Satellite image blind restoration based on surface fitting and multivariate model

Owing to the blurring effect from atmosphere and camera system in the satellite imaging, a blind image restoration algorithm is proposed which includes the modulation transfer function （MTF） estimation and the image restoration. In the MTF estimation stage, based on every degradation process of satellite imaging-chain, a combined parametric model of MTF is given and used to fit the surface of normalized logarithmic amplitude spectrum of degraded image. In the image restoration stage, a maximum a posteriori （MAP） based edge-preserving image restoration method is presented which introduces multivariate Laplacian model to characterize the prior distribution of wavelet coefficients of original image. During the image restoration, in order to avoid solving high nonlinear equations, optimization transfer algorithm is adopted to decom- pose the image restoration procedure into two simple steps： Landweber iteration and wavelet thresholding denoising. In the numerical experiment, the satellite image restoration results from SPOT-5 and high resolution camera （HR） of China ＆ Brazil earth resource satellite （CBERS-02B） ane compared, and the proposed algorithm is superior in the image edge preservation and noise inhibition.     

CALCULATIONS OF RUIN PROBABILITIES CONCERNING WITH CLAIM OCCURRENCES

In this article, we consider the perturbed classical surplus model. We study the probability that ruin occurs at each instant of claims, the probability that ruin occurs between two consecutive claims occurrences, as well as the distribution of the ruin time that lies in between two consecutive claims. We give some finite expressions depending on derivatives for Laplace transforms, which can allow computation of the probabilities concerning with claim occurrences. Further, we present some insight on the shapes of probability functions involved.     

图和线图的邻接谱及拉普拉斯谱的关系

图谱理论是图论研究的重要领域之一,也是非常活跃的研究方向。实践表明,对特征值的计算十分复杂,但可以研究不同定义的谱之间的关系确定特征值的上下界。通过利用对称矩阵和半正定矩阵的一些性质,讨论简单无向图G及其线图Gl的邻接谱之间的一些关系,推广已有的结果。同时也讨论图的邻接谱和拉普拉斯谱之间的关系。对判定某些图的邻接谱和拉普拉斯谱的范围具有一定的指导作用。     

宇宙处处都是叙说新故事的地方——“拉普拉斯妖”随笔之七

一 拉普拉斯妖消失了.从前一篇文章中我们看到,他消失在微观的量子世界里,消失在宏观的混乱世界里.     

Mixed eigenvalues of discrete p-Laplacian

This paper deals with the principal eigenvalue of discrete p-Laplacian on the set of nonnegative integers. Alternatively, it is studying the optimal constant of a class of weighted Hardy inequalities. The main goal is the quantitative estimates of the eigenvalue. The paper begins with the case having reflecting boundary at origin and absorbing boundary at infinity. Several variational formulas are presented in different formulation： the difference form, the single summation form, and the double summation form. As their applications, some explicit lower and upper estimates, a criterion for positivity （which was known years ago）, as well as an approximating procedure for the eigenvalue are obtained. Similarly, the dual case having absorbing boundary at origin and reflecting boundary at presented at the end of Section 2 to infinity is also studied. Two examples are illustrate the value of the investigation.     

基于改进高斯滤波的医学图像边缘增强

医学图像的边缘包含了图像的很多重要信息,对医学诊断的效率和精准性影响较大,文中研究了一种医学图像边缘增强的方法。为了在图像去噪阶段保留更多的图像细节信息,文中在传统高斯滤波算法基础上提出了一种标准差选取自适应的滤波算法。在图像增强阶段,利用传统的拉普拉斯算子结合强度权重控制图像增强的效果。经过算法分析和实验,验证了两种算法的结合提高了去噪效果,有效保留了图像的边缘细节信息,能够实现医学图像的边缘增强。     

一种快速低秩的判别子字典学习算法及图像分类

本文提出了一种快速低秩的判别子字典学习算法。在训练阶段,构造一个子字典的低秩约束项和拉普拉斯矩阵正则化项,加入判别字典学习的目标函数中。将原始样本映射到一个新的空间中,使同一类别的相邻点彼此靠近,同时增强子字典对同类样本的重构能力,针对每类样本的判别性特征,学习出相应的学习字典。在测试阶段,利用k NN分类器估计测试样本的类别标签。同时,将算法应用在3种数据集上,与其他的字典学习算法进行比较,取得了较好的分类结果。