乘性和加性噪声中二维谐波的参数估计

本文从循环平稳的观点出发来研究乘性和加性噪声中二维谐波的参数估计问题,利用循环累积量的性质证明了二维二阶循环累积量单一记录估计的统计性质.在此基础上,对于零均值乘性噪声中的二维谐波信号提出了基于二阶循环累积量的二维谐波分量个数和频率对的估计方法,并分别得到了估计的强收敛速度.仿真试验验证了所提方法的性能.     

乘性和加性噪声中谐波恢复的循环统计量方法

本文从循环平衡的观点出发来研究乘性和加性噪声中的谐波恢复问题.首先，在一定条件下建立了一般复过程的有限长付里叶变换的大样本性质．然后，得到了任意阶循环矩的样本估计关于循环频率的一致收敛速度．对于乘性和加性噪声中的谐波信号，建立了一、二、三阶循环矩样本估计的统计性质．在此基础上，分别提出了基于不同阶循环矩的谐波分最个数和频率的估计方法，并得到了估计的强相容性质和强收敛速度，最后给出了模拟实验结果．     

乘性和加性噪声中谐波恢复和循环统计量方法

本文从循环平衡的观点出发来研究乘性和加性噪声的谐波恢复问题。首先，在一定条件下建立了一般复过程的有限长付里叶变换的大样本性质。然后，得到了任意阶循环矩的样本估计关于循环频率的一致收敛速度。对于乘性和加性噪声中的谐波信号，建立了一、二、三阶循环矩样本估计的统计性质。在此基础上，分别提出了基于不同阶循环矩的谐波分量个数和频率的估计方法，并得到了估计的强相容性质和强收敛速度，最后给出了模拟实验结果。     

一种基于循环小波累积量的谐波恢复方法

循环统计量是乘性和加性噪声中谐波恢复问题的主要分析工具之一。本文在其基础上提出了一种新的理论与方法——基于循环小波累积量的谐波恢复方法。首先,提出了循环小波累积量的定义。然后,建立了基于一阶、二阶、三阶循环小波累积量的谐波分量的频率和相位的估计方法。在此基础上,采用了一种可调参数的小波,通过调节其参数来改善传统方法中频率分辨率低的缺陷。最后给出了模拟实验结果。     

基于遗传算法的二维谐波频率估计

针对高斯有色噪声背景下的二维谐波频率估计问题,本文利用二维四阶累积量对高斯噪声不敏感,却包含有二维谐波的频率与幅度信息,将该问题转化为一个多元函数的极值问题,然后提出了基于遗传算法的二维谐波信号参数估计算法.该算法可以直接估计出谐波的频率与振幅,并且不需要考虑频率的配对问题,使得估计过程得到了简化.仿真实验证明了算法的有效性.     

基于遗传算法的复杂背景噪声中二维谐波的二次耦合分析

本文利用二维循环统计量方法对乘性噪声之间相关,乘性噪声和加性噪声之间也相关这种复杂噪声背景中二维谐波的二次非线性耦合问题做了分析。利用当且仅当二维谐波中存在二次非线性耦合谐波时,所定义的二维三阶时间平均矩谱仅在参与二次耦合谐波频率处取得极值的性质,提出了采用遗传算法来分析二维谐波的：二次非线性耦合问题的算法。仿真实验证明了算法的有效性。     

非高斯有色噪声背景下二维谐波频率估计的累积量投影方法

针对非高斯有色噪声中的二维谐波频率估计问题,该文提出了复数线性非高斯过程的二维累积量投影定理。应用该定理并巧妙地构造观测信号的高阶累积量求得非高斯噪声的自相关,并通过求解一个广义特征值对噪声空间进行预白化,然后结合高分辨率的子空间方法二维MUSIC估计得到二维谐波参量。该文方法解决了非高斯有色噪声中的二维谐波频率估计问题,特别地当非高斯噪声为对称分布和谐波信号中存在二次相位耦合时该文方法同样有效。仿真实验验证了该文结论。     

四元数在多个频率对共用同一个频率下的二维谐波恢复

针对二维谐波频率估计中的分维配对问题,本文首先对一般二维谐波信号模型进行变换,构造了符合四元数结构的新的信号模型.接着讨论了Hamilton四元数、三维超复数在二维谐波频率估计中的可能性.同时利用Hua的思想,根据上述模型利用特殊的四阶累积量切片并构造增广矩阵分析了有多个频率对共享同一个频率时的二维谐波频率估计问题.     

