A graph-theoretic approach for studying the convergence of fractalencoding algorithm

We present a graph-theoretic interpretation of convergence of fractal encoding based on partial iterated function system (PIFS). First we have considered a special circumstance, where no spatial contraction has been allowed in the encoding process. The concept leads to the development of a linear time fast decoding algorithm from the compressed image. This concept is extended for the general scheme of fractal compression allowing spatial contraction (on averaging) from larger domains to smaller ranges. A linear time fast decoding algorithm is also proposed in this situation, which produces a decoded image very close to the result obtained by an ordinary iterative decompression algorithm.     

AR modeling of myoelectric interference signals during a rampcontraction

The authors investigated the time-varying behavior of the autoregressive (AR) parameters in a myoelectric (ME) signal detected during a linear force increasing contraction. The AR parameters of interest mere the reflection coefficients, the AR model spectrum, and the prediction errors. The authors used well-conditioned ME signals for which the complete time record of the motor units firings was available. In addition, the influence of the recruitment of a new motor unit, the conduction velocity of action potentials, and additive broad-band noise were investigated using simulated ME signals. The simulated ME signals were constructed from a selected group of the available motor unit action potential trains. The results revealed that, as the contraction progressed, the AR parameters displayed a time-varying behavior which coincided with the recruitment of newly recruited motor units whose spectrum of the waveform differed from that of the rest of the ME signal. This property of the AR parameters was obscured by the presence of broad-band noise and low-amplitude motor unit action potentials, both of which are more pronounced during low-level force contractions     

Self-affine mapping system and its application to object contourextraction

A self-affine mapping system which has conventionally been used to produce fractal images is used to fit rough lines to contours. The self-affine map's parameters are detected by analyzing the blockwise self-similarity of a grayscale image using a simplified algorithm in fractal encoding. The phenomenon that edges attract mapping points in self-affine mapping is utilized in the proposed method. The boundary of the foreground region of an alpha mask is fitted by mapping iterations of the region. It is shown that the proposed method accurately produces not only smooth curves but also sharp corners, and has the ability to extract both distinct edges and blurred edges using the same parameter. It is also shown that even large gaps between the hand-drawn line and the contour can be fitted well by the recursive procedure of the proposed algorithm, in which the block size is progressively decreased. These features reduce the time required for drawing contours by hand.     

Linear bispectrum of signals and identification of nonminimum phaseFIR systems driven by colored input

The identification of non-minimum-phase finite-impulse-response (FIR) systems driven by third-order stationary colored signals that are not linear processes is addressed. Modeling the linear part of the bispectrum of a signal is discussed. The bispectrum of a signal is decomposed into two multiplicative factors. The linear bispectrum is defined as the factor of the bispectrum that can exactly be modeled using a third-order white-noise-driven linear shift-invariant (LSI) system. The linear bispectrum of the output of the unknown LSI system is represented using an ARMA (autoregressive moving average) model, where the MA parameters correspond to the unknown FIR system impulse response coefficients, and the AR parameters model the linear bispectrum of the input signal. An algorithm for identifying the MA and AR parameters is given. How the proposed method is different from fitting an ARMA model directly to the bicumulants or the bispectrum of the system output is discussed. The method is applied to blur identification     

语音识别的非线性方法

语音信号是一个复杂的非线性过程，这使得基于线性系统理论发展起来的传统语音识别技术性能难以进一步提高。近年来人们开始逐渐重视非线性在语音识别技术中的应用，本文概括地介绍了非线性理论在语音识别技术中的所取得的成果和发展方向，除了涉及较为流行的隐马尔柯夫过程和人工神经网络在语音识别中的应用外，文中着重论述了近年来发展迅猛的混沌，分形理论在语音识别中的应用，本文最后还提到不可忽视的分形理论在语音编码中的应     

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     

Signal classification through multifractal analysis and complex domain neural networks

This paper describes a system capable of classifying stochastic self-affine nonstationary signals produced by nonlinear systems. The classification and the analysis of these signals are important because these are generated by many real-world processes. The first stage of the signal classification process entails the transformation of the signal into the multifractal dimension domain, through the computation of the variance fractal dimension trajectory (VFDT). Features can then be extracted from the VFDT using a Kohonen self-organizing feature map. The second stage involves the use of a complex domain neural network and a probabilistic neural network to determine the class of a signal based on these extracted features. The results of this paper show that these techniques can be successful in creating a classification system which can obtain correct classification rates of about 87% when performing classification of such signals without knowing the number of classes.     

