Spectral characteristic of a pulsed hollow Gaussian beam passing through a circular aperture

The spectral characteristics of a pulsed hollow Gaussian beam passing through a circular aperture are studied. Based on the vectorial Rayleigh diffraction integrals, the analytical expressions of the spectra for the complex analytic signal representation and for the complex amplitude envelope representation are derived, respectively, and the comparison between them is made. The influences of the truncation parameter and the beam order on the spectral shifts and on the spectral switches are illustrated. It is shown that the spectrum for the complex analytic signal representation and that for the complex amplitude envelope representation are obvious different as the pulse shorter than an optical period.     

Integrating the original face images and “symmetrical faces” to perform face recognition

Using the original and ‘symmetrical face’ training samples to perform representation based face recognition was first proposed in [1]. It simultaneously used the original and ‘symmetrical face’ training samples to perform a two-step classification and achieved an outstanding classification result. However, in [1] the “symmetrical face” is devised only for one method. In this paper, we do some improvements on the basis of [1] and combine this “symmetrical faces” transformation with several representation based methods. We exploit all original training samples, left “symmetrical face” training samples and right “symmetrical face” training samples for classification and use the score fusion for ultimate face recognition. The symmetry of the face is first used to generate new samples, which is different from original face image but can really reflect some possible appearance of the face. It effectively overcomes the problem of non-sufficient training samples. The experimental results show that the proposed scheme can be used to improve a number of traditional representation based methods including those that are not presented in the paper.     

A hierarchical structure with improved OMP sparse representation used with face recognition

With the rapid development of the face recognition technology, more and more optical products are applied in people's real life. The recognition accuracy can be improved by increasing the number of training samples, but the colossal training samples will result in the increase of computational complexity. In recent years, sparse representation method becomes a research hot spot on face recognition. In this paper we propose an energy constrain orthogonal matching pursuit (ECOMP) algorithm for sparse representation to select the few training samples and a hierarchical structure for face recognition. We filter the training samples with ECOMP algorithm and then we compute the weights by all selected training samples. At last we find the closest recovery sample to the test sample. Simultaneously the experimental results in AR, ORL and FERET database also show that our proposed method has better recognition performance than the LRC and SRC_OMP method.     

Blind image deconvolution using sparse and redundant representation

This work devotes to the image deconvolution problem that restores clear image from its blurred and noisy measurements with little prior about the blur. A deconvolution method based on sparse and redundant representation theory is developed in this paper. It firstly represents the blur and image over different redundant dictionaries and imposes sparsity constraint to their representation coefficients respectively, then alternately estimates them using an iterative algorithm employing optimization technique. Experimental results on astronomical images show that the proposed method can achieve as good performance as the method requiring a known blur, which demonstrates its effectiveness.     

量子力学混合态表象

在以往的文献中量子力学的表象都是纯态表象,在本文中我们从算符的合理排序和概率统计的正态分布思想出发,首次提出了量子力学混合态表象的概念,并证明了其完备性和正交性.量子力学混合态表象的优点是可以反映算符的多种表示以及其相应的排序规则.     

多个正态总体均值相等的VDR检验

本文将随机估计由一维参数扩展至多维参数,基于随机估计的密度函数提出VDR检验.在总体方差已知和未知的两种情形下,本文讨论多个正态总体均值是否相同的VDR检验过程,而且得到精确的检验.单因素方差分析是VDR检验的特例.模拟研究表明,VDR检验是一个普遍适用的方法.     

稀疏表示及其在人脸识别中的应用

稀疏表示是近年来新兴的一种数据表示方法,是对人类大脑皮层编码机制的模拟。稀疏表示以其良好的鲁棒性、抗干扰能力、可解释性和判别性等优势,广泛应用于模式识别领域。基于稀疏表示的分类器在人脸识别领域取得了令人惊喜的成就,它将训练样本看成字典,寻求测试样本在字典下的最稀疏的表示,即用尽可能少的训练样本的线性组合来重构测试样本。但是经典的基于稀疏表示的分类器没有考虑训练样本的类别信息,以致被选中的训练样本来自许多类,不利于分类,因此基于组稀疏的分类器被提出。组稀疏方法考虑了训练样本的类别相似性,其目的是用尽可能少类别的训练样本来表示测试样本,然而这类方法的缺点是同类的训练样本或者同时被选中或者同时被丢弃。在实际中,人脸受到光照、表情、姿势甚至遮挡等因素的影响,样本之间关系比较复杂,因此最后介绍局部加权组结构稀疏表示方法。该方法尽量用来自于与测试样本相似的类的训练样本和来自测试样本邻域的训练样本来表示测试样本,以减轻不相关类的干扰,并使得表示更稀疏和更具判别性。