From Fourier Expansions to Arithmetic-Haar Expressions on Quaternion Groups

Arithmetic expressions for switching functions are introduced through the replacement of Boolean operations with arithmetic equivalents. In this setting, they can be regarded as the integer counterpart of Reed-Muller expressions for switching functions. However, arithmetic expressions can be interpreted as series expansions in the space of complex valued functions on finite dyadic groups in terms of a particular set of basic functions. In this case, arithmetic expressions can be derived from the Walsh series expansions, which are the Fourier expansions on finite dyadic groups. In this paper, we extend the arithmetic expressions to non-Abelian groups by the example of quaternion groups. Similar to the case of finite dyadic groups, the arithmetic expressions on quaternion groups are derived from the Fourier expansions. Attempts are done to get the related transform matrices with a structure similar to that of the Haar transform matrices, which ensures efficiency of computation of arithmetic coefficients. Received: October 5, 1999; revised version: June 14, 2000     

捷联式航姿系统中四元素算法Kalman滤波器的实现研究

本文基于四元素算法推导了姿态算法和捷联惯导系统误差模型,并设计了Kalman滤波器。在此基础上分析了误差模型的随机噪声补偿和提出了航向修正。仿真结果表明,本文讨论的这种Kalman滤波器能保证航向精度,具有实际应用意义。     

Multiple-image encryption based on chaotic phase mask and equal modulus decomposition in quaternion gyrator domain

In order to transmit multiple-image synchronously, this paper introduces an encryption algorithm by combining equal modulus decomposition with quaternion gyrator transform. Firstly, each color image is encoded into a quaternion-valued matrix for a holistic processing. With the chaotic random phase mask, the quaternion gyrator spectrum is obtained. It is subsequently split into a complex-valued interim matrix and the equal modulus decomposition is performed to enhance the security, where the spectrum is divided into two complex-valued masks. Thereafter, the two set of phase masks are respectively superimposed and followed by gyrator transforms. Finally, a real-valued matrix is constructed as the final ciphertext image by splicing the real and imaginary parts together. The phase masks that are generated using the chaotic and real-valued ciphertext are convenient to storage and transmission. Moreover, the initial conditions are closely related with the plaintext images, which makes the cryptosystem achieve high security. Numerical simulations are made to demonstrate the reliability of the proposed cryptosystem.     

Disturbance observer-based quadrotor attitude tracking control for aggressive maneuvers

In this paper, a disturbance observer-based quadrotor attitude controller for aggressive maneuvering is presented. The controller is made up of the cascade connection between two control-loops: an outer quaternion-based attitude control-loop and an inner disturbance observer-based angular velocity tracking control-loop. The disturbance observer is designed to estimate and compensate for the Coriolis term and the external disturbances. It is shown that, for fast maneuvers, the disturbance observer needs to take into account the motor dynamics. This allows to notably increase the observer bandwidth, leading to significant improvements in the disturbance rejection capabilities. The stability of the resulting closed-loop is analyzed. Also, different simulations and flight tests are carried out to validate the main results, showing an outstanding tracking performance when aggressive attitude maneuvers are being executed, even in the presence of strong disturbances such as suspended payloads.     

Quaternion-MUSIC for near-field strictly noncircular sources with large-scale polarization array

In this paper, a novel localization method is proposed for DOA, range and polarization estimation of near-field noncircular sources in massive multiple-input-multiple-output (MIMO) systems. Compared with traditional MUSIC-based algorithms, the proposed algorithms can separate the polarization parameters from the spatial spectrum function, avoiding the four-dimensional (4-D) spectrum search and realizing the fast localization of the near-field source with high accuracy. First, the dimension-reduced MUSIC (DR-MUSIC) algorithm is proposed for DOA and range estimation with low computational complexity, and given a closed-form expression of polarization estimation. Next, based on the quaternion theory, a novel algorithm named quaternion non-circular MUSIC (QNC-MUSIC) is proposed for parameter estimation of non-circular signals with high estimation accuracy. In addition, the analysis of the computational complexity and simulations of the proposed method are provided, showing that the proposed method yields a better performance than DR-MUSIC in massive MIMO systems.     

基于自适应四元数奇异值分解的图像拼接检测

图像拼接将来源不同的图像合并成一幅图,由此引起图像中光照方向、噪声等特性出现不一致的情况。目前多数方法根据拼接图像中噪声的不一致性来检测伪造区域,但是普遍对不同大小图像块的噪声估计准确性不高,导致真阳性率较低,且当噪声差异较小时会检测失败。针对该问题,提出一种基于自适应四元数奇异值分解（QSVD）的噪声估计方法。对图像进行超像素分割,利用自适应QSVD估计超像素的噪声,结合图像亮度并利用多项式拟合建立图像噪声-亮度函数,得到各超像素到该函数曲线的最小距离测度。为提高检测精确率,利用色温估计算法提取超像素的色温特征,将距离测度与色温特征相融合作为最终的特征向量,利用FCM模糊聚类定位拼接区域。在Columbia IPDED拼接图像数据集上进行实验,结果表明,该方法在未经后处理图像集上的检测TPR值较对比方法至少提升8.21个百分点,且对高斯模糊、JPEG压缩和伽马校正表现出较好的鲁棒性。     

基于四元数矢量积算法的彩色图像区域生长算法

针对传统区域生长大多只应用于灰度图像而且存在对彩色信息不敏感、生长准则单一等问题,新算法采用LUV彩色模型,将基于四元数矢量积性质的区域生长算法应用到复杂背景下的彩色图像中。实验结果表明,该方法可以准确地细分区域和对象。     

Quaternion pseudo-Zernike moments combining both of RGB information and depth information for color image splicing detection

The quaternion representation (QR) used in current quaternion-based color image processing creates redundancy when representing a color image of three components by a quaternion matrix having four components. In this paper, both RGB and depth (RGB-D) information are considered to improve QR for efficiently representing RGB-D images. The improved QR fully utilizes the four-dimensional quaternion domain. Using this improved QR, firstly we define the new quaternion pseudo-Zernike moments (NQPZMs) and then propose an efficient computational algorithm for NQPZMs through the conventional pseudo-Zernike moments (PZMs). Finally, we propose an algorithm for color image splicing detection based on the NQPZMs and the quaternion back-propagation neural network (QBPNN). Experimental results on four public datasets (DVMM, CASIA v1.0 and v2.0, Wild Web) demonstrate that the proposed splicing detection algorithm can achieve almost 100% accuracy with the appropriate feature dimensionality and outperforms 14 existing algorithms. Moreover, the comparison of six color spaces (RGB, HSI, HSV, YCbCr, YUV, and YIQ) shows that the proposed algorithm using YCbCr color space has the overall best performance in splicing detection.