四元数矩阵正交特征向量系的求解方法及其在彩色人脸识别中的应用

针对四元数矩阵正交特征矢量系求解困难的缺点, 本文提出一种获取四元数矩阵正交特征矢量集等效、便捷的方法, 其基本思路为: 首先, 构造四元数矩阵定义于复数域的导出阵, 并利用该导出阵特征矢量空间的一种特殊的等价空间间接获取相应特征值所对应的特征矢量. 然后, 将复数矢量转换为四元数矢量, 按如此方式获取的对应所有特征值的非零特征矢量则构成原始四元数矩阵的正交特征矢量系. 同时, 本文将定义于实数域的主成分分析方法 (Principal component algorithm, PCA) 向四元数体作合理的推广, 给出详细的数学推导过程, 证明该方法的合理性及其在统计模式识别领域得以应用的可能性. 最后, 作者将彩色图像像素的R、G、B三分量作为四元数的三个虚数部分, 首次在人脸识别中引入基于四元数的彩色人脸识别方法. 较传统的基于灰度图像的识别方法, 本文方法不仅利用了人脸图像灰度值的空间分布信息, 而且充分利用不同人脸之间的色彩差异, 从而得到更多的鉴别信息.在四川大学人工智能研究所的彩色人脸库上进行的实验表明, 所提出的基于四元数的识别方法不仅大幅度提高了识别率, 而且具有较高的鲁棒性.     

基于四元数组的球形永磁步进电机控制研究

提出了一种控制球形电机的简便方法,利用四元数作为描述电机转动的数学工具,分析了电机定子线圈换向与转动的规律,求解出当前位置下符合旋转条件的永磁体对/线圈对,记录在表中,查找能产生与给定转轴相近的旋转的永磁体对/线圈对。多次旋转的误差为累积误差,当误差超出某角度阈值,进行一次位置修正。MATLAB仿真表明,利用四元数的数学工具简化了球形电机的计算与控制过程,可以使电机按预定轨迹转动,是一种行之有效的方法。     

Attention selection using global topological properties based on pulse coupled neural network

Topological properties are with invariance and take priority over other features, which play an important role in cognition. This paper introduces a new attention selection model called TPA (topological properties-based attention), which adopts topological properties and quaternion. In TPA, using Unit-linking PCNN (Pulse Coupled Neural Network) hole-filter expresses an important topological property (the connectivity) in visual attention selection. Meanwhile, using the quaternion Fourier transform based phase spectrum of an image or a frame in a video obtains the spatio-temporal saliency map, which shows the result of attention selection. Adjusting the weight of a topological channel can change its influence. The experimental results show that TPA reflects the real attention selection more accurately than PQFT (Phase spectrum of Quaternion Fourier Transform).     

基于四元数的双彩色图像盲水印算法

提出一种基于四元数的双彩色图像盲水印算法。对载体图像和水印图像分别进行离散四元数傅里叶变换后,对水印图像频域的低频、中频和高频系数做混沌置乱处理,并利用脉冲编码调制方法,在载体图像的低频、中频和高频嵌入置乱后水印的相应频带系数,通过逆离散四元数傅里叶变换得到嵌入水印的图像。实验结果表明,该算法保证水印具有较高的透明性,对剪切、叠加噪声、JPEG压缩等常见的攻击具有较好的鲁棒性。     

四元数域对合增广宽线性自适应波束形成

该文提出一种基于4元数的宽线性自适应波束形成方法,该方法在利用4元数构建单个阵元输出的基础上,通过充分挖掘4元数的3种对合信息,联合信号的非圆特性,建立4元数域对合增广信号模型,进而实现4元数域宽线性自适应波束形成。同传统4元数波束形成技术相比,该方法对非圆信号的接收性能显著提升,同时可以实现阵列虚拟孔径扩展,增大自适应波束形成干扰抑制自由度。仿真实验验证了所提波束形成方法的性能。     

