Algorithm for Optimal Estimation of Appearance Times of Pulsed Signals in Discrete Time

Using the methods of optimal nonlinear Markov filtering, we obtain an algorithm for optimal mean-square estimation of appearance times of random pulsed variations in signal parameters against the background of white Gaussian noise in discrete time. Linear difference equations are used to describe signals, noise, and the observed processes. Equations of the algorithm permitting real-time calculations of the a posteriori variances and optimal estimations of pulse-appearance times are obtained in the approximation of Gaussian conditional probability densities. We present simulation results for algorithm operation in the particular problem of estimating the appearance times of two pulsed signals having the known shapes and observed against noise background.     

室内两步法监督式学习双耳声源距离估计

提出一种室内环境下两步法监督式学习双耳声源距离估计算法,该算法通过预先估计声源方位角信息以克服声源方位角的变化对声源距离估计性能的不利影响.该算法第1步利用深度神经网络模型估计声源的方位角,并将不同方位角的双耳信号分类;第2步中对每个方位角的双耳信号采用独立的深度神经网络模型进行声源距离估计,其中距离特征选用双耳信号的一些双耳特征和统计特性。在仿真和实际环境下,本文提出的两步法声源距离估计算法的距离估计准确率比现有算法提高了3%~5%左右,并且在各种不匹配环境下的距离估计准确率比现有算法高出5%~10%左右。实验结果表明利用声源方位角信息可以有效提高双耳声源距离估计算法的性能。      

A blind algorithm for reverberation-time estimation using subband decomposition of speech signals

An algorithm for blind estimation of reverberation time (RT) in speech signals is proposed. Analysis is restricted to the free-decaying regions of the signal, where the reverberation effect dominates, yielding a more accurate RT estimate at a reduced computational cost. A spectral decomposition is performed on the reverberant signal and partial RT estimates are determined in all signal subbands, providing more data to the statistical-analysis stage of the algorithm, which yields the final RT estimate. Algorithm performance is assessed using two distinct speech databases, achieving 91% and 97% correlation with the RTs measured by a standard nonblind method, indicating that the proposed method blindly estimates the RT in a reliable and consistent manner.     

Numerical evaluation of linearized image reconstruction based on finite element method for biomedical photoacoustic imaging

An image reconstruction algorithm for biomedical photoacoustic imaging is discussed. The algorithm solves the inverse problem of the photoacoustic phenomenon in biological media and images the distribution of large optical absorption coefficients, which can indicate diseased tissues such as cancers with angiogenesis and the tissues labeled by exogenous photon absorbers. The linearized forward problem, which relates the absorption coefficients to the detected photoacoustic signals, is formulated by using photon diffusion and photoacoustic wave equations. Both partial differential equations are solved by a finite element method. The inverse problem is solved by truncated singular value decomposition, which reduces the effects of the measurement noise and the errors between forward modeling and actual measurement systems. The spatial resolution and the robustness to various factors affecting the image reconstruction are evaluated by numerical experiments with 2D geometry.     

Using short curved vertical arrays in ocean acoustic tomography

We consider the possibility of reconstructing the ocean mode structure based on measurements with short (not covering the entire ocean waveguide) arrays curved in an unknown way by ocean currents, which corresponds to the conditions of a real experiment. We have developed an algorithm for estimating the arrival times of various mode signals by solving a system of linear equations. The mode reconstruction accuracy as a function of the array length and profile curvature is investigated. The cases of using both the ocean noise field and deterministic signals as a sound source are considered. Comparison with the commonly used mode filtering method is made.     

Classical problems of nonlinear acoustics and wave theory

Focusing of a vibration field in finite sized elastic systems using time reversal of signals from a point’s wideband source is theoretically analyzed. It is shown that the result of space and time focusing for a classical reversal algorithm in limited systems with small losses depends of the positional relationship of the source and the signal receiver. A focusing algorithm eliminating this dependence and increasing the efficiency of the focusing of the vibration field is proposed. Theoretical estimates are confirmed with the results of numerical experiments with the models of elastic bodies.     

