Kernel dictionary learning based discriminant analysis

Sparse representation based classification (SRC) has been successfully applied in many applications. But how to determine appropriate features that can best work with SRC remains an open question. Dictionary learning (DL) has played an import role in the success of sparse representation, while SRC treats the entire training set as a structured dictionary. In addition, as a linear algorithm, SRC cannot handle the data with highly nonlinear distribution. Motivated by these concerns, in this paper, we propose a novel feature learning method (termed kernel dictionary learning based discriminant analysis, KDL-DA). The proposed algorithm aims at learning a projection matrix and a kernel dictionary simultaneously such that in the reduced space the sparse representation of the data can be easily obtained, and the reconstruction residual can be further reduced. Thus, KDL-DA can achieve better performances in the projected space. Extensive experimental results show that our method outperforms many state-of-the-art methods.     

A video semantic detection method based on locality-sensitive discriminant sparse representation and weighted KNN

Video semantic detection has been one research hotspot in the field of human-computer interaction. In video features-oriented sparse representation, the features from the same category video could not achieve similar coding results. To address this, the Locality-Sensitive Discriminant Sparse Representation (LSDSR) is developed, in order that the video samples belonging to the same video category are encoded as similar sparse codes which make them have better category discrimination. In the LSDSR, a discriminative loss function based on sparse coefficients is imposed on the locality-sensitive sparse representation, which makes the optimized dictionary for sparse representation be discriminative. The LSDSR for video features enhances the power of semantic discrimination to optimize the dictionary and build the better discriminant sparse model. More so, to further improve the accuracy of video semantic detection after sparse representation, a weighted K-Nearest Neighbor (KNN) classification method with the loss function that integrates reconstruction error and discrimination for the sparse representation is adopted to detect video semantic concepts. The proposed methods are evaluated on the related video databases in comparison with existing sparse representation methods. The experimental results show that the proposed methods significantly enhance the power of discrimination of video features, and consequently improve the accuracy of video semantic concept detection.     

基于修改核函数的RLS-SVM多用户检测算法

为了解决支持向量机算法在多用户检测中存在的模型复杂及产生的支持向量数目较多的问题,该文提出一种新的非线性多用户检测算法。该算法在第一次小样本训练时引入了遗忘因子,该因子使支持向量数减少了28％。在第一次训练后产生的支持向量的基础上,将黎曼几何结构引入到输入空间,利用黎曼几何结构将分类器中的核函数进行修改,在第二次训练中再次减少了支持向量数目。此方法在牺牲较少误比特率的基础上,简化了算法模型和降低计算复杂度。仿真实验表明,该算法抑制了多径引起的码间干扰,性能接近于最优多用户检测器。     

基于组合相似性的视频检索

该文研究基于镜头的视频检索问题,提出了一种新的基于组合相似性的镜头相似性度量方法。首先把镜头看成由帧序列组成的一个组合,镜头的相似性通过帧组合的相似性来度量。其次通过用一个非线性映射,把帧组合所在的空间映射到一个高维空间,在这个空间中,假设帧组合服从正态分布,利用核方法,抽取出关键帧序列,并计算出两个正态分布之间的概率距离,这个距离表明了帧组合的相似程度,从而得到两个镜头之间的相似性。最后将这种方法应用于基于镜头的视频检索中,实验表明在相同条件下,基于该方法的检索效果明显优于传统的欧式距离和直方图交方法。     

傍轴黎曼几何光学·Ⅰ理论

利用微分几何方法研究光束传输。从三维黎曼流形的曲率出发，构造了一个复空间。它的流线能兼容几何光学与波动光学的信息。     

傍轴黎曼几何光学．──Ⅱ．应用基础

利用微分几何方法研究光束传输。从黎曼三维流形的曲率出发，构造了一个复空间．它的流线能兼容几何光学与波动光学的信息。列举了复空间应用于光束传输的一些例子。     

在Grassmann流形上构造非相干酉空时码

研究基于Grassmann流形的非相干酉空时星座图的设计方法。首先定义了非相干空时码在流形上的酉矩阵框架结构;然后在此框架约束下,将已有的Grassmann流形上最优包络分布的最小Frobenius弦距离作为阈值,通过设置合适的步长来改变酉矩阵中各元素的幅值和相位,在流形上搜索最小Frobenius弦距离大于阈值的点,搜索到事先设定的星座图点数,即构成酉空时星座图。数值仿真结果表明本框架结构非相干Grassmannian酉空时码的性能均优于现有的其他形式非相干酉空时码的性能。     

