Image clustering using higher-order statistics

Traditional algorithms for clustering image data have used Euclidean or Mahalanobis distance. Here, a more general higher-order statistics-based closeness measure derived from a series expansion for a multivariate probability density function in terms of the Gaussian function and the Hermite polynomials is proposed for clustering. The superiority of this measure is demonstrated with an example application     

Batch processing algorithms for blind equalization using higher-order statistics

Statistical signal processing has been one of the key technologies in the development of wireless communication systems, especially for broadband multiuser communication systems which severely suffer from intersymbol interference (ISI) and multiple access interference (MAI). This article reviews batch processing algorithms for blind equalization using higher-order statistics for mitigation of the ISI induced by single-input, single-output channels as well as of both the ISI and MAI induced by multiple-input, multiple-output channels. In particular, this article reviews the typical inverse filter criteria (IFC) based algorithm, super-exponential algorithm, and constant modulus algorithm along with their relations, performance, and improvements. Several advanced applications of these algorithms are illustrated, including blind channel estimation, simultaneous estimation of multiple time delays, signal-to-noise ratio (SNR) boost by blind maximum ratio combining, blind beamforming for source separation in multipath, and multiuser detection for direct sequence/code division multiple access (DS/CDMA) systems in multipath.     

A comprehensive approach to DOA estimation using higher-order statistics

The algorithms developed in this paper rely on cumulants, or higher-order statistics, to eliminate Gaussian noise. A simple relation between the signal model parameters and the cumulant matrices computed from the received signals forms the basis for the development of these algorithms. The block Hankel structure of matrices formed from the cumulant matrices enables the directions of arrival (DOAs) to be estimated using the well-known MUSIC and ESPRIT approaches to DOA estimation. The effectiveness of the methods proposed here is demonstrated by the results of extensive computer simulation studies.This work was supported by the National Sciences and Engineering Research Council of Canada.     

Lyapunov stability analysis of higher-order 2-D systems

In this paper we prove a necessary and sufficient condition for the asymptotic stability of a 2-D system described by a system of higher-order linear partial difference equations. We show that asymptotic stability is equivalent to the existence of a vector Lyapunov functional satisfying certain positivity conditions together with its divergence along the system trajectories. We use the behavioral framework and the calculus of quadratic difference forms based on four-variable polynomial algebra.     

Harmonic retrieval using higher order statistics: a deterministicformulation

Given a single record, the authors consider the problem of estimating the parameters of a harmonic signal buried in noise. The observed data are modeled as a sinusoidal signal plus additive Gaussian noise of unknown covariance. The authors define novel higher order statistics-referred to as “mixed” cumulants-that can be consistently estimated using a single record and are insensitive to colored Gaussian noise. Employing fourth-order mixed cumulants, they estimate the sinusoid parameters using a consistent, nonlinear matching approach. The algorithm requires an initial estimate that is obtained from a consistent, linear estimator. Finally, the authors examine the performance of the proposed method via simulations     

Hybrid higher-order statistics learning in multiuser detection

In this paper, we explore the significance of second- and higher-order statistics learning in communication systems. The final goal in spread-spectrum communication systems is to receive a signal of interest completely free from interference caused by other concurrent signals. To achieve this end, we exploit the structure of the interference by designing second-order statistics detectors, such as the minimum square error, in conjunction with higher-order statistics (HOS) techniques, such as the blind source separation (BSS). This hybrid higher-order statistics (HyHOS) approach enables us to alleviate BSS algorithms of one of their main problems, that is, their sensitiveness to high levels of noise. In addition, we benefit from remarkable properties of BSS in learning such as fast learning (superefficiency) and independence of the initial settings of the problem (equivariance). We successfully applied the results of this approach to the design of multiuser detectors in code-division multiple access channels.     

Almost-sure identifiability of multidimensional harmonic retrieval

Two-dimensional (2-D) and, more generally, multidimensional harmonic retrieval is of interest in a variety of applications, including transmitter localization and joint time and frequency offset estimation in wireless communications. The associated identifiability problem is key in understanding the fundamental limitations of parametric methods in terms of the number of harmonics that can be resolved for a given sample size. Consider a mixture of 2-D exponentials, each parameterized by amplitude, phase, and decay rate plus frequency in each dimension. Suppose that I equispaced samples are taken along one dimension and, likewise, J along the other dimension. We prove that if the number of exponentials is less than or equal to roughly IJ/4, then, assuming sampling at the Nyquist rate or above, the parameterization is almost surely identifiable. This is significant because the best previously known achievable bound was roughly (I+J)/2. For example, consider I=J=32; our result yields 256 versus 32 identifiable exponentials. We also generalize the result to N dimensions, proving that the number of exponentials that can be resolved is proportional to total sample size     