An algorithm for the superresolution of the sources of narrow-band signals on the basis of a solution of a system of observation equations

An algorithm for the superresolution of the sources of narrow-band signals on the basis of the solution of a system of observation equations is proposed. In accordance with this algorithm, the angular coordinates of sources are the roots of a single equation. To reliably estimate the coordinates, the number of time samples of observed signals must exceed the number of sources by at least one. In the case of a linear equidistant antenna array, a stable estimate of the angular coordinates requires that the number of time samples exceed the half-number of sources by at least one. A partial solution that provides minimization of the variance of the estimate errors is selected from the general solution. When the number of time samples that are used to estimate angular coordinates increases, the mathematical expectations of their errors tend to zero and the variances are larger than the minimally possible ones (determined from the Rao-Kramer inequality) by a factor of 1–1.2.     

Segmentation of the period of the fundamental tone of a voice source

The extrema of the logarithmic derivative of the mean energy of a voice signal in the frequency range of 1000–3000 Hz are used to determine the instants of opening and closure of the glottis. The inaccuracy of analysis is estimated with the Arctic CMU database, which contains synchronous recordings of speech signals and electro-glottograms. The estimates of the instants of opening and closure of the glottis, found by the developed algorithm, are compared with the instants of the maximum and minimum of the derivative from electro-glottogram signals, which are taken as the “true” instants. The mean square deviation of the glottal opening instant from the extrema of the derivative from the electro-glottogram signals for different speakers is in the range of 1.03–1.64 ms. The error rate of a false estimate of the glottal opening instant is from 0.01 to 0.14%, and the error rate of omission is from 0.42 to 2.38%. An error-detection algorithm is developed. The mean square deviation with an relative—to the period of the fundamental tone—error in detecting the glottal opening instant is in the range of 13–18% for the most probable error from 0 to +5%.     

Projecting low and extensive dimensional chaos from spatio-temporal dynamics

We review the spatio-temporal dynamical features of the Ananthakrishna model for the Portevin-Le Chatelier effect, a kind of plastic instability observed under constant strain rate deformation conditions. We then establish a qualitative correspondence between the spatio-temporal structures that evolve continuously in the instability domain and the nature of the irregularity of the scalar stress signal. Rest of the study is on quantifying the dynamical information contained in the stress signals about the spatio-temporal dynamics of the model. We show that at low applied strain rates, there is a one-to-one correspondence with the randomly nucleated isolated bursts of mobile dislocation density and the stress drops. We then show that the model equations are spatio-temporally chaotic by demonstrating the number of positive Lyapunov exponents and Lyapunov dimension scale with the system size at low and high strain rates. Using a modified algorithm for calculating correlation dimension density, we show that the stress-strain signals at low applied strain rates corresponding to spatially uncorrelated dislocation bands exhibit features of low dimensional chaos. This is made quantitative by demonstrating that the model equations can be approximately reduced to space independent model equations for the average dislocation densities, which is known to be low-dimensionally chaotic. However, the scaling regime for the correlation dimension shrinks with increasing applied strain rate due to increasing propensity for propagation of the dislocation bands. The stress signals in the partially propagating to fully propagating bands turn to have features of extensive chaos.     

结合盲源分离的非直单线阵多目标左右舷分辨

针对单线阵左右舷模糊问题,提出了结合盲源分离的非直单线阵多目标左右舷分辨算法。该算法首先通过离散傅里叶变换将阵列接收信号离散化为若干个窄带频谱分量,之后对每个频点的窄带数据讲行盲源分离,得到每个频点上各个来波信号的导向向量;然后通过常规波束形成对各个导向向量进行方位谱估计,并根据左右舷抑制比进行单目标左右舷分辨,确定各个频点上的来波方向;最后对所有频点上的来波方向进行聚类,得到各个真实目标的方位,从而实现多目标左右舷分辨。仿真实验中,相比常规波束形成方法(CBF)和最小方差无畸变响应算法(MVDR),该算法更准确地估计出了目标数目,且保持了较快的计算速度;海试数据处理中,该算法排除了目标镜像的干扰,准确估计出了船只目标的轨迹。仿真及海试数据处理均表明,该算法可以分辨真实目标与目标镜像,具有比CBF和MVDR算法更好的左右舷分辨能力。      

Gradient method for blind chaotic signal separation based on proliferation exponent

A new method to perform blind separation of chaotic signals is articulated in this paper, which takes advantage of the underlying features in the phase space for identifying various chaotic sources. Without incorporating any prior information about the source equations, the proposed algorithm can not only separate the mixed signals in just a few iterations, but also outperforms the fast independent component analysis(FastICA) method when noise contamination is considerable.     