Three-dimensional tumor perfusion reconstruction using fractal interpolation functions

It has been shown that the perfusion of blood in tumor tissue can be approximated using the relative perfusion index determined from dynamic contrast-enhanced magnetic resonance imaging (DE-MRI) of the tumor blood pool. Also, it was concluded in a previous report that the blood perfusion in a two-dimensional (2-D) tumor vessel network has a fractal structure and that the evolution of the perfusion front can be characterized using invasion percolation. In this paper, the three-dimensional (3-D) tumor perfusion is reconstructed from the 2-D slices using the method of fractal interpolation functions (FIF), i.e., the piecewise self-affine fractal interpolation model (PSAFIM) and the piecewise hidden variable fractal interpolation model (PHVFIM). The fractal models are compared to classical interpolation techniques (linear, spline, polynomial) by means of determining the 2-D fractal dimension of the reconstructed slices. Using FIFs instead of classical interpolation techniques better conserves the fractal-like structure of the perfusion data. Among the two FIF methods, PHVFIM conserves the 3-D fractality better due to the cross correlation that exists between the data in the 2-D slices and the data along the reconstructed direction. The 3-D structures resulting from PHVFIM have a fractal dimension within 3%-5% of the one reported in literature for 3-D percolation. It is, thus, concluded that the reconstructed 3-D perfusion has a percolation-like scaling. As the perfusion term from bio-heat equation is possibly better described by reconstruction via fractal interpolation, a more suitable computation of the temperature field induced during hyperthermia treatments is expected.     

Maximum likelihood estimation of signals in autoregressive noise

Time series modeling as the sum of a deterministic signal and an autoregressive (AR) process is studied. Maximum likelihood estimation of the signal amplitudes and AR parameters is seen to result in a nonlinear estimation problem. However, it is shown that for a given class of signals, the use of a parameter transformation can reduce the problem to a linear least squares one. For unknown signal parameters, in addition to the signal amplitudes, the maximization can be reduced to one over the additional signal parameters. The general class of signals for which such parameter transformations are applicable, thereby reducing estimator complexity drastically, is derived. This class includes sinusoids as well as polynomials and polynomial-times-exponential signals. The ideas are based on the theory of invariant subspaces for linear operators. The results form a powerful modeling tool in signal plus noise problems and therefore find application in a large variety of statistical signal processing problems. The authors briefly discuss some applications such as spectral analysis, broadband/transient detection using line array data, and fundamental frequency estimation for periodic signals     

Using iterated function systems to model discrete sequences

Two iterated function system (IFS) models are explored for the representation of single-valued discrete-time sequences: the self-affine fractal model and the piecewise self-affine fractal model. Algorithms are presented, one of which is suitable for a multiprocessor implementation, for identification of the parameters of each model. Applications of these models to a variety of data types are given where signal-to-noise ratios are presented, quantization effects of the model parameters are investigated, and compression ratios are computed     

基于分形迭代函数系统的语音合成新算法

本文根据语音信号具有局部自相似性的特点，提出一种基于分形迭代函数系统的语音合成新算法，给出了两种数值解法。与传统的方法相比，本文的方法结构更简单，且合成语音的质量更高。     

海杂波AR谱多重分形特性及微弱目标检测方法

该文研究了海杂波功率谱的多重分形特性。为了克服频谱傅里叶分析的缺点,用现代谱估计的方法来计算海杂波的功率谱。AR模型是一个线性预测模型,它通过序列的自相关函数矩阵来估计功率谱,并且具有更精确的频谱分辨率。该文主要分析基于AR谱估计的海杂波功率谱的多重分形特性,以及在微弱目标检测中的应用。首先,以分数布朗运动(FBM)模型为例,证明其功率谱具有多重分形特性。其次,根据X波段雷达的实测海杂波数据,通过多重去趋势分析法(MF-DFA)验证了海杂波AR谱的多重分形特性。最后,分析了海杂波AR谱的广义Hurst指数以及影响参数,并提出一种基于局部AR谱广义Hurst指数的目标检测方法。实验结果表明,该种检测方法具有海杂波背景下微弱目标检测的能力。与现有的分形检测方法和传统的CFAR检测方法对比,该算法在低信杂比情况下具有较好的检测性能。     

Maximum likelihood estimation for array processing in colored noise

Direction of arrival estimation of multiple sources, using a uniform linear array, in noise with unknown covariance is considered. The noise is modeled as a spatial autoregressive process with unknown parameters. Both stochastic and deterministic signal models are considered. For the random signal case, an approximate maximum likelihood estimator of the signal and noise parameters is derived. It requires numerical maximization of a compressed likelihood function over the unknown arrival angles. Analytical expressions for the MLEs of the signal covariance and the AR parameters are given. Similar results for the case of deterministic signals are also presented     

Autoregressive Modeling of Temporal Envelopes

Autoregressive (AR) models are commonly obtained from the linear autocorrelation of a discrete-time signal to obtain an all-pole estimate of the signal's power spectrum. We are concerned with the dual, frequency-domain problem. We derive the relationship between the discrete-frequency linear autocorrelation of a spectrum and the temporal envelope of a signal. In particular, we focus on the real spectrum obtained by a type-I odd-length discrete cosine transform (DCT-Io) which leads to the all-pole envelope of the corresponding symmetric squared Hilbert temporal envelope. A compact linear algebra notation for the familiar concepts of AR modeling clearly reveals the dual symmetries between modeling in time and frequency domains. By using AR models in both domains in cascade, we can jointly estimate the temporal and spectral envelopes of a signal. We model the temporal envelope of the residual of regular AR modeling to efficiently capture signal structure in the most appropriate domain.     

