Iterative lavrentiev regularization for symmetric kernel-driven operator equations: with application to digital image restoration problems

~~Iterative Lavrentiev regularization for symmetric kernel-driven operator equations: with application to digital image restoration problems1. Roggemann, M. C, WeJsh, B., Imaging Through Turbulence. New York. CRC Press, 1996. 2. Bertero, M., Boccacci, P., Introduction to Inverse Prolems in Imaging, Bristol: IOP Publishing, 1998. 3. George, S., Nair, M. T., A class of discrepancy principles for the simplified regularization of ill-posed problems, J. Austral. Math. Soc, Ser.…     

A new radiosity approach for regular objects: application to ruled surfaces

This paper introduces a new approach in the radiosity method. The main principle applied here, is the improvement of form factor computation by the knowledge of the model properties. More precisely, if surfaces describing a scene are “regular”, the values of the form factor and its “derivatives” between any patch B and a patch A intervening in the meshing of a given surface, enable us to evaluate (with a required precision) the form factors values between B and the neighboring patches of A. We will also show that the mathematical relation we have obtained, 1) is especially efficient with ruled surfaces, 2) significantly decreases the computation time, 3) is well-adapted to refinement or subdivision techniques and 4) gives us an interesting variety of surfaces. Calculation times are equivalent to those obtained with a projective method (hemi-cube for example) but with an efficient control of the generated errors.     

A new nonconvex approach for image restoration with Gamma noise

In this paper, a new total generalized variational(TGV) model for restoring images with multiplicative noise is proposed, which contains a nonconvex fidelity term and a TGV term. We use a difference of convex functions algorithm (DCA) to deal with the proposed model. For multiplicative noise removal, there exist many models and algorithms, most of which focus on convex approximation so that numerical algorithms with guaranteed convergence can be designed. Unlike these algorithms, we use the DCA algorithm to remove multiplicative noise. By numerical experiments, it is shown that the proposed approach leads to a better solution compared with the gradient projection algorithm for solving the classic multiplicative noise removal models. We prove that the sequence generated by the DCA algorithm converges to a stationary point, which satisfies the first order optimality condition. Finally, we demonstrate the performance of our whole scheme by numerical examples. A comparison with other methods is provided as well. Numerical results demonstrate that the proposed algorithm significantly outperforms some previous methods for multiplicative Gamma noise removal.     

A regularization framework for multiclass classification: A deterministic annealing approach

In this paper, we propose a general regularization framework for multiclass classification based on discriminant functions. Since the objective function in the primal optimization problem of this framework is always not differentiable, the optimal solution cannot be obtained directly. With the aid of the deterministic annealing approach, a differentiable objective function is derived subject to a constraint on the randomness of the solution. The problem can be approximated by solving a sequence of differentiable optimization problems, and such approximation converges to the original problem asymptotically. Based on this approach, class-conditional posterior probabilities can be calculated directly without assuming the underlying probabilistic model. We also notice that there is a connection between our approach and some existing statistical models, such as Fisher discriminant analysis and logistic regression.     

改进的正则化模型在图像恢复中的应用

目的 由拟合项与正则项组成的海森矩阵,如果不具有特殊结构,其逆矩阵计算比较困难,为克服此缺点,提出一种海森矩阵可分块对角化的牛顿投影迭代算法。方法 首先,用L₂范数描述拟合项,用自变量是有界变差函数的复合函数刻画正则项,建立能量泛函正则化模型。其次,引入势函数,将正则化模型转化为增广能量泛函。再次,构造预条件矩阵,使得海森矩阵可分块对角化。最后,为防止牛顿投影迭代算法收敛到局部最优解,采用回溯线性搜索算法和改进的Barzilai-Borwein步长更新准则使得算法全局收敛。结果 针对图像去模糊正则化模型容易使边缘平滑和产生阶梯效应“两难”问题,提出一种新的正则化模型和牛顿投影迭代算法。仿真结果表明,“两难”问题通过本文算法得到了很好的解决。结论 与其他正则化图像去模糊模型相比,本文算法明显改善图像的质量,如有效地保护图像的边缘,抑制阶梯效应,相对偏差和误差较小,较高的峰值信噪比和结构相似测度。     