快速收敛最小方差无畸变响应算法研究及应用

常规最小方差无畸变响应(MVDR)自适应波束形成是一种高分辨窄带波束形成器,它是利用实际声场的窄带互谱密度矩阵(CSDM)估计出自适应波束形成权向量。在实际应用中,MVDR算法需要较长的观测时间估计协方差矩阵,不利于对高速运动目标进行定位;对于宽带目标信号,MVDR算法需要对每一个CSDM进行求逆运算,计算量较大;在相干源条件下,目标信号之间会发生"对消"现象,MVDR算法性能急剧恶化。本文提出了基于子带子阵处理的快速收敛MVDR自适应波束形成方法。首先将全频带划分成一组子带,将接收线阵划分成一组子阵,然后对每一子带计算降维的驾驶协方差矩阵(STCM),从而得到快速收敛MVDR自适应波束形成的权值和空间谱估计结果。同时采用双向空间平滑方法对相干源进行MVDR空间谱估计。仿真和海试数据处理结果表明该算法在保证高分辨力的同时,具有瞬时收敛的性能,双向空间平滑技术具有良好的解相干性能。      

Sequential reconstruction of driving-forces from nonlinear nonstationary dynamics

This paper describes a functional analysis-based method for the estimation of driving-forces from nonlinear dynamic systems. The driving-forces account for the perturbation inputs induced by the external environment or the secular variations in the internal variables of the system. The proposed algorithm is applicable to the problems for which there is too little or no prior knowledge to build a rigorous mathematical model of the unknown dynamics. We derive the estimator conditioned on the differentiability of the unknown system’s mapping, and smoothness of the driving-force. The proposed algorithm is an adaptive sequential realization of the blind prediction error method, where the basic idea is to predict the observables, and retrieve the driving-force from the prediction error. Our realization of this idea is embodied by predicting the observables one-step into the future using a bank of echo state networks (ESN) in an online fashion, and then extracting the raw estimates from the prediction error and smoothing these estimates in two adaptive filtering stages. The adaptive nature of the algorithm enables to retrieve both slowly and rapidly varying driving-forces accurately, which are illustrated by simulations. Logistic and Moran-Ricker maps are studied in controlled experiments, exemplifying chaotic state and stochastic measurement models. The algorithm is also applied to the estimation of a driving-force from another nonlinear dynamic system that is stochastic in both state and measurement equations. The results are judged by the posterior Cramer-Rao lower bounds. The method is finally put into test on a real-world application; extracting sun’s magnetic flux from the sunspot time series.     

Dynamical mean field theory with the density matrix renormalization group

A new numerical method for the solution of the dynamical mean field theory's self-consistent equations is introduced. The method uses the density matrix renormalization group technique to solve the associated impurity problem. The new algorithm makes no a priori approximations and is only limited by the number of sites that can be considered. We obtain accurate estimates of the critical values of the metal-insulator transitions and provide evidence of substructure in the Hubbard bands of the correlated metal. With this algorithm, more complex models having a larger number of degrees of freedom can be considered and finite-size effects can be minimized.     

基于匹配追踪的拉曼光谱信号重构算法

拉曼光谱技术是一种高灵敏度、无损伤、振动分子光谱技术,在医药、生物、分析化学等诸多领域有着重要的作用。然而,由于拉曼散射强度低,实际测得的拉曼信号容易被噪声所污染。特别是在较短的曝光时间,收集到的拉曼光谱的信噪比很低。因此,提出了一种基于匹配追踪算法的信号重构方法,用于提取低信噪比的拉曼信号。该方法首先通过阈值循环迭代的方法在平均谱上找出特征峰的位置、估计峰的区间。根据峰的位置区间等信息,用高斯密度函数生成字典。在噪声谱上,根据特征峰位置和区间,将其区分为有信号区间和无信号区间,在有信号区间上利用匹配追踪算法重构被噪声所掩盖的拉曼信号。该算法不仅能够很好的逼近掩盖在噪声中的拉曼信号,且在重构信号的过程中也会对基线进行扣除,无须作基线校正处理。在仿真和实验中对该算法与常规算法进行了比较,结果证明,该算法在低信噪比条件下能够较好的恢复拉曼信号。该算法不同于传统光谱去噪算法,能同时对拉曼光谱进行了基线扣除以及噪声的处理,且能取得较为理想的结果,不需要使用不同的算法对基线和噪声分别处理。其次,在算法上我们创造性地将匹配追踪算法用于拉曼光谱信号的稀疏逼近求解。     