3-D object recognition using 2-D views

We consider the problem of recognizing 3-D objects from 2-D images using geometric models and assuming different viewing angles and positions. Our goal is to recognize and localize instances of specific objects (i.e., model-based) in a scene. This is in contrast to category-based object recognition methods where the goal is to search for instances of objects that belong to a certain visual category (e.g., faces or cars). The key contribution of our work is improving 3-D object recognition by integrating Algebraic Functions of Views (AFoVs), a powerful framework for predicting the geometric appearance of an object due to viewpoint changes, with indexing and learning. During training, we compute the space of views that groups of object features can produce under the assumption of 3-D linear transformations, by combining a small number of reference views that contain the object features using AFoVs. Unrealistic views (e.g., due to the assumption of 3-D linear transformations) are eliminated by imposing a pair of rigidity constraints based on knowledge of the transformation between the reference views of the object. To represent the space of views that an object can produce compactly while allowing efficient hypothesis generation during recognition, we propose combining indexing with learning in two stages. In the first stage, we sample the space of views of an object sparsely and represent information about the samples using indexing. In the second stage, we build probabilistic models of shape appearance by sampling the space of views of the object densely and learning the manifold formed by the samples. Learning employs the Expectation-Maximization (EM) algorithm and takes place in a "universal," lower-dimensional, space computed through Random Projection (RP). During recognition, we extract groups of point features from the scene and we use indexing to retrieve the most feasible model groups that might have produced them (i.e., hypothesis generation). The likelihood of each hypothesis is then computed using the probabilistic models of shape appearance. Only hypotheses ranked high enough are considered for further verification with the most likely hypotheses verified first. The proposed approach has been evaluated using both artificial and real data, illustrating promising performance. We also present preliminary results illustrating extensions of the AFoVs framework to predict the intensity appearance of an object. In this context, we have built a hybrid recognition framework that exploits geometric knowledge to hypothesize the location of an object in the scene and both geometrical and intesnity information to verify the hypotheses.     

Unvoiced/voiced classification and voiced harmonic parameters estimation using the third-order statistics

Unvoiced/voiced classification of speech is a challenging problem especially under conditions of low signal-to-noise ratio or the non-white-stationary noise environment. To solve this problem, an algorithm for speech classification, and a technique for the estimation of pairwise magnitude frequency in voiced speech are proposed. By using third order spectrum of speech signal to remove noise, in this algorithm the least spectrum difference to get refined pitch and the max harmonic number is given. And this algorithm utilizes spectral envelope to estimate signal-to-noise ratio of speech harmonics. Speech classification, voicing probability, and harmonic parameters of the voiced frame can be obtained. Simulation results indicate that the proposed algorithm, under complicated background noise, especially Gaussian noise, can effectively classify speech in high accuracy for voicing probability and the voiced parameters.     

谐波过程的高阶广义各态历经性的分析与应用

高阶统计在信号处理的许多领域得到了广泛应用。但在实际应用的许多情况下,由于只能得到观测过程的一个样本,所以只能用样本的时间平均来代替其统计平均。其前提是过程对该统计量具有广义的各态历经性,该文分析了谐波过程高阶统计量的各态历经性,得到了谐波过程满足三阶、四阶矩和累积量广义各态历经的充要条件。然后研究了这些条件在高阶统计量的相位耦合识别、高阶阵列处理方法等问题中的应用,并进行了模拟实验验证。     

Two-dimensional harmonic retrieval and its time-domain analysistechnique

The two-dimensional harmonic retrieval is examined in theory by confirming that the 2-D sinusoids in white noise are modeled as a special 2-D autoregressive moving average (ARMA) process whose AR parameters are identical to the MA ones. A new analysis technique for resolving 2-D sinusoids in white noise is proposed     

NEW APPROACH TO HARMONIC RETRIEVAL IN NOISE

This paper addresses the harmonic retrieval problem in non-Gaussian ARMA noise. A hybrid ESPRIT approach using second-and third-order statistics is proposed. First, third-order statistics are used to identify the AR part of the non-Gaussian noise process, then the noisy measurements are filtered by AR polynomial, finally, the harmonic signal parameters are estimated. Simulation examples show the effectiveness and high resolution of the new approach.     