混合特性正则化约束的运动模糊盲复原

目的 为了提高运动模糊图像盲复原清晰度,提出一种混合特性正则化约束的运动模糊盲复原算法。方法 首先利用基于局部加权全变差的结构提取算法提取显著边缘,降低了噪声对边缘提取的影响。然后改进模糊核模型的平滑与保真正则项,在保证精确估计的同时,增强了模糊核的抗噪性能。最后改进梯度拟合策略,并加入保边正则项,使图像梯度更加符合重尾分布特性,且保证了边缘细节。结果 本文通过两组实验验证改进模型与所提算法的优越性。实验1以模拟运动模糊图像作为实验对象,通过对比分析5种组合步骤算法的复原效果,验证了本文改进模糊核模型与改进复原图像模型的鲁棒性较强。实验结果表明,本文改进模型复原图像的边缘细节更加清晰自然,评价指标明显提升。实验2以小型无人机真实运动模糊图像为实验对象,通过与传统算法进行对比,对比分析了所提算法的鲁棒性与实用性。实验结果表明,本文算法复原图像的标准差提升约11.4%,平均梯度提升约30.1%,信息熵提升约2.2%,且具有较好的主观视觉效果。结论 针对运动模糊图像盲复原,通过理论分析和实验验证,说明了本文改进模型的优越性,所提算法的复原效果较好。     

A fuzzy approach to segment touching characters

Despite many years of research, correct and reliable segmentation of touching characters is still a hard task to solve. In the recent years, many methods and algorithms have been proposed; nevertheless the problem is still open. In this paper, we propose a novel method based on fuzzy logic that combines three different techniques to segment touching characters. These techniques have already been used in other studies but they have never been used all together. We propose a 3–input/1–output fuzzy inference system with fuzzy rules that are specifically optimized to segment touching Latin characters. The method is applicable to both printed and handwritten characters. We discuss the performances of our method by comparing it with state of the art. Results show that our method provide a better accuracy to segment characters even with noisy touching characters.     

A fusion-based approach to digital movie restoration

Many algorithms have been proposed in literature for digital movie restoration; unfortunately, none of them ensures a perfect result whichever is the image sequence to be restored. Here we propose a new digital scratch restoration algorithm which achieves accuracy results higher than that of already existing algorithms and naturally adapts for implementation into high-performance computing environments.The basic idea of the proposed algorithm is to adopt several relatively well-settled algorithms for the problem at hand and combine obtained results through suitable image fusion techniques, with the aim of taking advantage of the adopted algorithms’ capabilities and, at the same time, limiting their deficiencies.Extensive experiments on real image sequences deeply investigate both accuracy results of the presented scratch restoration approach, which is shown to outperform other existing approaches, and performance of its parallel implementation, which allows for real-time restoration.     

A new approach to code motion and its application to hoisting

An approach to code motion and hoisting, a program optimization technique, is discussed. The safety and profitability of optimization in general and hoisting in particular are analyzed. By restricting the analysis to a spanning tree imposed on the program graph, a linear algorithm is developed that provides sufficient but not necessary conditions for hoisting.     

A new hesitant fuzzy QFD approach: An application to computer workstation selection

Computer workstation selection is a multiple criteria decision making problem that is generally based on vague linguistic assessments, which represent human judgments and their hesitancy. In this paper, a new fuzzy quality function deployment (QFD) approach is used to effectively determine the design requirements (DRs) of a computer workstation. Hesitant fuzzy linguistic term sets (HFLTS) are innovatively employed to capture the hesitancy of the experts in this approach. More precisely, the proposed new QFD approach is the first study that determines the importance of customer requirements (CRs), the relations between CRs and DRs and the correlations among DRs via HFLTS. Additionally, HFLTS based Analytic Hierarchy Process (AHP) and Technique for Order Performance by Similarity to Ideal Solution (TOPSIS) methods are utilized in the computational steps to select the best computer workstation. A real industrial application is carried out to validate the implementation of the proposed approach.     

