Fusion of magnetometer and gradiometer sensors of MEG in the presence of multiplicative error

Novel neuroimaging techniques have provided unprecedented information on the structure and function of the living human brain. Multimodal fusion of data from different sensors promises to radically improve this understanding, yet optimal methods have not been developed. Here, we demonstrate a novel method for combining multichannel signals. We show how this method can be used to fuse signals from the magnetometer and gradiometer sensors used in magnetoencephalography (MEG), and through extensive experiments using simulation, head phantom and real MEG data, show that it is both robust and accurate. This new approach works by assuming that the lead fields have multiplicative error. The criterion to estimate the error is given within a spatial filter framework such that the estimated power is minimized in the worst case scenario. The method is compared to, and found better than, existing approaches. The closed-form solution and the conditions under which the multiplicative error can be optimally estimated are provided. This novel approach can also be employed for multimodal fusion of other multichannel signals such as MEG and EEG. Although the multiplicative error is estimated based on beamforming, other methods for source analysis can equally be used after the lead-field modification.     

Nonlinear quantization and the design of coded and uncoded signalconstellations

The author analyzes the effects of nonlinear quantizers, used in T1 carrier systems, on the performance of QAM (quadrature amplitude modulation) and TCM (trellis coded modulation) voiceband data communication modems, and introduces a method to counteract the effects of these nonlinearities. The effect of nonlinear quantizers is modeled as a source of multiplicative noise whose variance is proportional to the amplitude of the quantized signal. The relation between variance of the multiplicative noise, characteristics of the nonlinear quantizer, and impulse response of the pulse shaping filters used in the modems is derived. Effects of multiplicative noise on the performance of QAM and TCM modems are analyzed. A method for the design of QAM and TCM signal constellations is introduced which counteracts the harmful effects of nonlinear quantizers. The new constellations provide 2-3 dB performance improvements in multiplicative noise channels while losing less than 0.5 dB in additive noise channels     

去除乘性噪声的二阶总广义变分模型及算法

针对总变分去噪模型容易导致阶梯效应的缺陷,提 出了一种新的乘性噪声去噪模型。在新模型中,二阶总广义变分(TGV)是正则项,它能自动平 衡一阶和二阶导数项,使得新模型在去除乘性噪声的同时不但能够保 持图像的边缘信息,而且还能去除阶梯效应。为了有效的计算该模型,设计了一个快速迭代算 法。在算法中,首先采用分裂方法和交替方向法将原问题变为两个相关的子问题,然后分别对 子问题利用牛顿法和原始-对偶算法。实验结果表明,与同类模型相比,本文方法无论是在视 觉效果还是定量指标,如峰值信噪比(PSNR)等都有明显地提高。     

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。      

Multiplicative filtering in the fractional Fourier domain

In this article, we investigate the multiplicative filtering in the fractional Fourier transform (FRFT) domain based on the generalized convolution theorem which states that the convolution of two signals in time domain results in simple multiplication of their FRFTs in the FRFT domain. In order to efficiently implement multiplicative filtering, we express the generalized convolution structure by the conventional convolution operation. Utilizing the generalized convolution structure, we convert the multiplicative filtering in the FRFT domain easily to the time domain. Based on the model of multiplicative filtering in the FRFT domain, a practical method is proposed to achieve the multiplicative filtering through convolution in the time domain. This method can be realized by classical Fast Fourier transform (FFT) and has the same capability compared with the method achieved in the FRFT domain. As convolution can be performed by FFT, this method is more useful from practical engineering perspective.     