Optimal estimation of pulse signals with random amplitudes and times of occurrence

We have obtained an algorithm for optimal evaluation of pulse signals of a given shape with random amplitudes and times of occurrence observed against a background of Gaussian white noise. Equations for real-time estimates that are optimal in the rms sense and the a posteriori variances of signal amplitudes and times of occurrence are found. Computer simulation results illustrating the operation of synthesized algorithms are given.N. I. Lobachevskii State University, Nizhny Novgorod. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 38, No. 12, pp. 1257–1266, December, 1995.     

Research and application of fast-convergent minimum variance distortionless response algorithm

The conventional MVDR adaptive beamformer is a high-resolution narrowband beamformer which estimates the optimal beamforming weights using narrowband CSDM of real acoustic field.In practical applications,MVDR algorithm needs long observation time to estimate the covariance matrix.This inherent property makes it difficult to localize fast-moving targets.For wideband signals,MVDR algorithm needs inverting every CSDM which increases the computational demands.For correlated sources,the performance of MVDR will degrade dramatically because the signals will cancel each other.A fast-convergent MVDR algorithm based on subband subarray processing is proposed.The full frequency band is divided into sets of subbands and the line array is divided into sets of subarrays.For every subband the STCM of reduced dimensions is calculated.Then adaptive beamforming weight of fast-convergent MVDR algorithm and spatial spectrum estimation are obtained.At the same time,spatial spectrum estimation can be made for correlated sources using the two-sided spatial smoothing method. Results of simulation and trial data show that the proposed method has high-resolution and near-instantaneous convergence property,two-sided spatial smoothing has satisfactory validity of decorrelation.     

A novel algorithm for the reduction of undersampling artefacts in magnetic resonance images

An innovative algorithm is presented which is effective in reducing the truncation artefacts occurring in magnetic resonance images due to missing k-space samples. The algorithm works first by filling the incomplete matrix of coefficients with zeroes and then adjusting, by an iterative process, the missing coefficients by performing a reduction of the undersampling artefacts. Then, this set of coefficients is used as a basis for a superresolution algorithm that estimates the missing coefficients by modeling the data as a linear combination of increasing and decreasing exponential functions using Prony's method. In fact, the Prony's method consists of the interpolation of a given data set with a sum of exponential functions: the MRI signals can be well represented as a sum of exponential functions and the missing data can be extrapolated by this representation. The algorithm has been proven to perform better than either a simple algorithm, which detects and then reduces the undersampling artefacts, or an algorithm that models the measured data with approximation functions. The presented algorithm is quite simple and is applicable both to missing rows (phase-frequency acquisitions) and to radial-missing angle (acquisition from projections) undersampling. Experimental results are reported; comparisons, made between the results obtained using the presented algorithm and the alternative methods described above, clearly demonstrate the superiority of the algorithm.     

A simulation algorithm for ultrasound liver backscattered signals

In this study, we present a simulation algorithm for the backscattered ultrasound signal from liver tissue. The algorithm simulates backscattered signals from normal liver and three different liver abnormalities. The performance of the algorithm has been tested by statistically comparing the simulated signals with corresponding signals obtained from a previous in vivo study. To verify that the simulated signals can be classified correctly we have applied a classification technique based on an artificial neural network. The acoustic features extracted from the spectrum over a 2.5 MHz bandwidth are the attenuation coefficient and the change of speed of sound with frequency (dispersion). Our results show that the algorithm performs satisfactorily. Further testing of the algorithm is conducted by the use of a data acquisition and analysis system designed by the authors, where several simulated signals are stored in memory chips and classified according to their abnormalities.