Xiaoping Shen

• Ph. D in Applied Mathematics
• Professor (Full) at Ohio University

Human occupancy detection (HOD) in an enclosed space, such as indoors or inside of a vehicle, via passive cognitive radio (CR) is a new and challenging research area. Part of the difficulty arises from the fact that a human subject cannot easily be detected due to spectrum variation. In this paper, we present an advanced HOD system that dynamically...

This paper deals with the theoretical aspect of bat echolocation and bionics, and image processing-based target recognition and identification methods. The state estimation methods utilizing the linear rustic filters such as fixed gain and Kalman filters are studied and implemented for echolocation bionics for estimating the LOS distance. A complet...

In this paper, we explore sparse reconstruction of RF tomography with sensors pseudo randomly distributed on a ring. Multilevel scattering and multipath propagation are considered in the system model. A novel approach of dynamically building dictionary for reconstruction is proposed. Under the assumption of sparse target, the proposed method can si...

Multiscale Signal Analysis and Modeling presents recent advances in multiscale analysis and modeling using wavelets and other systems. This book also presents applications in digital signal processing using sampling theory and techniques from various function spaces, filter design, feature extraction and classification, signal and image representat...

Over the last several years, there has been a strong emphasis on developing heat sinks for high heat flux systems. Consequently new materials are being developed and novel thermal transport mechanisms are being investigated. Some of the novel materials are composites with thermal conductivity exceeding 500 W/mK. In this paper we examine the effect...

In this paper, we construct a positive definite kernel associated with Slepian semi-wavelets. The kernel possesses multiscale structure and exhibits a strong localization property. It is convolution type associated with asymptotic sparse Gram matrix and allows the use of thresholding methods. We then focus on developing practical numerical algorith...

This paper explores the connection between uncertainty and memory effects of time series associated with complex system. Traditionally, information theory based algorithms, such as Shannon entropy and its relatives, are employed as measurements to describe uncertainty quantitatively. This study brings into focus the important role of the long range...

This paper examines the use of wavelets to analyze EEG signals. Wavelets provide time and frequency analysis simultaneously and offer different approaches for data analysis with a number of properties and flexibility. It is intended to seek similarities and correlations of EEG signals.

Financial ratio based multivariate discriminant analysis (MDA) has been used as a tool for business forecasting for long time. In this article, we study some of the key issues of MDA in context of bankruptcy prediction, including reducing number of nancial ratios used in the model, the selection of optimal accounting review intervals and noise cont...

This paper proposes an approach to integrate the self-organizing map (SOM) and kernel density estimation (KDE) techniques for the anomaly-based network intrusion detection (ABNID) system to monitor the network traffic and capture potential abnormal behaviors. With the continuous development of network technology, information security has become a m...

An Energy Difference of Multiresolution Analysis (EDMRA) method for power quality (PQ) disturbances analysis has been proposed in this paper. At each wavelet decomposition level, the squared value of the detail information is calculated as their energy to construct the feature vector for analysis. Following the criteria proposed in this paper, diff...

This paper proposes a novel feature ranking method, DensityRank, based on kernel estimation on the feature spaces to improve the classification performance. As the availability of raw data in many of today's applications continues to grow at an explosive rate, it is critical to assess the learning capabilities of different features and select the i...

Wavelet analysis has been applied in several fields of signal analysis with notable success. Unfortunately, a digression of wavelet series is the Gibbs phenomenon around the jump discontinuity of signal samples. This article discusses the phenomenon in the wavelet hybrid sampling series and the summability methods used to overcome this drawback.

Feature selection is an active research area in machine learning for high dimensional dataset analysis. The idea is to perform the learning process solely on the top ranked feature spaces instead of the entire original feature space, and therefore to improve the understanding of the inherent characteristics of such dataset as well as reduce the com...

This paper presents the research of using bootstrap methods for time-series prediction. Unlike the traditional single model (neural network, support vector machine, or any other types of learning algorithms) based time-series prediction, we propose to use bootstrap methods to construct multiple learning models, and then use a combination function t...

Periodic prolate spheroidal wavelets (periodic PS wavelets), based on the periodizaton of the first prolate spheroidal wave function (PSWF), were recently introduced by the authors. Because of localization and other properties, these periodic PS wavelets could serve as an alternative to Fourier series for applications in modeling periodic signals....

Microarray expression data analysis is critical for clinical treatment and biomedical research. Although many research results have been reported in literature, it is still very difficult to learn, predict and understand such complex gene expression data. The major difficulty arises from the inherent characteristics of such data set including extre...

In this article, we will restrict our attention to the applications of the density estimators. We introduced an algorithm based on discrete convolution which can be used to compute the density estimator effectively. To test the capability, the kernel density estimator is used to model fading envelop of long range fading signals with flat spectral....

Wavelet methods have been of considerable interest in many engineering applications such as signal and image processing. However, like other classical orthogonal expansions, wavelet expansions also exhibit the Gibbs phenomenon around discontinuities of the original signal. In a previous work, summability methods for removing the Gibbs phenomenon in...

In this paper, we introduce a regularization procedure based on band limited orthogonal wavelets–-the Meyer wavelets–-for a class of convolution equations of the first kind. A regularizer based on these wavelets which maps into the wavelet subspace Vm is introduced. The regularizer is then used to solve the problem in the case where the kernel and...

In this article, we study a class of biorthogonal sampling functions in the con- text of bandlimited wavelets, Meyer type wavelets. Originally raised in the construc- tion of bandlimited wavelets, these sampling functions also possess a similar structure to the scaling functions of wavelets with ad- justable bandwidth parameters. In addition, these...

