14649490
Generation of finite tight frames by Householder transformations
Finite tight frames are widely used for many applications. An important problem is to construct finite frames with prescribed norm for each vector in the tight frame. In this paper we provide a fast and simple algorithm for such a purpose. Our algorithm employs the Householder transformations. For a finite tight frame consisting of m vectors in ℝn or ℂn only O(nm) operations are needed. In addition, we also study the following question: Given a set of vectors in ℝn or ℂn, how many additional vectors, possibly with constraints, does one need to add in order to obtain a tight frame?
15709234
Sigma–delta quantization errors and the traveling salesman problem
In transmission, storaging and coding of digital signals we frequently perform A/D conversion using quantization. In this paper we study the maximal and mean square errors as a result of quantization. We focus on the sigma–delta modulation quantization scheme in the finite frame expansion setting. We show that this problem is related to the classical Traveling Salesman Problem (TSP) in the Euclidean space. It is known [Benedetto et al., Sigma–delta ($\Sigma\Delta$) quantization and finite frames, IEEE Trans. Inform. Theory 52, 1990–2005 (2006)] that the error bounds from the sigma–delta scheme depends on the ordering of the frame elements. By examining a priori bounds for the Euclidean TSP we show that error bounds in the sigma–delta scheme is superior to those from the pulse code modulation (PCM) scheme in general. We also give a recursive algorithm for finding an ordering of the frame elements that will lead to good maximal error and mean square error.
2456151
Subdivision Schemes and Refinement Equations with Nonnegative Masks
We consider the two-scale refinement equation f(x)=@?^N"n"="0c"nf(2x-n) with @?"nc"2"n=@?"nc"2"n"+"1=1 where c"0, c"N 0 and the corresponding subdivision scheme. We study the convergence of the subdivision scheme and the cascade algorithm when all c"n>=0. It has long been conjectured that under such an assumption the subdivision algorithm converge, and the cascade algorithm converge uniformly to a continuous function, if and only if only if 00} is 1. We prove the conjecture for a large class of refinement equations.
17444206
The Uniformity of Non-Uniform Gabor Bases
There have been extensive studies on non-uniform Gabor bases and frames in recent years. But interestingly there have not been a single example of a compactly supported orthonormal Gabor basis in which either the frequency set or the translation set is non-uniform. Nor has there been an example in which the modulus of the generating function is not a characteristic function of a set. In this paper, we prove that in the one dimension and if we assume that the generating function g(x) of an orthonormal Gabor basis is supported on an interval, then both the frequency and the translation sets of the Gabor basis must be lattices. In fact, the Gabor basis must be the “trivial” one in the sense that |g(x)|=cχΩ(x) for some fundamental interval of the translation set. We also give examples showing that compactly supported non-uniform orthonormal Gabor bases exist in higher dimensions.
117639554
Multidimensional two-scale dilation equations
Abstract . This work involves the study of multidimensional scaling functions. These functions satisfy a two-scale dilation equation, just as the 1-D scaling functions which are used to construct 1-D wavelets. Two frameworks are presented for studying these dilation equations. Fourier methods are used to analyze existence, uniqueness and regularity of solutions. Expansions with infinite matrix products are used to derive an iterated function system (IFS) algorithm for generating the scaling function. Application to subdivision schemes for surface generation is presented, as a genuine multidimensional example where scaling functions arise and the IFS algorithm can be applied.
7385162
On the use of high-order ambiguity function for multi-component polynomial phase signals
Abstract Nonstationary signals appear often in real-life applications and many of them can be modeled as polynomial-phase signals (PPS). High-order ambiguity function (HAF) was first introduced to estimate the parameters of a single-component PPS, but has not been widely used for multi-component PPS because of its nonlinearity. Multi-component PPS arise for example, in Doppler radar applications when multiple objects are tracked simultaneously. In this paper, we show that HAF is virtually additive for multi-component PPS and suggest an algorithm to estimate their parameters. Numerical examples are presented to illustrate the theories.
