Fractal modeling techniques for spatial data

The paper presents convolutional linear data models for the processing of one-dimensional (1D) and two-dimensional (2D) spatial data. The models assume that the measured data is the superposition of a stochastic innovation process and a deterministic system function. The innovation process is described by a fractal scaling noise, which has a power spectral density proportional to some power (-β) of the frequency. The system function is assumed to be symmetric and is constructed using autoregressive (AR) filtering procedures. Iterative deconvolution procedures are developed to recover the fractal innovation from the data. For computational convenience, these procedures assume a spectrally white (β=0) innovation, but modify the data prior to inversion by prewhitening the a priori assumed fractal innovation. The filter coefficients recovered by inverting the modified data are then applied to the original data to recover the fractal innovation. The ability of the deconvolution procedures to recover the fractal innovation is demonstrated using 1D and 2D synthetic data sets. As a practical example, the 2D deconvolution technique is applied to an aeromagnetic map from northeastern Ontario, Canada, and is shown to be effective in enhancing magnetic field anomalies     

Estimating the entropy of a signal with applications

We present a new estimator of the entropy of continuous signals. We model the unknown probability density of data in the form of an AR spectrum density and use regularized long-AR models to identify the AR parameters. We then derive both an analytical expression and a practical procedure for estimating the entropy from sample data. We indicate how to incorporate recursive and adaptive features in the procedure. We evaluate and compare the new estimator with other estimators based on histograms, kernel density models, and order statistics. Finally, we give several examples of applications. An adaptive version of our entropy estimator is applied to detection of law changes, blind deconvolution, and source separation     

The Marple algorithm for the autoregressive spectral estimates of the SMMW fourier transform spectroscopy data

The Marple algorthm for the autoregressive spectral estimates has been applied to the SMMW Fourier transform spectrum analysis. The experimental results have shown that this method yields AR spectra with three times higher resolution than the FFT method does. The improvements obtained from the Marple algorithm over the maximum entropy algorithm include higher resolution, less bias in the spectral peak frequency estimation and absence of observed spectral line splitting. The effects of the structure of the spectral lines and the noise on the resolution are discussed.     

基于TWSTFT进行钟差预报方法分析

用多项式拟合、频谱分析、改进的AR模型3种方法对由TWSTFT（卫星双向时间频率传递）得出的钟差时间序列进行了拟合和预报分析。为了抵制钟差时间序列中异常值的影响,引入了“抗差等价权”。利用TWSTFT得到的一天的钟差,按不同采样率、不同时间跨度进行计算分析,结果表明：抗差估计的预报精度明显高于最小二乘估计;平滑值的预报精度高于采样值;由于钟差时闻序列中有明显的周期变化,多项式进行钟差预报的精度不可靠;用谱分析进行钟差预报的精度不高,但可以发现钟差时间序列中的主要周期变化;改进的AR模型预报精度最高,预报RMS在1ns左右。     

Multichannel seismic deconvolution

Deals with Bayesian estimation of 2D stratified structures from echosounding signals. This problem is of interest in seismic exploration, but also for nondestructive testing or medical imaging. The proposed approach consists of a multichannel Bayesian deconvolution method of the 2D reflectivity based upon a theoretically sound prior stochastic model. The Markov-Bernoulli random field representation introduced by Idier et al. (1993) is used to model the geometric properties of the reflectivity, and emphasis is placed on representation of the amplitudes and on deconvolution algorithms. It is shown that the algorithmic structure and computational complexity of the proposed multichannel methods are similar to those of single-channel B-G deconvolution procedures, but that explicit modeling of the stratified structure results in significantly better performances. Simulation results and examples of real-data processing illustrate the performances and the practicality of the multichannel approach     

Maximum entropy spectral analysis and ARMA processes (Corresp.)