基于独立分量分析新算法的含噪图像盲分离

由于乘性噪声的存在,严重限制了标准ICA的使用。在分析独立分量分析的基本模型的基础上,讨论了有噪信号的独立分量分析(Noisy ICA)。提出一种新的基于四阶统计量的方法来消除乘性噪声,分离出独立的源信号。通过寻求噪声线性转换的统计结构,依据代价函数最小来获取解混阵B,从而分离出多维观测信号。最后把算法应用于含噪的混合图像,通过仿真显示算法很好的分离了源信号。     

Convolution,correlation, and sampling theorems for the offset linear canonical transform

The offset linear canonical transform (OLCT), which is a time-shifted and frequency-modulated version of the linear canonical transform, has been shown to be a powerful tool for signal processing and optics. However, some basic results for this transform, such as convolution and correlation theorems, remain unknown. In this paper, based on a new convolution operation, we formulate convolution and correlation theorems for the OLCT. Moreover, we use the convolution theorem to investigate the sampling theorem for the band-limited signal in the OLCT domain. The formulas of uniform sampling and low-pass reconstruction related to the OLCT are obtained. We also discuss the design method of the multiplicative filter in the OLCT domain. Based on the model of the multiplicative filter in the OLCT domain, a practical method to achieve multiplicative filtering through convolution in the time domain is proposed.     

A new multiplicative denoising variational model based on mth root transformation

In coherent imaging systems, such as the synthetic aperture radar (SAR), the observed images are contaminated by multiplicative noise. Due to the edge-preserving feature of the total variation (TV), variational models with TV regularization have attracted much interest in removing multiplicative noise. However, the fidelity term of the variational model, based on maximum a posteriori estimation, is not convex, and so, it is usually difficult to find a global solution. Hence, the logarithmic function is used to transform the nonconvex variational model to the convex one. In this paper, instead of using the log, we exploit the m th root function to relax the nonconvexity of the variational model. An algorithm based on the augmented Lagrangian function, which has been applied to solve the log transformed convex variational model, can be applied to solve our proposed model. However, this algorithm requires solving a subproblem, which does not have a closed-form solution, at each iteration. Hence, we propose to adapt the linearized proximal alternating minimization algorithm, which does not require inner iterations for solving the subproblems. In addition, the proposed method is very simple and highly parallelizable; thus, it is efficient to remove multiplicative noise in huge SAR images. The proposed model for multiplicative noise removal shows overall better performance than the convex model based on the log transformation.     

Detection of multiplicative noise in stationary random processesusing second- and higher order statistics

This paper addresses the problem of detecting the presence of colored multiplicative noise, when the information process can be modeled as a parametric ARMA process. For the case of zero-mean multiplicative noise, a cumulant based suboptimal detector is studied. This detector tests the nullity of a specific cumulant slice. A second detector is developed when the multiplicative noise is nonzero mean. This detector consists of filtering the data by an estimated AR filter. Cumulants of the residual data are then shown to be well suited to the detection problem. Theoretical expressions for the asymptotic probability of detection are given. Simulation-derived finite-sample ROC curves are shown for different sets of model parameters     

A nonparametric method for automatic correction of intensitynonuniformity in MRI data

A novel approach to correcting for intensity nonuniformity in magnetic resonance (MR) data is described that achieves high performance without requiring a model of the tissue classes present. The method has the advantage that it can be applied at an early stage in an automated data analysis, before a tissue model is available. Described as nonparametric nonuniform intensity normalization (N3), the method is independent of pulse sequence and insensitive to pathological data that might otherwise violate model assumptions. To eliminate the dependence of the field estimate on anatomy, an iterative approach is employed to estimate both the multiplicative bias field and the distribution of the true tissue intensities. The performance of this method is evaluated using both real and simulated MR data     

Imaging of biomedical data using a multiplicative regularizedcontrast source inversion method

In this paper, the recently developed multiplicative regularized contrast source inversion method is applied to microwave biomedical applications. The inversion method is fully iterative and avoids solving any forward problem in each iterative step. In this way, the inverse scattering problem can efficiently be solved. Moreover, the recently developed multiplicative regularizer allows us to apply the method blindly to experimental data. We demonstrate inversion from experimental data collected by a 2.33-GHz circular microwave scanner using a two-dimensional (2-D) TM polarization measurement setup. Further some results of a feasibility study of the present inversion method to the 2-D TE polarization and the full-vectorial three-dimensional measurement will be presented as well     