Nonlinear considerations in EEG signal classification

We investigate the effect of incorporating modeling of nonlinearity on the classification of electroencephalogram (EEG) signals using an artificial neural network (ANN). It is observed that the ANN's predictive ability is improved after preprocessing EEG signals using a particular nonlinear modeling technique, viz. a bilinear model, compared with those obtained by using a particular classical linear analysis method, viz. an autoregressive (AR) model. Until recently, linear time-invariant Gaussian modeling has dominated the development of time series modeling and feature extraction. The advantage of such classical models lies in the fact that a complete signal processing theory is available. In the case of EEG signals, where the underlying theory regarding the dynamical law governing the generation of these signals (e,g., the underlying physiological factors) is not completely understood, a case can be made for using improved signal processing models that are not subject to linear constraints. Such models should recognize important features of the observed data that may not be well modeled by a linear time-invariant model. It is known that EEG signals are nonstationary, and it is possible that they may be nonlinear as well. Thus, one way of gaining further insights on the structure of EEG signals is to introduce nonlinear models and higher order spectra. This paper compares the results of classification using a linear AR model with those obtained from a bilinear model. It is shown that in certain cases, the nonlinearity of the EEG signals is an important factor that ought to be taken into consideration during preprocessing of the signals prior to the classification task     

Speed-up fractal image compression with a fuzzy classifier

This paper presents a fractal image compression scheme incorporated with a fuzzy classifier that is optimized by a genetic algorithm. The fractal image compression scheme requires to find matching range blocks to domain blocks from all the possible division of an image into subblocks. With suitable classification of the subblocks by a fuzzy classifier we can reduce the search time for this matching process so as to speedup the encoding process in the scheme. Implementation results show that by introducing three image classes and using fuzzy classifier optimized by a genetic algorithm the encoding process can be speedup by about 40% of an unclassified encoding system.     

基于HFM和感知后滤波器的语音增强

研究了只能获得带噪信号的情况下的语音增强问题。将语音信号看作由高斯噪声激励的自回归(AR)过程,观测噪声为加性高斯白噪声,把信号转化为状态空间模型。首先用隐马尔可夫模型(HMM)估计AR参数和噪声的方差作为卡尔曼滤波器初值,估计信号作为参数估计的中间值给出,然后将估计信号通过一个感知滤波器平滑以消除残余噪声。仿真结果表明该算法有良好的性能。     

A robust method for parameter estimation of AR systems using empirical mode decomposition

This paper presents a robust algorithm for parameter estimation of autoregressive (AR) systems in noise using empirical mode decomposition (EMD) method. The basic idea is to represent the autocorrelation function of the noise-free AR signal as the summation of damped sinusoidal functions and use EMD for extracting these component functions as intrinsic mode functions (IMFs). Unlike conventional correlation-based techniques, the proposed scheme first estimates the damped sinusoidal model parameters from the IMFs of autocorrelation function using a least-squares based method. The AR parameters are then directly obtained from the extracted sinusoidal model parameters. Simulation results show that EMD is a very promising tool for AR system identification at a very low signal-to-noise ratio (SNR).     

Analysis and simulation of changes in EMG amplitude during high-level fatiguing contractions

Changes in surface electromyographic (EMG) amplitude during sustained, fatiguing contractions are commonly attributed to variations in muscle fiber conduction velocity (MFCV), motor unit firing rates, transmembrane action potentials and the synchronization or recruitment of motor units. However, the relative contribution of each factor remains unclear. Analytical relationships relating changes in MFCV and mean motor unit firing rates to the root mean square (RMS) and average rectified (AR) value of the surface EMG signal are derived. The relationships are then confirmed using model simulation. The simulations and analysis illustrate the different behaviors of the surface EMG RMS and AR value with changing MFCV and firing rate, as the level of motor unit superposition varies. Levels of firing rate modulation and short-term synchronization that, combined with variations in MFCV, could cause changes in EMG amplitude similar to those observed during sustained isometric contraction of the brachioradialis at 80% of maximum voluntary contraction were estimated. While it is not possible to draw conclusions about changes in neural control without further information about the underlying motor unit activation patterns, the examples presented illustrate how a combined analytical and simulation approach may provide insight into the manner in which different factors affect EMG amplitude during sustained isometric contractions.     

Blind deconvolution of symmetric noncausal impulse responses usingtwo-sided linear prediction

Considers the problem of estimating the time-symmetric, noncausal impulse response of a linear time-invariant system from measurements of the response of the system to an unknown input signal, which is assumed to be a realization of a white random process. The symmetric impulse response is modeled by a two-sided AR or ARMA system model. The two-sided AR coefficients are estimated using a two-step procedure. First, an estimate of an unconstrained parameter vector is computed by solving a close-to-Toeplitz-plus-Hankel system of equations using previously developed fast algorithms. Then, the polynomial square root of the result is obtained by solving a constrained least-squares problem which has a simple solution. Unlike previous methods, this approach requires no iterative procedure. However, it may lead to an unstable model in some extreme cases. Simulation results illustrate the performance of the proposed methods