使用同一能量约束形式.针对传统正则化模型中单一先验假设的缺陷,提出了基于卷积神经网络的正则化方法,并将其应用于图像复原问题.该方法的创新之处在于将图像复原看作一个分类问题,利用卷积神经网络对图像子块的特征进行提取和分类,然后针对不同特征区域采用不同的先验形式进行正则化约束,使正则化方法不再局限于单一的先验假设.实验表明基于卷积神经网络的正则化方法的图像复原结果优于传统的单一先验假设模型.     

Bregman交替迭代遥感图像复原方法

针对多种退化因素的遥感图像复原问题,提出一种基于Bregman迭代的遥感图像消除不规则采样、去模糊和去噪总变差复原方法。在此基础上,结合非局部正则化方法,提出一种自适应计算非局部均值滤波器参数的方法。求解时使用交替最小化方法将复杂的复原问题分割为两个容易求解的子问题。实验结果表明,本文方法比其他基于Bregman迭代的方法收敛速度快、复原效果好,且加入非局部正则化后具有更好的纹理细节信息保持能力。     

基于稀疏表示的多正则优化图像复原

由于单正则化图像复原算法所利用的先验信息有限,影响了复原图像的质量。为克服此类算法的不足,融入更多的先验信息,改善图像复原的效果。在稀疏表示的理论框架下,提出了一种多正则优化图像复原算法。该算法将图像复原表示为含多正则项的全局优化问题,为有效处理这一复杂的图像复原问题,采用交替优化策略并借助变量分裂将其分解为若干优化子问题。其中,[uj+1]子问题可微,可直接得到其解析解。不可微的[wj+1]和[vj+1]子问题,则通过邻近映射求解。实验过程中对三种不同类型的退化图像进行了复原,所得结果验证了该算法的有效性。与FISTA（Fast Iterative Shrinkage-Thresholding Algorithm）和Split Bregman等单正则化图像复原算法相比,所提算法的复原效果和时间性能更优。     

原对偶积极集法求解改进的有界约束图像恢复问题

为了提高模糊加噪声图像的恢复质量,提出了一种用于图像恢复处理的改进的带约束的正则化模型。该模型首先利用Levine等人提出的变指数、线性增长函数作为正则项,并根据图像局部特征选择合适的正则参数,这样既保留了总变差正则化方法在恢复图像边缘方面的优势,又减少了梯子现象;其次,为进一步提高恢复图像的质量,在此基础上再添加有界约束条件,如将灰度值固定在某范围内,以形成约束优化问题。由于它的求解相对复杂,为此可应用原对偶积极集法求解,其实质就是用半光滑Newton法来求解由约束优化问题转化所得到的方程组。数值实验表明,此方法是可行的和有效的。     

空域中基于正则化的自适应超分辨率图像复原

对于模糊图像的复原问题,从正则化技术克服问题病态性的思想出发,研究了一种有效的超分辨率图像复原方法.在Nguyen等人的正则图像复原框架的基础上,根据Roberts交叉梯度算子构造正则项,从自适应的角度生成正则化参数,并用共轭梯度法求解该模型的目标泛函极小值.计算机仿真结果表明,该方法可较好的再现图像的重要信息,复原图像的相对误差降低,同时,峰值信噪比和主观视觉效果方面都有明显的提高.     

基于区间必然集的测试用例生成方法

针对自动化单元测试中面向路径的测试用例生成问题,通过改进传统的基于符号执行的测试用例生成方法,提出“符号化区间”来表示和分析变量的静态取值范围,并给出简单表达式和逻辑表达式中“区间可能集”和“区间必然集”的计算方法.提出了面向路径的值区间分析算法,通过对给定路径进行前向数据流分析来计算各条边上的区间上下文环境以及各符号的必然取值区间,在路径出口处的符号值区间必然集中任意取值,可得到覆盖给定路径的测试用例.与基于约束求解的传统方法相比,文中方法省去了表达式变换及调用约束求解器的过程,对输入变量弱关联的情况能够快速、准确地生成测试用例.     

基于Besov空间的图像盲复原算法

针对Chan-Wong全变差正则化思想的不足,提出了一种Besov空间的图像盲复原算法.该算法用一个B11,1项代替BV项,采用交替最小化的思想在小波域上求解,将全变差盲复原中求解复杂的偏微分方程转化为简单的小波软阈值问题.实验结果表明:该算法不仅减少了全变差盲复原中出现的阶梯效应,而且运算时间大大减少.     