四元数和超复数在二维二次非线性相位耦合分析中的应用

针对二维二次非线性相位耦合分析中的分维配对问题,本文首先对一般二维谐波信号模型进行变换,构造了符合四元数结构的新的信号模型.接着讨论了Hamilton四元数、三维超复数及"新四元数"在估计二维谐波频率中的可能性.最后根据上述模型利用特殊的三阶累积量切片分析了加性高斯有色噪声中二维二次非线性相位耦合及联合Hamilton四元数和超复数在二维二次非线性相位耦合中的应用前景.此方法避免了在复数模型的二维二次非线性相位耦合分析中构造复杂的增广矩阵,并从根本上解决了通过分维求取频率之后,频率配对中所有可能产生的错误频率对,以及有可能产生的两维频率估计精度的不平衡性.仿真实验验证了本文的理论.     

乘性噪声背景下基于三阶循环矩的二维近场源定位方法

 本文提出一种基于三阶循环矩的近场源二维参数估计方法.该方法以均匀线阵为接收传感器阵列,通过构造三个三阶循环矩矩阵估计出近场源的方位角和距离参数,利用循环统计量去除加性噪声,通过预校准法消除乘性噪声,适用于乘性噪声或乘性噪声和加性噪声共存背景下的二维近场源定位.仿真实验验证了该方法的有效性.     

乘性和加性噪声相关背景下的二维谐波频率估计

本文利用二维循环统计量方法对乘性噪声之间相关、乘性噪声和加性噪声之间也相关这种复杂噪声背景下的谐波恢复问题进行了研究.首先,提出了二维噪声互可混的概念,用它来体现多个二维噪声之间的关系;然后,在乘性噪声为非零均值时,定义了二维循环均值来估计信号频率.在乘性噪声和加性噪声为零均值时,定义特殊的二维六阶时间平均多矩谱切片来估计信号频率.仿真实验证明了算法的有效性.     

乘性和加性噪声中二维谐波频率估计

噪声中的谐波恢复问题是信号处理领域的一个典型问题,在众多领域中有着广泛的应用。本文主要研究零均值乘性和加性噪声并存下的二维谐波信号频率估计问题,提出了一种基于数据矩阵的奇异值分解和子空间的旋转不变性的零均值乘性和加性噪声中的谐波频率的估计方法。乘性噪声为零均值情形下传统的估计方法往往难以直接应用或估计失效。本文利用谐波模型信号特征,通过对观测信号进行平方运算构造了一个数据矩阵。通过对数据矩阵的特征值进行理论分析,结合子空间旋转不变性,得到了零均值乘性和加性噪声中的谐波频率和数据矩阵之间的一种内在关系。这个性质可以用于零均值乘性和加性噪声并存下的二维谐波信号频率估计,并且所得的二维频率能自动配对。仿真实验验证了本文所提算法的有效性。      

Efficient mixed-spectrum estimation with applications to targetfeature extraction

We present a decoupled parameter estimation (DPE) algorithm for estimating sinusoidal parameters from both 1-D and 2-D data sequences corrupted by autoregressive (AR) noise. In the first step of the DPE algorithm, we use a relaxation (RELAX) algorithm that requires simple fast Fourier transforms (FFTs) to obtain the estimates of the sinusoidal parameters. We describe how the RELAX algorithm may be used to extract radar target features from both 1-D and 2-D data sequences. In the second step of the DPE algorithm, a linear least-squares approach is used to estimate the AR noise parameters. The DPE algorithm is both conceptually and computationally simple. The algorithm not only provides excellent estimation performance under the model assumptions, in which case the estimates obtained with the DPE algorithm are asymptotically statistically efficient, but is also robust to mismodeling errors     

Estimation of dynamically evolving ellipsoids with applications to medical imaging