基于稀疏稠密结构表示与在线鲁棒字典学习的视觉跟踪

L1跟踪对适度的遮挡具有鲁棒性,但是存在速度慢和易产生模型漂移的不足。为了解决上述两个问题,该文首先提出一种基于稀疏稠密结构的鲁棒表示模型。该模型对目标模板系数和小模板系数分别进行L2范数和L1范数正则化增强了对离群模板的鲁棒性。为了提高目标跟踪速度,基于块坐标优化原理,用岭回归和软阈值操作建立了该模型的快速算法。其次,为降低模型漂移的发生,该文提出一种在线鲁棒的字典学习算法用于模板更新。在粒子滤波框架下,用该表示模型和字典学习算法实现了鲁棒快速的跟踪方法。在多个具有挑战性的图像序列上的实验结果表明：与现有跟踪方法相比,所提跟踪方法具有较优的跟踪性能。     

基于中心对齐多核学习的稀疏多元逻辑回归算法

稀疏多元逻辑回归(SMLR)作为一种广义的线性模型被广泛地应用于各种多分类任务场景中。SMLR通过将拉普拉斯先验引入多元逻辑回归(MLR)中使其解具有稀疏性,这使得该分类器可以在进行分类的过程中嵌入特征选择。为了使分类器能够解决非线性数据分类的问题,该文通过核技巧对SMLR进行核化扩充后得到了核稀疏多元逻辑回归(KSMLR)。KSMLR能够将非线性特征数据通过核函数映射到高维甚至无穷维的特征空间中,使其特征能够充分地表达并最终能进行有效的分类。此外,该文还利用了基于中心对齐的多核学习算法,通过不同的核函数对数据进行不同维度的映射,并用中心对齐相似度来灵活地选取多核学习权重系数,使得分类器具有更好的泛化能力。实验结果表明,该文提出的基于中心对齐多核学习的稀疏多元逻辑回归算法在分类的准确率指标上都优于目前常规的分类算法。     

基于PCA的非局部聚类稀疏表示图像重建方法

针对腐化图像恢复不足的问题,提出一种基于PCA的非局部聚类稀疏表示模型.首先,用图像非局部自相似性来取得稀疏系数值;然后,对观测图像的稀疏编码系数进行集中聚类;最后,通过学习字典使降噪图像的稀疏编码系数接近原始图像的编码系数.实验结果表明,提出的方法在重建图像性能上较同类方法有显著提高,获得了更好的图像恢复质量.     

Adjusting samples for obtaining better l2-norm minimization based sparse representation

l₂-norm sparse representation (l₂-SR) based face recognition method has attracted increasing attention due to its excellent performance, simple algorithm and high computational efficiency. However, one of the drawbacks of l₂-SR is that the test sample may be conspicuous difference from the training samples even from the same class and thus the method shows poor robustness. Another drawback is that l₂-SR does not perform well in identifying the training samples that are trivial in correctly classifying the test sample. In this paper, to avoid the above imperfection, we proposed a novel l₂-SR. We first identifies the training samples that are important in correctly classifying the test sample and then neglects components that cannot be represented by the training samples. The proposed method also involve in-depth analysis of l₂-SR and provide novel ideas to improve previous methods. Experimental results on face datasets show that the proposed method can greatly improve l₂-SR.     

一种基于稀疏分解的窄带信号频率估计算法

针对窄带多分量信号频率估计问题,该文提出一种基于稀疏分解的频率估计算法,能够同时对多个窄带信号的频率进行估计。首先利用传统方法进行频率预估计,然后根据频率预估计的结果建立冗余字典,对信号进行稀疏表示,最后通过匹配追踪算法得到精确的频率估计。该算法极大地减小了字典的长度和稀疏分解的运算量,而且在迭代过程中利用了全局信息更新残差向量,估计结果更为精确,在低信噪比情况下性能也较为稳健。仿真结果验证该算法的有效性和正确性。     

Multi-stage image denoising based on correlation coefficient matching and sparse dictionary pruning

We present a novel image denoising method based on multiscale sparse representations. In tackling the conflicting problems of structure extraction and artifact suppression, we introduce a correlation coefficient matching criterion for sparse coding so as to extract more meaningful structures from the noisy image. On the other hand, we propose a dictionary pruning method to suppress noise. Based on the above techniques, an effective dictionary training method is developed. To further improve the denoising performance, we propose a multi-stage sparse coding framework where sparse representations are obtained in different scales to capture multiscale image features for effective denoising. The multi-stage coding scheme not only reduces the computational burden of previous multiscale denoising approaches, but more importantly, it also contributes to artifact suppression. Experimental results show that the proposed method achieves a state-of-the-art denoising performance in terms of both objective and subjective quality and provides significant improvements over other methods at high noise levels.     

在低维空间实现的基于MP的图像稀疏分解

研究利用MatchingPursuit(MP)方法实现的图像稀疏分解算法,针对其中关键难题,提出利用在低维空间的搜索实现高维空间的搜索的快速方法。算法的有效性为实验结果所证实。