Analytical formula for two‐dimensional ring artefact suppression

Ring artefacts are the most disturbing artefacts when reconstructed volumes are segmented. A lot of effort has already been put into better X‐ray optics, scintillators and detectors in order to minimize the appearance of these artefacts. However, additional processing is often required after standard flat‐field correction. Several methods exist to suppress artefacts. One group of methods is based on minimization of the Tikhonov functional. An analytical formula for processing of a single sinogram was developed. In this paper a similar approach is used and a formula for processing two‐dimensional projections is found. Thus suppression of ring artefacts is organized as a two‐dimensional convolution of `averaged' projections with a given filter. Several approaches are discussed in order to find elements of the filter in a faster and accurate way. Examples of experimental datasets processed by the proposed method are considered.     

具x/ζ型卷积核的奇异积分方程的求解

讨论了具x/ζ型卷积核的奇异积分方程的求解问题.通过Fourier积分变换,将所讨论的积分方程转化成在一定可解条件下与其同解意义下等价的Riemann边值问题.利用Riemann边值问题理论,分别讨论了在正则和非正则两种情况下的Riemann边值问题,进而得到相对应的x/ζ变量比型卷积核的积分方程一般解及可解条件.     

The time discretization in classes of integro‐differential equations with completely monotonic kernels: Weighted asymptotic convergence

We consider the time discretization for the solution of the equation with . Here, the operators L_j are densely defined positive self‐adjoint linear operator on a Hilbert space H and have spectral decompositions with respect to a common resolution of the identity in H . The kernel functions , are assumed to be completely monotonic on (0,∞) and locally integrable, but not constant. The considered time discretization method comes from [Da Xu, Science China Mathematics 56 (2013), 395–424], where the backward Euler method is combined with order one convolution quadrature for approximating the integral term. In this article, the convergence properties of the time discretization are given in the weighted and norm, where ρ is a given weighted function. Numerical experiments show the theoretical results. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 896–935, 2016     

Convolution of discrete measures on linear groups

Let p,q∈R such that 1<p<2 and . Define

(∗)     

Decompositions of the free additive convolution

We introduce and study a new type of convolution of probability measures, denoted μν and called the s-free additive convolution, which is defined by the subordination functions associated with the free additive convolution. We derive an alternating decomposition of μν for compactly supported μ and ν, using another convolution called orthogonal additive convolution. This decomposition leads to two types of ‘complete’ alternating decompositions of the free additive convolution μ?ν. More importantly, we develop an operatorial approach to the subordination property and introduce the associated notion of s-free independence. Moreover, we establish relations between convolutions associated with the main notions of noncommutative independence (free, monotone and boolean). Finally, our result leads to natural decompositions of the free product of rooted graphs.     

Solutions to arithmetic convolution equations

In the -algebra of arithmetic functions , endowed with the usual pointwise linear operations and the Dirichlet convolution, let denote the convolution power with factors . We investigate the solvability of polynomial equations of the form

with fixed coefficients . In some cases the solutions have specific properties and can be determined explicitly. We show that the property of the coefficients to belong to convergent Dirichlet series transfers to those solutions , whose values are simple zeros of the polynomial . We extend this to systems of convolution equations, which need not be of polynomial-type.

     

卷积反投影法重建温度场

电子散斑干涉技术是近年发展起来的一门新兴的测量技术,它由光干涉原理测量物理场的密度、温度分布等,这种测量技术是由物理场在不同截面、不同方向上的投影值反求场分布,这非常类似于CT技术。简述二维重建的基本原理,着重介绍卷积反投影重建算法。依此原理,模拟了双高斯分布函数的投影,并由平行束卷积法重建出模拟的温度场。为了指导电子散斑干涉实验,模拟了三种可能实验误差,并分别给出了重建结果。由于电子散斑干涉测量(投影)的方向个数小,提出了双线性滤波算法,使在测量值稀疏的条件下得到较好重建结果。     

测度值分枝过程与移民过程

本文介绍了测度值分枝过程和由斜卷积半群定义的伴随移民过程的基本理论和研究现状,主要内容包括：分枝粒子系统的收敛;超过程的基本正则性和极限定理;非线性微分方程;广义分枝模型;斜卷积半群和进入律;用Ｋｕｚｎｅｔｓｏｖ过程构造移民过程等。     

一维空洞卷积神经网络的矿物光谱分类

矿物光谱综合反映了岩矿的物理化学特性、组分和内部结构特征,已被应用于岩矿识别研究.传统的矿物光谱分类方法需要先对矿物光谱进行预处理,再采用不同方法分析光谱特征,从而实现分类目的.但同时也会造成部分光谱信息丢失,导致最终分类精度不高且操作过程繁琐、效率低下,难以应对日益增长的大数据处理需求.因此,建立一个准确、高效的矿物...