The maximum entropy spectral analysis for discrete-time stationary processes was first proposed by J. P. Burg. He showed that if a finite number of covariance lag values of a stationary process are known, then an autoregressive (AR) process with the given autocorrelation values best fits the given constraints in the sense of maximizing thc differential entropy rate of the model. A more general type of prior knowledge of the process is considered, and it is shown that the maximum entropy method, subject to our constraints, is equivalent to fitting a mixed autoregressive moving average (ARMA) model.     

Mapping of sp2/sp3 in DLC thin film by signal processed ESI series energy-loss image

A set of signal processing methods comprising fast Fourier transform interpolation, maximum entropy deconvolution and wavelet transformation has been successfully integrated to improve the equality of the extracted C K-edge spectra from electron spectroscopic imaging (ESI) series. Fast Fourier transform interpolation is used to improve the dispersion arising from discrete sampling of ESI series in the energy space. The maximum entropy method is used to dispel the convolution effect resulting from that ESI series acquired with a finite energy window. Wavelet transformation is applied to de-noise the extracted ESI spectrum. The post-processed ESI spectrum has quality as good as that of a probe-acquired spectrum and makes semi-quantitative analysis of the two-dimensional sp2/sp3 ratio map in diamond-like carbon thin film possible. In general, this method is applicable for reconstructing good quality core-loss electron energy-loss spectra from a nanometre-sized area, so that it may be possible to quantitatively analyse two-dimensional information about electronic structure in materials with near nanometre resolution.     

Adaptive blind deconvolution of linear channels using Renyi's entropy with Parzen window estimation

Blind deconvolution of linear channels is a fundamental signal processing problem that has immediate extensions to multiple-channel applications. In this paper, we investigate the suitability of a class of Parzen-window-based entropy estimates, namely Renyi's entropy, as a criterion for blind deconvolution of linear channels. Comparisons between maximum and minimum entropy approaches, as well as the effect of entropy order, equalizer length, sample size, and measurement noise on performance, will be investigated through Monte Carlo simulations. The results indicate that this nonparametric entropy estimation approach outperforms the standard Bell-Sejnowski and normalized kurtosis algorithms in blind deconvolution. In addition, the solutions using Shannon's entropy were not optimal either for super- or sub-Gaussian source densities.     

一种新的最大熵谱近似估计方法

本文提出了最大熵谱估计的一种新方法，由其所获得的自回归系数的估值，使反映前、后向预测误差的能量以及前、后向预测误差与信号之间交关系的一个综合目标函数极小化。仿真结果表明，该法不仅具有良好的估计质量和较小的谱峰位移，而且消除了谱线分裂现象。     

Adaptive AR modeling of nonstationary time series by means ofKalman filtering

An adaptive on-line procedure is presented for autoregressive (AR) modeling of nonstationary multivariate time series by means of Kalman filtering. The parameters of the estimated time-varying model can be used to calculate instantaneous measures of linear dependence. The usefulness of the procedures in the analysis of physiological signals is discussed in two examples: first, in the analysis of respiratory movement, heart rate fluctuation, and blood pressure, and second, in the analysis of multichannel electroencephalogram (EEG) signals. It was shown for the first time that in intact animals the transition from a normoxic to a hypoxic state requires tremendous short-term readjustment of the autonomic cardiac-respiratory control. An application with experimental EEG data supported observations that the development of coherences among cell assemblies of the brain is a basic element of associative learning or conditioning     

On the Information Time Scale of Geophysical Records in Maximum Entropy Spectral Analysis

The length of maximum entropy spectral analysis (MESA) filter M must be such that it contains all, and only, the physical information. A new original, conceptually simple criterion is suggested for estimating M on the basis of intrinsic memory time of the signal that is obtained from the autocovariances ?t by means of the following quantity: begin{equation*}frac{Sigma_t |phi_t|}{phi_0}.end{equation*} This approach appears particularly suitable when it is applied to geophysical data set.     

Multidimensional multichannel FIR deconvolution using Gr?bner bases.

