电容层析成像图像重建的总变差正则化算法

针对电容层析成像（ECT）逆问题解的不适定性,本文提出一种基于总变差（total variation,TV）正则化的图像重建算法。同传统的2范数Tikhonov正则化方法相比,该算法（基于1范数正则化）不仅保证了逆问题求解的稳定性,而且提高了对介质非连续分布的区域成像的分辨能力,具有良好的保边缘性。仿真及实验结果表明,该算法在重建图像质量和重建速度两方面均具有优势。     

Robust incremental compensation of the light attenuation with depth in 3D fluorescence microscopy

Fluorescent signal intensities from confocal laser scanning microscopes (CLSM) suffer from several distortions inherent to the method. Namely, layers which lie deeper within the specimen are relatively dark due to absorption and scattering of both excitation and fluorescent light, photobleaching and/or other factors. Because of these effects, a quantitative analysis of images is not always possible without correction. Under certain assumptions, the decay of intensities can be estimated and used for a partial depth intensity correction. In this paper we propose an original robust incremental method for compensating the attenuation of intensity signals. Most previous correction methods are more or less empirical and based on fitting a decreasing parametric function to the section mean intensity curve computed by summing all pixel values in each section. The fitted curve is then used for the calculation of correction factors for each section and a new compensated sections series is computed. However, these methods do not perfectly correct the images. Hence, the algorithm we propose for the automatic correction of intensities relies on robust estimation, which automatically ignores pixels where measurements deviate from the decay model. It is based on techniques adopted from the computer vision literature for image motion estimation. The resulting algorithm is used to correct volumes acquired in CLSM. An implementation of such a restoration filter is discussed and examples of successful restorations are given.     

多自由度系统非线性参数识别的灵敏度方法

为了识别多自由度系统的非线性参数（3次阻尼系数、3次刚度系数和干摩擦力），提出一种基于灵敏度分析用测量响应（位移、速度或加速度）识别非线性参数的方法。将结构抽象为由线性和非线性阻尼、刚度连接的集中质量系统，用四阶Runge—Kutta法求解多自由度非线性系统的振动响应和振动响应对非线性参数的灵敏度。假定非线性参数为零初值，根据计算响应与测试响应的差值，由基于正则化的阻尼最小二乘法迭代识别系统的非线性参数值。算例表明，该方法可以有效地识别多自由度系统的非线性参数。     

复合正则化的图像超分辨率复原方法

图像超分辨率复原是计算机视觉领域的一个基础研究方向.为提高具有高度结构化特征图像超分辨率复原效果,提出了一种基于复合正则化的超分辨率复原方法.该方法整合了多个不同种类范数的正则化项,将具有旋转不变性的方向全变分组稀疏正则化(TI-DTV)方法以及小波分析方法嵌入至目标函数中.全变分组稀疏正则化(TI-DTV)方法是一种可以有效解决高度结构化图像中直线边缘区域超分辨率复原的方法,但TI-DTV中的全变分(TV)和方向全变分(DTV)模型可能会导致图像阶梯化效应(staircase artifacts),而小波分析项则可以提高图像纹理信息的复原效果,可减小阶梯化效应的影响.为了解决不同范数下的混合正则化问题,利用一阶对偶圆锥形解法(TFOCS)的思想,推导出了一阶对偶形式的快速解法.结果表明,在真实图像集的实验中,通过与全变分、小波分析、TI-DTV等超分辨率复原方法的比较,可以明显的看出该方法结果较其他方法更清晰,对直线型结构复原效果有一定的提高,同时保留了更多的细节信息,峰值信噪比(PSNR)和结构相似性(SSIM)也有明显提高.     

A numerical study of variable coefficient elliptic Cauchy problem via projection method

In this paper, we investigate a numerical method for the solution of an inverse problem of recovering lacking data on some part of the boundary of a domain from the Cauchy data on other part for a variable coefficient elliptic Cauchy problem. In the process, the Cauchy problem is transformed into the problem of solving a compact linear operator equation. As a remedy to the ill-posedness of the problem, we use a projection method which allows regularization solely by discretization. The discretization level plays the role of regularization parameter in the case of projection method. The balancing principle is used for the choice of an appropriate discretization level. Several numerical examples show that the method produces a stable good approximate solution.     

FUZZIFYING THE “PRECISE”

Based on the fuzzy-integral model, methods and algorithms are developed for identifying the “input–output” operator of continuous and stationary discrete extremal fuzzy dynamic systems (EFDS). The EFDS “input–output” operator is restored by means of experimental data with possibilistic uncertainty, the source of which is extremal fuzzy time intervals. The regularization conditions for obtaining quasi-optimal estimates are substantiated by the proved theorems. The corresponding algorithms are provided. The results obtained are illustrated by examples in the case of a finite set of EFDS states.     

Oriented total variation l1/2 regularization

Total Variation (TV) is a widely used image restoration/decomposition model. It is observed that the classical TV l1 and TV l2 regularization, on the one hand, do not favor higher-gradient structures over lower-gradient details as expected for structure preserving image processing, and on the other hand, tend to reduce the horizontal and vertical gradients, and thus inevitably blur the oblique edges in images. In this paper, we address these two problems by defining Oriented Total Variation l1/2 (OTV l1/2). It is theoretically and experimentally demonstrated that applying l1/2 regularization to the directional derivatives of images leads to superior structure preservation. OTV l1/2 regularization can be applied to image denoising and video compression, and the experimental results verify that OTV l1/2 outperforms other similar models.     

Domain reduction for Benders decomposition based global optimization

While domain reduction has been successfully applied in branch-and-bound based global optimization over the last two decades, it has not been systematically studied for decomposition based global optimization, which is usually more efficient for problems with decomposable structures. This paper discusses integration of domain reduction in Benders decomposition based global optimization, specifically, generalized Benders decomposition (GBD) and nonconvex generalized Benders decomposition (NGBD). Revised GBD and NGBD frameworks are proposed to incorporate bound contraction operations or/and range reduction calculations, which can reduce the variable bounds and therefore improve the convergence rate and expedite the solution of nonconvex subproblems. Novel customized bound contraction problems are proposed for GBD and NGBD, and they are easier to solve than the classical bound contraction problems because they are defined on reduced variable spaces. The benefits of the proposed methods are demonstrated through a gas production operation problem and a power distribution system design problem.     

Solution for the general integral‐type nonlocal plasticity model with Tikhonov regularization

A new solution approach, based on Tikhonov regularization on the Fredholm integral equations of the first kind, is proposed to find the approximate solutions of the strain softening problems. In this approach, the consistency condition is regularized with the Tikhonov stabilizers along with a regularization parameter, and the internal variable increments are solved from the resulting Euler's equations. It is shown that, as the regularization parameter is increased, the solutions converge to a unique one. A nonlocal yield condition and a nonlocal return mapping algorithm are proposed to carry out the integration of constitutive equations in the time and spatial domains. A global plastic dissipation principle is proposed to relax the classical local plastic dissipation postulate. Numerical examples show that the proposed approach leads to objective, mesh‐independent solutions of the softening‐induced localization problems. A comparison of the results from the proposed approach with those from the gradient‐dependent plasticity model shows that the two models give close solutions.