A Review of Wavelets for Digital Wireless Communication

Wavelets have been favorably applied in almost all aspects of digital wireless communication systems including data compression, source and channel coding, signal denoising, channel modeling and design of transceivers. The main property of wavelets in these applications is in their flexibility and ability to characterize signals accurately. In this paper recent trends and developments in the use of wavelets in wireless communications are reviewed. Major applications of wavelets in wireless channel modeling, interference mitigation, denoising, OFDM modulation, multiple access, Ultra Wideband communications, cognitive radio and wireless networks are surveyed. The confluence of information and communication technologies and the possibility of ubiquitous connectivity have posed a challenge to developing technologies and architectures capable of handling large volumes of data under severe resource constraints such as power and bandwidth. Wavelets are uniquely qualified to address this challenge. The flexibility and adaptation provided by wavelets have made wavelet technology a strong candidate for future wireless communication. Madan Kumar Lakshmanan was born in Chennai, India, in 1979. He received the B.E. (with distinction) in electrical engineering from the University of Madras, Chennai, India, in 2000. He joined the Indian Software firm, Polaris Software Labs Ltd., in 2000 where he wrote software for Telecommunication applications. At Polaris, he was awarded the “On The Spot Of Excellence Award” for his efforts. In 2003, he moved to the Indian Institute of Technology-Madras, to develop and establish a wireless communications network for rural connectivity. In 2004, he was awarded the Royal Dutch/Shell Chevning scholarship to pursue a Master degree in Telecommunications at the Delft University of Technology (TUDelft). At TUDelft he is affiliated to the International Research Center for Telecommunications-Transmission and Radar (IRCTR) where he is undertaking research in the field of wavelets applications in Wireless Communications. Homayoun Nikookar received his Ph.D. in Electrical Engineering from Delft University of Technology (TUDelft), The Netherlands, in 1995. From 1995 to 1998 he was a postdoc researcher at the International Research Center for Telecommunications-Transmission and Radar, TUDelft, where since 1999 he has been an Assistant Professor. Dr. Nikookar has done research on different areas of wireless communications, including wireless channel modeling, UWB, MIMO, multicarrier transmission, Wavelet-based OFDM and CDMA. He is a senior member of the IEEE.     

Nonlinear black-box modeling in system identification: a unified overview

A nonlinear black-box structure for a dynamical system is a model structure that is prepared to describe virtually any nonlinear dynamics. There has been considerable recent interest in this area, with structures based on neural networks, radial basis networks, wavelet networks and hinging hyperplanes, as well as wavelet-transform-based methods and models based on fuzzy sets and fuzzy rules. This paper describes all these approaches in a common framework, from a user's perspective. It focuses on what are the common features in the different approaches, the choices that have to be made and what considerations are relevant for a successful system-identification application of these techniques. It is pointed out that the nonlinear structures can be seen as a concatenation of a mapping form observed data to a regression vector and a nonlinear mapping from the regressor space to the output space. These mappings are discussed separately. The latter mapping is usually formed as a basis function expansion. The basis functions are typically formed from one simple scalar function, which is modified in terms of scale and location. The expansion from the scalar argument to the regressor space is achieved by a radial- or a ridge-type approach. Basic techniques for estimating the parameters in the structures are criterion minimization, as well as two-step procedures, where first the relevant basis functions are determined, using data, and then a linear least-squares step to determine the coordinates of the function approximation. A particular problem is to deal with the large number of potentially necessary parameters. This is handled by making the number of ‘used’ parameters considerably less than the number of ‘offered’ parameters, by regularization, shrinking, pruning or regressor selection.     

CAS wavelet method for solving the fractional integro-differential equation with a weakly singular kernel

In this paper, a computational method for numerical solution of a class of integro-differential equations with a weakly singular kernel of fractional order which is based on Cos and Sin (CAS) wavelets and block pulse functions is introduced. Approximation of the arbitrary order weakly singular integral is also obtained. The fractional integro-differential equations with weakly singular kernel are transformed into a system of algebraic equations by using the operational matrix of fractional integration of CAS wavelets. The error analysis of CAS wavelets is given. Finally, the results of some numerical examples support the validity and applicability of the approach.     

Rational wavelet decompositions of transfer functions in hardy-sobolev classes

The model approximation of transfer functions using rational wavelets (or molecular decompositions) is considered. By using techniques from Hardy-Sobolev spaces it is shown that Hilbert space methods such as a modified matching-pursuit algorithm and least-squares technique can be employed to obtain good approximations in bothH ² andH norms. Several theoretical results are given on rates of convergence when the methods are applied to delay systems and fractional filters.The research of the first author was supported by E.P.S.R.C.     