基于超图正则化的域适应偏最小二乘多工况软测量模型

针对流程工业中, 因多工况导致数据分布变化引起传统软测量模型预测性能恶化问题, 本文提出一种基于 超图正则化的域适应多工况软测量回归模型框架. 首先, 采用非线性迭代偏最小二乘回归算法为基模型, 在潜变量 空间利用历史工况数据重构当前工况数据, 以增强工况间的相关性, 有效减小数据分布差异; 同时, 对重构系数施加 低秩稀疏约束, 保留了数据的局部和全局子空间结构; 其次, 通过超图拉普拉斯正则项对域适应潜变量求解过程进 行约束, 避免在寻找潜变量过程中破坏数据结构. 最后, 利用交替方向乘子法优化求解模型参数. 在多个数据集上 的实验表明, 本文方法在多工况环境下可有效提高软测量模型的预测精度和泛化性能.     

基于变差正则化的超分辨率图像重建

针对超分辨率图像重建的求解病态性问题,从正则化求解的角度构建数据保真项和正则项,提出一种新的数据融合方法。讨论已有的数据融合方法,利用像素领域和帧间信息控制奇异点,考虑边缘区域的变差权值,避免重建图像的边缘区域过于平滑。实验结果表明,该方法能够提高重建图像质量,具有较好的鲁棒性。     

改进的二值图像复原方法研究

为了解决传统基于GBB方法的正则化二值图像复原算法放大背景噪声的问题,提出了一种基于GBB方法的改进的正则化二值图像复原算法。根据提出的算法进行实验,定性的对两种算法的图像复原结果进行了比较。同时,利用ISNR选取最佳参数,且在不同程度噪声的影响下定量的评价了两种复原方法的结果。实验结果表明,该方法对于模糊二值图像的复原效果有显著提升,有效降低了噪声对图像复原的影响。     

Augmented Lagrangian Method for Total Variation Based Image Restoration and Segmentation Over Triangulated Surfaces

Recently total variation (TV) regularization has been proven very successful in image restoration and segmentation. In image restoration, TV based models offer a good edge preservation property. In image segmentation, TV (or vectorial TV) helps to obtain convex formulations of the problems and thus provides global minimizations. Due to these advantages, TV based models have been extended to image restoration and data segmentation on manifolds. However, TV based restoration and segmentation models are difficult to solve, due to the nonlinearity and non-differentiability of the TV term. Inspired by the success of operator splitting and the augmented Lagrangian method (ALM) in 2D planar image processing, we extend the method to TV and vectorial TV based image restoration and segmentation on triangulated surfaces, which are widely used in computer graphics and computer vision. In particular, we will focus on the following problems. First, several Hilbert spaces will be given to describe TV and vectorial TV based variational models in the discrete setting. Second, we present ALM applied to TV and vectorial TV image restoration on mesh surfaces, leading to efficient algorithms for both gray and color image restoration. Third, we discuss ALM for vectorial TV based multi-region image segmentation, which also works for both gray and color images. The proposed method benefits from fast solvers for sparse linear systems and closed form solutions to subproblems. Experiments on both gray and color images demonstrate the efficiency of our algorithms.     

Domain Decomposition Methods for Nonlocal Total Variation Image Restoration

Nonlocal total variation (TV) regularization (Gilboa and Osher in Multiscale Model Simulat 7(3): 1005–1028, 2008; Zhou and Schölkopf in Pattern recognition, proceedings of the 27th DAGM symposium. Springer, Berlin, pp 361–368, 2005) has been widely used for the natural image processing, since it is able to preserve repetitive textures and details of images. However, its applications have been limited in practice, due to the high computational cost for large scale problems. In this paper, we apply domain decomposition methods (DDMs) (Xu et al. in Inverse Probl Imag 4(3):523–545, 2010) to the nonlocal TV image restoration. By DDMs, the original problem is decomposed into much smaller subproblems defined on subdomains. Each subproblem can be efficiently solved by the split Bregman algorithm and Bregmanized operator splitting algorithm in Zhang et al. (SIAM J Imaging Sci 3(3):253–276, 2010). Furthermore, by using coloring technique on the domain decomposition, all subproblems defined on subdomains with same colors can be computed in parallel. Our numerical examples demonstrate that the proposed methods can efficiently solve the nonlocal TV based image restoration problems, such as denoising, deblurring and inpainting. It can be computed in parallel with a considerable speedup ratio and speedup efficiency.     