We present a new method for general multidimensional multichannel deconvolution with finite impulse response (FIR) convolution and deconvolution filters using Gr?bner bases. Previous work formulates the problem of multichannel FIR deconvolution as the construction of a left inverse of the convolution matrix, which is solved by numerical linear algebra. However, this approach requires the prior information of the support of deconvolution filters. Using algebraic geometry and Gr?bner bases, we find necessary and sufficient conditions for the existence of exact deconvolution FIR filters and propose simple algorithms to find these deconvolution filters. The main contribution of our work is to extend the previous Gr?bner basis results on multidimensional multichannel deconvolution for polynomial or causal filters to general FIR filters. The proposed algorithms obtain a set of FIR deconvolution filters with a small number of nonzero coefficients (a desirable feature in the impulsive noise environment) and do not require the prior information of the support. Moreover, we provide a complete characterization of all exact deconvolution FIR filters, from which good FIR deconvolution filters under the additive white noise environment are found. Simulation results show that our approaches achieve good results under different noise settings.     

Multidimensional Multichannel FIR Deconvolution Using GrÖbner Bases

We present a new method for general multidimensional multichannel deconvolution with finite impulse response (FIR) convolution and deconvolution filters using GrÖbner bases. Previous work formulates the problem of multichannel FIR deconvolution as the construction of a left inverse of the convolution matrix, which is solved by numerical linear algebra. However, this approach requires the prior information of the support of deconvolution filters. Using algebraic geometry and GrÖbner bases, we find necessary and sufficient conditions for the existence of exact deconvolution FIR filters and propose simple algorithms to find these deconvolution filters. The main contribution of our work is to extend the previous GrÖbner basis results on multidimensional multichannel deconvolution for polynomial or causal filters to general FIR filters. The proposed algorithms obtain a set of FIR deconvolution filters with a small number of nonzero coefficients (a desirable feature in the impulsive noise environment) and do not require the prior information of the support. Moreover, we provide a complete characterization of all exact deconvolution FIR filters, from which good FIR deconvolution filters under the additive white noise environment are found. Simulation results show that our approaches achieve good results under different noise settings.     

Single-channel blind estimation of arterial input function and tissue impulse response in DCE-MRI

Multipass dynamic MRI and pharmacokinetic modeling are used to estimate perfusion parameters of leaky capillaries. Curve fitting and nonblind deconvolution are the established methods to derive the perfusion estimates from the observed arterial input function (AIF) and tissue tracer concentration function. These nonblind methods are sensitive to errors in the AIF, measured in some nearby artery or estimated by multichannel blind deconvolution. Here, a single-channel blind deconvolution algorithm is presented, which only uses a single tissue tracer concentration function to estimate the corresponding AIF and tissue impulse response function. That way, many errors affecting these functions are reduced. The validity of the algorithm is supported by simulations and tests on real data from mouse. The corresponding nonblind and multichannel methods are also presented.     

Laguerre-model blind system identification: cardiovascular dynamics estimated from multiple peripheral circulatory signals

This paper presents a method for comparing multiple circulatory waveforms measured at different locations to improve cardiovascular parameter estimation from these signals. The method identifies the distinct vascular dynamics that shape each waveform signal, and estimates the common cardiac flow input shared by them. This signal-processing algorithm uses the Laguerre function series expansion for modeling the hemodynamics of each arterial branch, and identifies unknown parameters in these models from peripheral waveforms using multichannel blind system identification. An effective technique for determining the Laguerre base pole is developed, so that the Laguerre expansion captures and quickly converges to the intrinsic arterial dynamics observed in the two circulatory signals. Furthermore, a novel deconvolution method is developed in order to stably invert the identified dynamic models for estimating the cardiac output (CO) waveform from peripheral pressure waveforms. The method is applied to experimental swine data. A mean error of less than 5% with the measured peripheral pressure waveforms has been achieved using the models and excellent agreement between the estimated CO waveforms and the gold standard measurements have been obtained.     