基于N分随机乘法模型的多重分形海杂波仿真

2分随机乘法模型的倍乘因子的分布要求是关于1/2对称的,所以基于此模型仿真出海杂波数据的多重分形谱函数形状比较受限制。该文在分析2分随机乘法模型构造过程的基础上,提出N分随机乘法模型,它是2分随机乘法模型的推广,但却突破倍乘因子分布关于1/2对称的限制,更利于仿真具有期望形状的多重分形谱函数的海杂波数据。理论推导和实验结果均表明倍乘因子的分布决定多重分形谱函数的形状。     

Robust Calibration Algorithm for Multiplicative Modeling Errors Against Location Deviations of Auxiliary Sources

It is well known that the azimuth deviations of the auxiliary sources severely degrade the performance of classical subspace-based calibration methods that assume the direction-of-arrivals of calibration sources are perfectly measured. Therefore, aiming at the effects of source location deviations, the estimation variance of the multiplicative modeling errors for the subspace-based calibration method is first derived by applying matrix eigen-perturbation theory and first-order perturbation analysis approach. The theoretical analysis is undertaken under the assumption that the azimuth deviations are small enough for the first-order perturbation analysis to be valid. In addition, to mitigate the effects of the location errors, a structured total least squares optimization model is established using first-order Taylor series expansion method. Then, the corresponding numerical algorithm is presented to provide a robust estimate for multiplicative modeling errors. The exact Cramér–Rao bound expressions for the unknowns are also deduced in the presence of the azimuth deviations. Simulation results confirm the effectiveness of the theoretical analysis and demonstrate the desirable behavior of the robust calibration algorithm in comparison with the subspace-based calibration methods.     

Multiplicative multifractal modelling of long‐range‐dependent network traffic

We present a multiplicative multifractal process to model traffic which exhibits long‐range dependence. Using traffic trace data captured by Bellcore from operations across local and wide area networks, we examine the interarrival time series and the packet length sequences. We also model the frame size sequences of VBR video traffic process. We prove a number of properties of multiplicative multifractal processes that are most relevant to their use as traffic models. In particular, we show these processes to characterize effectively the long‐range dependence properties of the measured processes. Furthermore, we consider a single server queueing system which is loaded, on one hand, by the measured processes, and, on the other hand, by our multifractal processes (the latter forming a MF_e/MF_g/1 queueing system model). In comparing the performance of both systems, we demonstrate our models to effectively track the behaviour exhibited by the system driven by the actual traffic processes. We show the multiplicative multifractal process to be easy to construct. Through parametric dependence on one or two parameters, this model can be calibrated to fit the measured data. We also show that in simulating the packet loss probability, our multifractal traffic model provides a better fit than that obtained by using a fractional Brownian motion model. Copyright © 2001 John Wiley & Sons, Ltd.     

On the Extension of Multidimensional Speckle Noise Model From Single-Look to Multilook SAR Imagery

Speckle noise represents one of the major problems when synthetic aperture radar (SAR) data are considered. Despite the fact that speckle is caused by the scattering process itself, it must be considered as a noise source due to the complexity of the scattering process. The presence of speckle makes data interpretation difficult, but it also affects the quantitative retrieval of physical parameters. In the case of one-dimensional SAR systems, speckle is completely determined by a multiplicative noise component. Nevertheless, for multidimensional SAR systems, speckle results from the combination of multiplicative and additive noise components. This model has been first developed for single-look data. The objective of this paper is to extend the single-look data model to define a multilook multidimensional speckle noise model. The asymptotic analysis of this extension, for a large number of averaged samples, is also considered to assess the model properties. Details and validation of the multilook multidimensional speckle noise model are provided both theoretically and by means of experimental SAR data acquired by the experimental synthetic aperture radar system, operated by the German Aerospace Center     

