基于方向信息测度的图像恢复

文章根据人眼对图像平滑区噪声敏感,而对边缘区不敏感这一特性,提出了基于图像信息测度的图像恢复方法。在图像恢复的过程中,在图像的平滑区加大平滑程度,从而减小噪声;而在边缘区,加大图像恢复程度,从而增强边缘,并且考虑了模糊程度随空间变化这一实际。实验证明本文的方法在增大图像边缘恢复程度,减小噪声放大之间能够达到一个很好的折衷,恢复出来的结果图像视觉效果良好。     

一种图象恢复效果接近最优的正则化方法

提出一种新的技术，它自适应地选取正则化参数以取得较理想的恢复效果．利用小波变换，分析正则化算子和正则化参数对图象残差的各子频段能量的影响．在本文条件下，我们论证正则化算子取拉普拉斯算子比取恒等算子恢复性能好,并且预测噪声能量．实验结果表明本文提出的方法不需要知道噪声能量，也能够自适应地确定正则化参数并且恢复性能比传统的方法好，恢复效果非常接近最优恢复．     

Isotropic Energies, Filters and Splines for Vector Field Regularization

The aim of this paper is to propose new regularization and filtering techniques for dense and sparse vector fields, and to focus on their application to non-rigid registration. Indeed, most of the regularization energies used in non-rigid registration operate independently on each coordinate of the transformation. The only common exception is the linear elastic energy, which enables cross-effects between coordinates. Cross-effects are yet essential to give realistic deformations in the uniform parts of the image, where displacements are interpolated.In this paper, we propose to find isotropic quadratic differential forms operating on a vector field, using a known theorem on isotropic tensors, and we give results for differentials of order 1 and 2. The quadratic approximation induced by these energies yields a new class of vectorial filters, applied numerically in the Fourier domain. We also propose a class of separable isotropic filters generalizing Gaussian filtering to vector fields, which enables fast smoothing in the spatial domain. Then we deduce splines in the context of interpolation or approximation of sparse displacements. These splines generalize scalar Laplacian splines, such as thin-plate splines, to vector interpolation. Finally, we propose to solve the problem of approximating a dense and a sparse displacement field at the same time. This last formulation enables us to introduce sparse geometrical constraints in intensity based non-rigid registration algorithms, illustrated here on intersubject brain registration.     

RKRLS及在混炼胶质量建模与预报中的应用研究

对递推最小二乘(RLS)进行了非线性的核(kernel)变换,并采用正则化技术改写了目标范函,提出了一种正则核变换递推最小二乘(regularized kernel,RLS)算法.获得了RKRLS模型的系数和误差表达式,分析了算法的推广能力并证明了KeYnel RLS算法为其特例,进而导出了RKRLS算法在限定、增长和缩减记忆三种不同模式下的递推公式均无需进行求逆计算.RKRLS算法具有三个特性:小样本、可控的推广能力和速度快,因而非常适合于工业应用场合.通过对橡胶混炼质量的门尼指标进行建模和预测分析表明,本算法具有较好的跟踪预测性能.     

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.