This paper presents a new nonparametric method to simulate probability density functions of some random variables raised in characterizing an anomaly based intrusion detection system (ABIDS). A group of kernel density estimators is constructed and the criterions for bandwidth selection are discussed. In addition, statistical parameters of these dis...

Prolate spheroidal wavelets (PS wavelets) were recently introduced by the authors. They were based on the first prolate spheroidal wave function (PSWF) and had many desirable properties lacking in other wavelets. In particular, the subspaces belonging to the associated multiresolution analysis (MRA) were shown to be closed under differentiation and...

In this paper, we construct infinite-band filterbanks for perfect reconstruction (PR) using Hermite polynomials and Hermite functions. The analysis filters are linear combinations of derivative operators based on these polynomials-the so-called chromatic derivative filters. Together with the synthesis filterbanks, they give PR for a large class of...

Slepian functions (Prolate Spheroidal Wave Functions) are obtained by maximizing the energy of a σ-bandlimited function (normalized with total energy 1) on a prescribed interval [-τ,τ]. The solution to this problem leads to an eigenvalue problem λf(t)=∫ -τ τ {sinσ(t-x)/π(t-x)}f(x)dx, whose solutions, in turn, form an orthogonal sequence {φ n }. Thi...

Efficient and rapid prediction of the future values of the fading envelop is important in fading compensation techniques. This paper is devoted to the discussion of modeling fading channels using kernel density estimation. Our kernel density estimators are non parametric density estimators. Although it will be assumed that the distribution has a pr...

In the past of two decades, wavelet methods have been adopted enthusiastically in many engineering applications such as signal and image processing. However, like most of the classic orthogonal expansions, wavelet expansions also exhibit Gibbs phenomenon around discontinuities of the original signals. Therefore, the recovered signals using wavelet...

The article is concerned with a particular multiresolution analysis (MRA) composed of Paley–Wiener spaces. Their usual wavelet basis consisting of sinc functions is replaced by one based on prolate spheroidal wave functions (PSWFs) which have much better time localization than the sinc function. The new wavelets preserve the high energy concentrati...

Third generation wireless communication systems should not only support more users, but should also transmit voice, video and multimedia traffic at higher data rates. Inevitably, these demands require more efficient fading compensation techniques. These techniques use properties of the channel transfer functions and need rapid prediction of the fut...

The continuous prolate spheroidal wave functions (Slepian functions) were found to be useful for analog signal processing several decades ago. But the digital revolution left them in the dust since they did not seem naturally adapted to discrete analysis. Yet they have many desirable, even unique, properties that originally made them fascinating an...

The prolate spheroidal wave functions (PSWFs) are used in sampling of bandlimited signals. Several formulae based on integer values of these PSWFs are derived and used to replace the sinc function in sampling theorems. They are also used to construct analysis and synthesis filter banks for sampled values. A type of multiresolution analysis based on...

This paper is devoted to the discussion of a “hybrid” sampling series, a series of translates of a nonnegative summability function used in place of an orthogonal scaling function. The coefficients in the series are taken to be sampled values of the function to be approximated. This enables one to avoid the integration which arises in the other ser...

Although it goes without saying that it would not be possible to give a comprehensive introduction on this subject in a single chapter, we do wish to highlight some of the most important analytical methods: separation of the variables and integral transforms, as well as numerical methods, the difference method and finite element method. We also hav...

In this paper we discuss a weighted trapezoidal rule based on sampling in Meyer wavelet subspaces. For a wide class of functions, we obtain convergence and error bounds. Some examples are given to construct sampling functions.

The research on extrapolation for the finite element method in solving partial differential equations began in the earlier 1980s. The pioneering work in this area was done mainly by the Chinese mathematician Qun Lin and his collaborators. In the last 20 years, their results have been developed further. The results during this period of time were on...

A Galerkin method based on bandlimited wavelet bases is proposed for solving the singular convolution equation on the real line of the form ∞ −∞ (H(t − s) + |t − s| −α)f (s)ds = g(t), 0 < α < 1, t ∈ R. The proposed method allows the discretized equation to be well posed due to the exceptional property of bandlimited wavelets in Fourier domain. Unde...

In this paper, we have a procedure based on band limited orthogonal wavelets, the Meyer wavelets, to solve convolution equations of the first kind, which is usually an ill-posed problem. The problem will be converted into a well-posed problem in the scaling subspaces, provided that the kernel k ε L1(R) and k̂(ω) Ĉ= 0. In the case k̂(ω) has a single...

It was shown by Janssen in 1993 that there are no continuous non-negative orthogonal scaling functions. For density estimation, we would like the estimators themselves to be densities, and hence non-negative. Thus the usual linear projection or the threshold estimators won't work without modification. In this paper, we introduce smooth non-negative...

Gibbs’ phenomenon almost always appears in the expansions using classical orthogonal systems. Various summability methods are used to get rid of unwanted properties of these expansions. Similar problems arise in wavelet expansions, but cannot be solved by the same methods. In a previous work [G. G. Walter and X. Shen, Contemp. Math. 216, 63-79 (199...

In classical orthogonal systems, various summability methods are used to get rid of unwanted problems of expansions. These usually involve excessive oscillations of the partial sums. Similar problems arise in wavelet expansions, but cannot be solved by the same methods. In this paper, two alternative procedures for wavelet expansions are introduced...