The estimation of dynamically evolving ellipsoids from noisy lower-dimensional projections is examined. In particular, this work describes a model-based approach using geometric reconstruction and recursive estimation techniques to obtain a dynamic estimate of left-ventricular ejection fraction from a gated set of planar myocardial perfusion images. The proposed approach differs from current ejection fraction estimation techniques both in the imaging modality used and in the subsequent processing which yields a dynamic ejection fraction estimate. For this work, the left ventricle is modeled as a dynamically evolving three-dimensional (3-D) ellipsoid. The left-ventricular outline observed in the myocardial perfusion images is then modeled as a dynamic, two-dimensional (2-D) ellipsoid, obtained as the projection of the former 3-D ellipsoid. This data is processed in two ways: first, as a 3-D dynamic ellipsoid reconstruction problem; second, each view is considered as a 2-D dynamic ellipse estimation problem and then the 3-D ejection fraction is obtained by combining the effective 2-D ejection fractions of each view. The approximating ellipsoids are reconstructed using a Rauch-Tung-Striebel smoothing filter, which produces an ejection fraction estimate that is more robust to noise since it is based on the entire data set; in contrast, traditional ejection fraction estimates are based only on true frames of data. Further, numerical studies of the sensitivity of this approach to unknown dynamics and projection geometry are presented, providing a rational basis for specifying system parameters. This investigation includes estimation of ejection fraction from both simulated and real data.     

一种新的双基地MIMO雷达快速多目标定位算法

针对双基地MIMO雷达目标定位问题,该文提出一种基于三阶张量分解的快速多目标定位算法。该算法首先将匹配滤波输出转化为三阶张量,并对其进行降维预处理,然后利用交替最小二乘(ALS)算法估计收发阵列流型矩阵和多普勒矩阵,最后通过谱估计算法恢复目标收发角和多普勒频率。同时利用线性搜索加快ALS算法的收敛速度。与现有算法相比,该算法避免了2维谱峰搜索和协方差矩阵估计,得到的目标三参数自动配对,不仅提高了估计性能,而且有效降低了运算量和存储量。仿真结果证明了所提算法的有效性和优越性。     

Two-dimensional Fourier series-based model for nonminimum-phaselinear shift-invariant systems and texture image classification

In this paper, Chi's (1997, 1999) real one-dimensional (1-D) parametric nonminimum-phase Fourier series-based model (FSBM) is extended to two-dimensional (2-D) FSBM for a 2-D nonminimum-phase linear shift-invariant system by using finite 2-D Fourier series approximations to its amplitude response and phase response, respectively. The proposed 2-D FSBM is guaranteed stable, and its complex cepstrum can be obtained from its amplitude and phase parameters through a closed-form formula without involving complicated 2-D phase unwrapping and polynomial rooting. A consistent estimator is proposed for the amplitude estimation of the 2-D FSBM using a 2-D half plane causal minimum-phase linear prediction error filter (modeled by a 2-D minimum-phase FSBM), and then, two consistent estimators are proposed for the phase estimation of the 2-D FSBM using the Chien et al. (1997) 2-D phase equalizer (modeled by a 2-D all-pass FSBM). The estimated 2-D FSBM can be applied to modeling of 2-D non-Gaussian random signals and 2-D signal classification using complex cepstra. Some simulation results are presented to support the efficacy of the three proposed estimators. Furthermore, classification of texture images (2-D non-Gaussian signals) using the estimated FSBM, second-, and higher order statistics is presented together with some experimental results. Finally, we draw some conclusions     

AR modelling of skewed signals using third-order cumulants

Algorithms for selecting the order and estimating the parameters of an AR process, which is driven by noise having an underlying non-Gaussian distribution, from the observed noisy time series are presented. The order selection algorithm makes use of the growing memory covariance predictive least-squares (GMCPLS) criterion together with diagonal slices of the third-order cumulant plane. A triangular region of the third-order cumulant plane is used to estimate the model parameters. Extensive simulation results are presented and based on these trends, one of which has been verified using real data obtained from a rotating machine, recommendations are made on the efficacy of methods for AR order selection and parameter estimation problems     

Estimation of depth fields suitable for video compression based on3-D structure and motion of objects

Intensity prediction along motion trajectories removes temporal redundancy considerably in video compression algorithms. In three-dimensional (3-D) object-based video coding, both 3-D motion and depth values are required for temporal prediction. The required 3-D motion parameters for each object are found by the correspondence-based E-matrix method. The estimation of the correspondences-two-dimensional (2-D) motion field-between the frames and segmentation of the scene into objects are achieved simultaneously by minimizing a Gibbs energy. The depth field is estimated by jointly minimizing a defined distortion and bit-rate criterion using the 3-D motion parameters. The resulting depth field is efficient in the rate-distortion sense. Bit-rate values corresponding to the lossless encoding of the resultant depth fields are obtained using predictive coding; prediction errors are encoded by a Lempel-Ziv algorithm. The results are satisfactory for real-life video scenes.