Multiplicative noise removal via adaptive learned dictionaries and TV regularization

Multiplicative noise removal is a key issue in image processing problem. While a large amount of literature on this subject are total variation (TV)-based and wavelet-based methods, recently sparse representation of images has shown to be efficient approach for image restoration. TV regularization is efficient to restore cartoon images while dictionaries are well adapted to textures and some tricky structures. Following this idea, in this paper, we propose an approach that combines the advantages of sparse representation over dictionary learning and TV regularization method. The method is proposed to solve multiplicative noise removal problem by minimizing the energy functional, which is composed of the data-fidelity term, a sparse representation prior over adaptive learned dictionaries, and TV regularization term. The optimization problem can be efficiently solved by the split Bregman algorithm. Experimental results validate that the proposed model has a superior performance than many recent methods, in terms of peak signal-to-noise ratio, mean absolute-deviation error, mean structure similarity, and subjective visual quality.     

Model Selection Criteria for Image Restoration

In this brief, the image restoration problem is approached as a learning system problem, in which a model is to be selected and parameters are estimated. Although the parameters which correspond to the restored image can easily be obtained, their quality depend heavily on a proper choice of the regularization parameter that controls the tradeoff between fidelity to the blurred noisy observed image and the smoothness of the restored image. By analogy between the model selection philosophy that constitutes a fundamental task in systems learning and the choice of the regularization parameter, two criteria are proposed in this brief for selecting the regularization parameter. These criteria are based on Bayesian arguments and the Kullback–Leibler divergence and they can be considered as extensions of the Bayesian information criterion (BIC) and the Akaike information criterion (AIC) for the image restoration problem.      

Multiplicative noise removal via combining total variation and wavelet frame

Total variation (TV) regularization has been proved effective for cartoon images restoration however it produces staircase effects, and properly wavelet frames were confirmed to provide a more smoothing approximation to the original image. In this paper, a new model for multiplicative noise removal was proposed, which combines wavelet frame-based regularization and TV regularization. A modified proximal linearized alternating direction method is developed to solve the proposed model, considering that adding a new regularization term to the TV model would yield more parameters, which will result in computational difficulties. For the new model, the existence of solution and the convergence property of the proposed algorithm are proved. Numerical experiments have proved that the proposed model has a superior performance in terms of the peak signal-to-noise ratio and the relative error values for non-piecewise constant images when compared with some state-of-the-art multiplicative noise removal models.     

自适应直方图均衡化改进的全变分图像修复

为了解决全变分(TV)模型修复窄带图像缺陷时产生的视觉不连通的问题, 改善图像修复的效果. 采用可以强化细节的自适应直方图均衡化(CLAHE)操作来扩大图像的动态范围; 在全变分变换后对图像不连通区域做形态学运算来平滑并消除图像中的孤立点. 文章给出了算法原理和实现步骤, 实验结果表明修复之后的图像峰值信噪比提高, 视觉连通效果较好.     

Automated Regularization Parameter Selection in Multi-Scale Total Variation Models for Image Restoration

Multi-scale total variation models for image restoration are introduced. The models utilize a spatially dependent regularization parameter in order to enhance image regions containing details while still sufficiently smoothing homogeneous features. The fully automated adjustment strategy of the regularization parameter is based on local variance estimators. For robustness reasons, the decision on the acceptance or rejection of a local parameter value relies on a confidence interval technique based on the expected maximal local variance estimate. In order to improve the performance of the initial algorithm a generalized hierarchical decomposition of the restored image is used. The corresponding subproblems are solved by a superlinearly convergent algorithm based on Fenchel-duality and inexact semismooth Newton techniques. The paper ends by a report on numerical tests, a qualitative study of the proposed adjustment scheme and a comparison with popular total variation based restoration methods.     

多网格法解总变分问题及在医学图像增强中的应用

传统的各向同性平滑方法，如拉普拉斯平滑方法，虽然能去掉图像的噪声，但同时也可能使图像的边缘信息模糊，甚至丢失。针对这种情况，基于总变分的平滑方法得到重视，因为该方法可以在去除噪声的同时，对边缘的信息进行增强，但是由于基于总变分的平滑方法计算量大，且用松弛法迭代的收敛速度比较慢，因此引入了多网格预处理的共轭梯度算法来解总变分问题。计算结果表明，共轭梯度法的收敛速度明显高于松弛法，而采用多网格法收敛速度还可以得到进一步提高。为说明该方法的优点，最后对用这两种方法处理的超声医学图像的收敛曲线和平滑结果进行了比较。