An Automated Brain Image Analysis System for Brain Cancer using Shearlets

In this paper, an Automated Brain Image Analysis (ABIA) system that classifies the Magnetic Resonance Imaging (MRI) of human brain is presented. The classification of MRI images into normal or low grade or high grade plays a vital role for the early diagnosis. The Non-Subsampled Shearlet Transform (NSST) that captures more visual information than conventional wavelet transforms is employed for feature extraction. As the feature space of NSST is very high, a statistical t-test is applied to select the dominant directional sub-bands at each level of NSST decomposition based on sub-band energies. A combination of features that includes Gray Level Co-occurrence Matrix (GLCM) based features, Histograms of Positive Shearlet Coefficients (HPSC), and Histograms of Negative Shearlet Coefficients (HNSC) are estimated. The combined feature set is utilized in the classification phase where a hybrid approach is designed with three classifiers; k-Nearest Neighbor (kNN), Naive Bayes (NB) and Support Vector Machine (SVM) classifiers. The output of individual trained classifiers for a testing input is hybridized to take a final decision. The quantitative results of ABIA system on Repository of Molecular Brain Neoplasia Data (REMBRANDT) database show the overall improved performance in comparison with a single classifier model with accuracy of 99% for normal/abnormal classification and 98% for low and high risk classification.     

Simultaneous speckle reduction and contrast enhancement for ultrasound images: Wavelet versus Laplacian pyramid

Speckle can be described as random multiplicative noise. It hampers the perception and extraction of fine details in the image. Speckle reduction techniques are applied to ultrasound images in order to reduce the noise level and improve the visual quality for better diagnoses. It is also used as preliminary treatment before segmentation and classification. Several methods have been proposed for speckle reduction in ultrasound images. Multiscale contrast enhancement has proven to be very efficient for x-ray images. A recent study by Dippel et al. doing a comparison, contrast enhancement of radiographs (x-ray and mammography), between the Laplacian pyramid and the wavelet one proves that the Laplacian pyramid method gives a better result than the wavelet one; the filtering aspect was not taken into account. In ultrasound images a strong contrast variation exists which is different from x-ray and mammography. In this paper a wavelet pyramid with simultaneous speckle reduction and contrast enhancement was applied for the first time on ultrasound images with the area of interest and compared to a Laplacian enhancement pyramid. The optimum choice of wavelet bases for ultrasound images is investigated in this study. In order to realize a fair comparison, the same nonlinear modification in both multiscale schemes is used. The comparison proves that the wavelet pyramid gives a much better result than the Laplacian one for simultaneous speckle reduction and contrast enhancement of ultrasound images. The text was submitted by the author in English. Ali Samir Saad, 1964. 1996 PhD in image processing, Polytechnics School of the Engineering University of Nantes, France. 1993 Masters in Electronics. 1990 Masters in Digital Image Processing, Institute of Computer Sciences and Communication University of Rennes, France. 1989 BS in Electrical Engineering, University of Saint-Etienne. Academy of Lyon, France. 1996–2000 Research associate at the National Center for Macromolecular Imaging. Baylor, Houston, Texas. Assistant professor at King Saud University, Dept. of Biomedical Technology. Area of research in medical image processing and analysis, 23 publications, member of the American Association for the Advancement of Sciences. Marquis Who’s Who in the World; Cambridge Blue Book 2006.     

基于冗余表决的行波小波系数极大值极性法配电网接地故障选线原理研究

研究了配电网中单相接地短路故障时暂态行波的特性,利用母线电压及各线路电流暂态行波0模初始波头的小波系数的极大值极性的特征,构成了新的基于小波分析的故障选线保护判据,通过识别初始波头小波系数的极大值,判断极大值极性特征,并对多次判断结果进行冗余表决,完成故障选线工作。该文利用M atlab建立了一个典型的配电网系统仿真模型,通过编写选线保护仿真程序,完成对仿真结果的计算和分析,证明了此方法的正确和有效,并对应用研究提出了有益的建议。     

BRDF Measurement Modelling using Wavelets for Efficient Path Tracing

Physically based rendering needs numerical models from real measurements, or analytical models from material definitions, of the Bidirectional Reflectance Distribution Function (BRDF). However, measured BRDF data sets are too large and provide no functionalities to be practically used in Monte Carlo path tracing algorithms. In this paper, we present a wavelet‐based generic BRDF model suitable for both physical analysis and path tracing. The model is based on the separation of spectral and geometrical aspect of the BRDF and allows a compact and efficient representation of isotropic, anisotropic and/or spectral BRDFs. After a brief survey of BRDF and wavelet theory, we present our software architecture for generic wavelet transform and how to use it to model BRDFs. Then, modelling results are presented on real and virtual BRDF measurements. Finally, we show how to exploit the multiresolution property of the wavelet encoding to reduce the variance by importance sampling in a path tracing algorithm. ACM CSS: I.3.7 Computer Graphics—Three‐Dimensional Graphics and Realism     

小波分析在三维地形数据简化中的应用研究

研究了小波分析在三维地形数据简化中的应用。在分析了小波多分辨率分析理论的基础上,重点探讨了小波多分辨率分析理论在三维地形简化中的应用,提出了实现三维地形数据简化的一种新的方法。