自适应混合滤波算法在微型飞行器姿态估计中的应用

针对低成本惯性测量单元(IMU)存在漂移和噪声干扰等问题,提出了一种具有自适应参数调节的混合滤波算法。采用四元数法进行系统模型的描述,用梯度下降法对加速度计测得的数据进行处理,再通过互补滤波器将其与陀螺仪测量值进行融合,形成混合滤波算法。同时,考虑到飞行姿态的复杂性,进行参数λ的自适应调节,因而改进后的混合滤波算法,能保证各种飞行姿态变化情况下实时姿态的最优估算。实际系统在线实时性能测试表明,提出的算法简单,估计精度高,易于在嵌入式系统中实现,具有较高推广应用价值。     

低阶线性Kalman滤波实时定姿算法的设计与实现

从Kalman滤波定姿算法的实时实现出发,设计一种降维Kalman滤波器。推导了加速度计、磁强计组合全方位姿态角的解算公式。基于四元数微分方程,采用四阶龙格-库塔法对陀螺仪输出的角速率数据进行处理,建立了递推关系式,并以姿态四元数作为系统的状态矢量,构成四维Kalman滤波器。在DM3730 Cortex-A8处理器平台上对算法进行实现和实验验证。实验结果表明,经过降维处理后的算法,显著降低算法的实现复杂度和计算量,滤波效果及实时性能均达到预期的目标,具有较强的实用性。     

Color impulsive noise removal based on quaternion representation and directional vector order-statistics

A new method for detecting and suppressing impulsive noise in color images is presented in this paper. The proposed method is a type of switching vector filters, where the impulse detection is based on the order-statistic information about the color samples in the horizontal, vertical, and diagonal directions. The new solution first uses quaternion-based representation of color differences and median deviation-based techniques to search for the edge direction with the maximum number of similar pixels, and then utilizes the samples aligning with this edge direction to judge whether the current pixel is noisy or not and control the switching between identity (no filtering) and vector median filtering actions. Extensive experimental comparisons exhibit the validity of the proposed approach by showing significant performance improvements over other well-known color image filtering techniques.     

An efficient and effective blind camera image quality metric via modeling quaternion wavelet coefficients

As an extension of Discrete and Complex Wavelet Transform, Quaternion Wavelet Transform (QWT) has attracted extensive attention in the past few years, because it can provide better analytic representation for 2D images. The QWT of an image consists of four parts, i.e., one magnitude part and three phase parts. The magnitude is nearly shift-invariant, which characterizes features at any spatial location, and the three phases represent the structure of these features. This indicates that QWT is more powerful in representing image structures, and thus is suitable for image quality evaluation. In this paper, an efficient and effective Camera Image Quality Metric (CIQM) is proposed based on QWT, which is utilized to describe the intrinsic structures of an image. For an image, it is first decomposed by QWT with three scales. Then, for each scale, the magnitude and entropy of the subband coefficients, and natural scene statistics of the third phase are calculated. The magnitude is utilized to describe the generalized spectral behavior, and the entropy is used to encode the generalized information of distortions. Since the third phase of QWT is considered to be texture feature, the natural scene statistics of the third phase of QWT is used to measure structure degradations in the proposed method. All these features reflect the self-similarity and independency of image content, which can effectively reflect image distortions. Finally, random forest is utilized to build the quality model. Experiments conducted on three camera image databases and two multiply distorted image databases have proved that CIQM outperforms the relevant state-of-the-art models for both authentically distorted images and multiply distorted images.     

Marginalized particle filter for spacecraft attitude estimation from vector measurements

An algorithm based on the marginalized particle filters (MPF) is given in details in this paper to solve the spacecraft attitude estimation problem: attitude and gyro bias estimation using the biased gyro and vector observations. In this algorithm, by marginalizing out the state appearing linearly in the spacecraft model, the Kalman filter is associated with each particle in order to reduce the size of the state space and computational burden. The distribution of attitude vector is approximated by a set of particles and estimated using particle filter, while the estimation of gyro bias is obtained for each one of the attitude particles by applying the Kalman filter. The efficiency of this modified MPF estimator is verified through numerical simulation of a fully actuated rigid body. For comparison, unscented Kalman filter (UKF) is also used to gauge the performance of MPF. The results presented in this paper clearly demonstrate that the MPF is superior to UKF in coping with the nonlinear model.