Segmentation of ultrasound B-mode images with intensity inhomogeneity correction

Displayed ultrasound (US) B-mode images often exhibit tissue intensity inhomogeneities dominated by nonuniform beam attenuation within the body. This is a major problem for intensity-based, automatic segmentation of video-intensity images because conventional threshold-based or intensity-statistic-based approaches do not work well in the presence of such image distortions. Time gain compensation (TGC) is typically used in standard US machines in an attempt to overcome this. However this compensation method is position-dependent which means that different tissues in the same TGC time-range (or corresponding depth range) will be, incorrectly, compensated by the same amount. Compensation should really be tissue-type dependent but automating this step is difficult. The main contribution of this paper is to develop a method for simultaneous estimation of video-intensity inhomogeities and segmentation of US image tissue regions. The method uses a combination of the maximum a posteriori (MAP) and Markov random field (MRF) methods to estimate the US image distortion field assuming it follows a multiplicative model while at the same time labeling image regions based on the corrected intensity statistics. The MAP step is used to estimate the intensity model parameters while the MRF step provides a novel way of incorporating the distributions of image tissue classes as a spatial smoothness constraint. We explain how this multiplicative model can be related to the ultrasonic physics of image formation to justify our approach. Experiments are presented on synthetic images and a gelatin phantom to evaluate quantitatively the accuracy of the method. We also discuss qualitatively the application of the method to clinical breast and cardiac US images. Limitations of the method and potential clinical applications are outlined in the conclusion.     

弱湍流条件下大气光通信的阈值优化方法

大气湍流引起的闪烁效应会严重影响大气光通信系统的性能。自适应判决阈值技术虽然可以有效改善大气光通信系统的误码率（BER）,但是难以进行实时应用。提出了一种根据各种参数统计值,将阈值设置为常量的阈值优化方法。主要考虑乘性高斯噪声并假设闪烁满足对数正态分布,分析了湍流信道中大气光通信系统的最优常量阈值,并将数值分析结果与弱湍流条件下的实验数据进行对比。对比的结果显示,最优常量阈值方法是有效可行的,相对于自适应阈值的性能降低也是可以接受的。分析还显示,在忽略孔径平均效应条件下,最优常量阈值主要取决于对数光强起伏方差和平均接收光功率,而其他参数的影响基本可以忽略。基于分析结果,提出了可以在实际应用中估计最优常量阈值的非线性模型。     

Two-dimensional adaptive block Kalman filtering of SAR imagery

A method for removing speckle from synthetic aperture radar (SAR) imagery by using 2-D adaptive block Kalman filtering is introduced. The image process is represented by an autoregressive model with a nonsymmetric half-plane (NSHP) region of support. New 2-D Kalman filtering equations are derived which taken into account not only the effect of speckles as multiplicative noise but also the effects of the additive receiver thermal noise and the blur. This method assumes local stationarity within a processing window, whereas the image can be assumed to be globally nonstationary. A recursive identification process using the stochastic Newton approach is also proposed which can be used on-line to estimate the filter parameters based upon the information within each new block of the image. Simulation results on several images are provided to indicate the effectiveness of the proposed method when used to remove the effects of speckle noise as well as those of the additive noise     

基于乘同余法产生的伪随机序列的区间预测

乘同余法是利用伸长与折叠操作来产生伪随机序列。在此基础上,提出了预测伪随机序列的区间预测方法,该方法不需要确定具体的预测模型,适应范围广,运算速度快。对几种乘同余法产生的伪随机序列实验结果表明,该方法能有效地预测此类伪随机序列,且在一定的信噪比上,预测性能仍然很好。     

知识与数据联合驱动的风力发电机叶片动态雷达散射截面统计模型

针对风力发电场对雷达等设备影响评估中所需风力发电机动态雷达散射截面(RCS)估计的问题,提出了一种知识与数据联合驱动的风力发电机动态RCS统计模型。首先,利用风力发电机叶片RCS随叶片旋转周期性变化的特点,建立叶片RCS单个单调变化区间内的变化函数。该变化函数由与叶片几何参数相关的峰值RCS、与叶片几何参数无关的调制函数、与材质和形状细节相关的乘性因子组成。其中峰值RCS由理论模型推算得到,针对RCS变化复杂的特点,调制函数和乘性因子利用实测训练数据估计得到。其次,对于待求解型号的风力发电机,根据风力发电机几何参数得到其叶片RCS变化函数,再通过参数估计的方法计算其概率密度函数统计模型。多种不同型号风力发电机实测数据的实验结果,验证了该文给出的风力发电机叶片动态RCS统计模型,与实测数据结果有良好的一致性。