12678817
Developing a multifunctional network laboratory for teaching and research
Adequate hands-on experience on networking and computing is becoming vital and necessary for students majored in programs such as Information Technology and Computer Science. However, building a hands-on experimental lab environment turns out to be challenging for many institutions, particularly for a new-born program or an urban university, due to space constraints, budget limitations, maintenance difficulty and so on. This paper presents and explores the design of a multifunctional lab environment for both teaching and research while taking the cost and space challenges into consideration. On one hand, the lab utilizes a number of industrial-strength Cisco routers, switches and wireless access points to setup a practical platform that allows students to configure and administrate their network design by applying the knowledge learned in the classroom. On the other hand, the lab is equipped with useful (and mostly free) software packages such as OPNET, Network Simulator (NS-2), Virtual PC, and CPLEX, which enable students to conduct various network modeling, simulation, optimization, and emulation together with their research projects. Accordingly, each iteration for the lab design and implementation as well as experiences learned and future integration with additional curriculum, are presented in this paper.
9587091
Topology control for delay-constraint data collection in wireless sensor networks
Data collection is one of the most important operations in wireless sensor networks. Many practical applications require the real-time data transmission, such as monitoring, tracking, etc. In this paper, we import and define the topology control problem for delay-constraint data collection (TDDC), and then formalize this problem into an integer programming problem. As NP-Hardness of this problem, we present a load-aware power-increased topology control algorithm (namely LPTC) to heuristically solve the problem. The theoretical analysis shows that this algorithm can reach O(1)-approximation ratio for the linear networks. And we also analyze the impact of the delay-constraint on the worst-case for the planar networks. Moreover, this paper designs two localized algorithms, called as SDEL and DDEL, based on the area division for TDDC problem. The experimental results show that LPTC algorithm can save at least 17% power consumptions compared with HBH algorithm in many situations.
16300996
Research on Optimization Algorithm for Attribute Reduction of Decision System
Attribute reduction is one of the central issue in the theoretical research of rough set, aiming at the NP-hard problem of acquiring minimal reduction and all reduction, an optimization algorithm is proposed to construct reduction tree based on discernibility matrix for acquiring attribute reduction. The discernibility set is acquired by improving discernibility matrix first, then the core and reduction candidate information are obtained, finally the minimal reduction and all reduction are sought fast and effectively by considering attribute frequency as heuristic information, and time cost of the algorithm is analyzed. The time complexity of the algorithm is lower than other presented algorithms.
13987121
A Unified Framework for Segmentation-Assisted Image Registration
This paper presents a unified variational framework for seamlessly integrating prior segmentation information into non-rigid registration procedures. Under this framework, in addition to the forces arise from the similarity measure in seeking for detailed correspondence, another set of forces generated by the prior segmentation contours can provide an extra guidance in assisting the alignment process towards a more meaningful, stable and noise-tolerant procedure. Local correlation (LC) is being used as the underlying similarity measures to handle intensity variations. We present several 2D/3D examples on synthetic and real data.
6133036
Serial hook-ups: a comparative usability study of secure device pairing methods
Secure Device Pairing is the bootstrapping of secure communication between two previously unassociated devices over a wireless channel. The human-imperceptible nature of wireless communication, lack of any prior security context, and absence of a common trust infrastructure open the door for Man-in-the-Middle (aka Evil Twin) attacks. A number of methods have been proposed to mitigate these attacks, each requiring user assistance in authenticating information exchanged over the wireless channel via some human-perceptible auxiliary channels, e.g., visual, acoustic or tactile.
 In this paper, we present results of the first comprehensive and comparative study of eleven notable secure device pairing methods. Usability measures include: task performance times, ratings on System Usability Scale (SUS), task completion rates, and perceived security. Study subjects were controlled for age, gender and prior experience with device pairing. We present overall results and identify problematic methods for certain classes of users as well as methods best-suited for various device configurations.