Application of evolutionary programming to adaptive regularization in image restoration

Image restoration is a difficult problem due to the ill-conditioned nature of the associated inverse filtering operation, which requires regularization techniques. The choice of the corresponding regularization parameter is thus an important issue since an incorrect choice would either lead to noisy appearances in the smooth regions or excessive blurring of the textured regions. In addition, this choice has to be made adaptively across, different image regions to ensure the best subjective quality for the restored image. We employ evolutionary programming (EP) to solve this adaptive regularization problem by generating a population of potential regularization strategies, and allowing them to compete under a new error measure which characterizes a large class of images in terms of their local correlational properties. The nonavailability of explicit gradient information for this measure motivates the adoption of EP techniques for its optimization, which allows efficient search at multiple error surface points. The adoption of EP also allows the broadening of the range of possible cost functions for image processing so that we can choose the most relevant function rather than the most tractable one for a particular image processing application.     

Multi-step virtual metrology for semiconductor manufacturing: A multilevel and regularization methods-based approach

In semiconductor manufacturing, wafer quality control strongly relies on product monitoring and physical metrology. However, the involved metrology operations, generally performed by means of scanning electron microscopes, are particularly cost-intensive and time-consuming. For this reason, in common practice a small subset only of a productive lot is measured at the metrology stations and it is devoted to represent the entire lot. Virtual Metrology (VM) methodologies are used to obtain reliable predictions of metrology results at process time, without actually performing physical measurements. This goal is usually achieved by means of statistical models and by linking process data and context information to target measurements. Since semiconductor manufacturing processes involve a high number of sequential operations, it is reasonable to assume that the quality features of a given wafer (such as layer thickness and critical dimensions) depend on the whole processing and not on the last step before measurement only. In this paper, we investigate the possibilities to enhance VM prediction accuracy by exploiting the knowledge collected in the previous process steps. We present two different schemes of multi-step VM, along with dataset preparation indications. Special emphasis is placed on regression techniques capable of handling high-dimensional input spaces. The proposed multi-step approaches are tested on industrial production data.     

A novel adaptive morphological approach for degraded character image segmentation

This work proposes a novel adaptive approach for character segmentation and feature vector extraction from seriously degraded images. An algorithm based on the histogram automatically detects fragments and merges these fragments before segmenting the fragmented characters. A morphological thickening algorithm automatically locates reference lines for separating the overlapped characters. A morphological thinning algorithm and the segmentation cost calculation automatically determine the baseline for segmenting the connected characters. Basically, our approach can detect fragmented, overlapped, or connected character and adaptively apply for one of three algorithms without manual fine-tuning. Seriously degraded images as license plate images taken from real world are used in the experiments to evaluate the robustness, the flexibility and the effectiveness of our approach. The system approach output data as feature vectors keep useful information more accurately to be used as input data in an automatic pattern recognition system.     

A new scheme to learn a kernel in regularization networks

In this paper, we propose a new scheme to learn a kernel function from the convex combination of finite given kernels in regularization networks. We show that the corresponding variational problem is convex and under certain conditions, the variational problem can be approximated by a semidefinite programming problem which coincides with the Micchelli and Pontil's (MP's) Model (Micchelli and Pontil, 2005 [10]).     

Besov空间下迭代全变差正则化的图像恢复模型

在Besov空间下,提出了一种用于图像恢复领域的迭代全变差正则化模型。通过使用一个加权的参数序列,给出了一个迭代正则化的变分问题,这个变分问题实际上是一个小波软硬阈值结合的迭代程序。给出了新模型的停止标准和一些好的性质,如单调性和收敛性等。数值实验表明与传统去噪方法相比,新方法不仅能较好地恢复图像,而且收敛速度较快。     

一种改进的最小二乘正则化的图像复原方法

在常用的最小二乘正则化方法的基础上,提出了一种改进的图像复原方法。在运算中,首先用四阶偏微分方程方法对模糊图像进行噪声处理,得到一幅中间图像,然后对这个中间图像采用最小二乘正则化方法进行处理,便得到了最终的复原图像。实验表明,该方法不仅能克服问题的病态性,而且复原后的图像比最小二乘正则化方法复原后的图像整体视觉效果和峰值信噪比都有明显的提高。