ARMA models, prewhitening, and minimum cross entropy

The problem of spectral estimation on the basis of observations from a finite stretch of a stationary time series is considered, in connection with knowledge of a prior estimate of the spectral density. A reasonable posterior spectral density estimate would be the density that is closest to the prior according to some measure of divergence, while at the same time being compatible with the data. The cross entropy has often been proposed to serve as such a measure of divergence. A correction of the original minimum-cross-entropy spectral analysis (MCESA) method of J.E. Shore (see IEEE Trans. Acoust. Speech Signal Process, vol.29, p.230-7, 1981) to traditional prewhitening techniques and to autoregressive moving average (ARMA) models is pointed out and a fast approximate solution of the minimum cross entropy problem is proposed. The solution is in a standard multiplicative form, that is, the posterior is equal to the prior multiplied by a correction factor     

Chrestenson最大熵谱估计的计算

本文研究p-平稳随机序列在Chrestenson变换意义下的功率谱密度及其最大熵谱估计的计算。得到了功率谱密度函数与熵率的关系式及最大熵谱估计的正规方程。在采样数据个数为p~m的情况下,最大熵谱估计可直接由已知的有限自相关数据表示。这些结果与Fourier意义下的最大熵谱估计有很大的不同。     

Gradient Adaptive Paraunitary Filter Banks for Spatio-Temporal Subspace Analysis and Multichannel Blind Deconvolution

Paraunitary filter banks are important for several signal processing tasks, including coding, multichannel deconvolution and equalization, adaptive beamforming, and subspace processing. In this paper, we consider the task of adapting the impulse response of a multichannel paraunitary filter bank via gradient ascent or descent on a chosen cost function. Our methods are spatio-temporal generalizations of gradient techniques on the Grassmann and Stiefel manifolds, and we prove that they inherently maintain the paraunitariness of the multichannel adaptive system over time. We then discuss the necessary practical approximations, modifications, and simplifications of the methods for solving two relevant signal processing tasks: (i) spatio-temporal subspace analysis and (ii) multichannel blind deconvolution. Simulations indicate that our methods can provide simple, useful solutions to these important problems.     

On the tracking of rapid dynamic changes in seizure EEG

Estimation of autospectra and coherence and phase spectra of the seizure electroencephalograph (EEG), using the fast Fourier transform (FFT) technique, will cause smearing of the rapid dynamic changes which occur during the seizure. This is inherent to FFT spectral estimation, due to the averaging process which is necessary in order to get consistent spectral estimates. A different approach suggested in the present study is to carry out multivariate autoregressive modeling of the multichannel seizure EEG, combined with adaptive segmentation. In order to obtain good estimates in cases of short record length, the vectorial autoregressive (AR) modeling was based on residual energy ratios. The method has been tested on multichannel seizure EEG recordings from rats with focal epilepsy, caused by intracerebral administration of Kainic acid, and in-depth EEG recordings in patients with temporal lobe epilepsy     

基于卡尔曼滤波的同步盲系统辨识与解卷积方法

在盲信道均衡或盲语音去混响应用中,盲多信道系统辨识通常是信号解卷积的前提条件,即盲辨识过程后跟一个解卷积过程。本文提出一种基于卡尔曼滤波的同步盲系统辨识与解卷积方法,其中卡尔曼滤波的状态矢量由多信道系统参数与源信号矢量组成,过程方程和测量方程则建立在单输入-多输出系统(SIMO)的输入输出关系及信道间交叉关联关系(Cross Relation)基础上。此外,盲系统辨识部分与解卷积部分是可以解耦的,生成两个看似独立的卡尔曼滤波问题,并且这两个卡尔曼滤波问题可以实现并行计算。与级联结构相比,这种并行结构更有利于算法优化和实时信号处理。仿真表明,对于无噪声理想信号模型,本算法可以实现完全系统辨识和解卷积(信号误差比可达到100 dB以上),说明理论正确;对于实测的混响语音信号亦可以实现一定的去混响效果。