Cumulant-based approach to harmonic retrieval and related problems

A frequently encountered problem in signal processing is that of estimating the frequencies and amplitudes of harmonics observed in additive colored Gaussian noise. In practice, the observed signals are contaminated with spatially and temporally colored noise of unknown power spectral density. A cumulant-based approach to these problems is proposed. The cumulants of complex processes are defined, and it is shown that specific 1-D slices of the fourth-order cumulant of the noisy signal for the direction of arrival (DOA) and retrieval of harmonics in noise (RHN) problems are identical to the autocorrelation of a related noiseless signal. Hence correlation-based high-resolution methods may be used with fourth-order cumulants as well. The effectiveness of the proposed methods is demonstrated through standard simulation examples     

A harmonic retrieval framework for discontinuous motion estimation

Motion discontinuities arise when there are occlusions or multiple moving objects in the scene that is imaged. Conventional regularization techniques use smoothness constraints but are not applicable to motion discontinuities. In this paper, we show that discontinuous (or multiple) motion estimation can be viewed as a multicomponent harmonic retrieval problem. From this viewpoint, a number of established techniques for harmonic retrieval ran be applied to solve the challenging problem of discontinuous (or multiple) motion. Compared with existing techniques, the resulting algorithm is not iterative, which not only implies computational efficiency but also obviates concerns regarding convergence or local minima. It also adds flexibility to spatio-temporal techniques which have suffered from lack of explicit modeling of discontinuous motion. Experimental verification of our framework on both synthetic data as well as real image data is provided.     

Statistical analysis of state-space approach in harmonic retrieval

The author presents a statistical analysis of the performance of the state-variable balancing for estimating the parameters of exponential signals in the presence of additive noise. The case of frequency estimation for a single damped sinusoid is carried out in detail because the analysis can be presented more clearly; the formulas are simpler and provide insight; and the results are applicable in radar, sonar, communication, and data modelling. Analytical expressions for the variances of the frequency estimate at high signal-to-noise ratios is derived. Both analytical and experimental results are presented to illustrate the performance of the state-variable balancing method     

Camera constraint-free view-based 3-D object retrieval

Recently, extensive research efforts have been dedicated to view-based methods for 3-D object retrieval due to the highly discriminative property of multiviews for 3-D object representation. However, most of state-of-the-art approaches highly depend on their own camera array settings for capturing views of 3-D objects. In order to move toward a general framework for 3-D object retrieval without the limitation of camera array restriction, a camera constraint-free view-based (CCFV) 3-D object retrieval algorithm is proposed in this paper. In this framework, each object is represented by a free set of views, which means that these views can be captured from any direction without camera constraint. For each query object, we first cluster all query views to generate the view clusters, which are then used to build the query models. For a more accurate 3-D object comparison, a positive matching model and a negative matching model are individually trained using positive and negative matched samples, respectively. The CCFV model is generated on the basis of the query Gaussian models by combining the positive matching model and the negative matching model. The CCFV removes the constraint of static camera array settings for view capturing and can be applied to any view-based 3-D object database. We conduct experiments on the National Taiwan University 3-D model database and the ETH 3-D object database. Experimental results show that the proposed scheme can achieve better performance than state-of-the-art methods.     

小波包和高阶统计量相结合的红外弱小目标检测

针对单帧红外图像中的弱小目标检测问题,提出了一种结合小波包和高阶统计量的新方法。首先,利用小波包变换对图像进行频域上的分解。然后,针对小波包树上的节点,由低到高采用基于四阶累计量的高斯判别准则合并相邻四个全高斯性小波包系数,得到图像的最优划分。接下来,将最低频带上的小波包系数和高斯性小波包系数置零来分别抑制背景杂波和噪声。最后,采用这些新的系数即可重建检测结果。实验结果表明:该方法能够稳健、有效地检测红外弱小目标。     

Non-relativistic particle higher-order harmonic radiation based short-wavelength laser and the operation stability

Under classical mechanics,the general equation of particle motion in the periodic field is derived.In the dampless case,the existence possibility of the higher-order harmonic radiation is explored by using Bessel function expansion of a generalized trigonometrical function and the multi-scale method.In the damping case,the critical properties and a chaotic behavior are discussed by the Melnikov method.The results show that the use of a higher-order harmonic radiation of non-relativistic particles as a short-wavelength laser source is perfectly possible,and the system critical condition is related to its parameters.only by adjusting parameters suitablely,the stable higher-order harmonic radiation with bigger intensity can be obtained.     

Image data compression using 2-D lattice predictor

The outline of an approach for image data compression using a 2-D lattice predictor is presented. Preliminary results indicate that acceptable quality images (quantised to 15 levels) at information rates, bit rates and signal/noise ratios ranging, respectively, from 1.16 to 1.38 bpp, 1.19 to 1.40 bpp and 20.6 to 22.5 dB have been obtained for lattice stages 1 to 5.