Elimination of Edge Effects Using Spline Wavelets Which Maintain a Uniform Two-Scale Relation

Use of the compactly supported B-spline wavelet of Chui and Wang is hindered by loss of accuracy on decomposition, through truncation of weight sequences which are countably infinite. Adaptations to finite intervals often encounter significant problems with error near boundaries, called edge effects. For multiresolution analysis on a finite interval which employ the piecewise linear B-wavelet the present research provides a frontal approach to decomposition which avoids truncation of weight sequences, experiences no error at boundaries, and which exhibits a factor of three increase in computational efficiency, over the usual approach characterized by truncation of infinite weight sequences. As a further modest contribution, a simple derivation of the piecewise linear B-spline wavelet for L\sb2(R) is given. The simple technique is then applied to the derivation of supplementary boundary wavelets, which are necessary in order to complete the piecewise linear B-wavelet basis on a finite interval. There is also presented a modification to the Chui and Quak piecewise-cubic spline multiresolution analysis for the finite interval. The modification is intended to simplify implementation. Boundary scaling functions with multiple nodes at interval endpoints are rejected, in favor of the classical B-spline scaling function restricted to the interval. This necessitates derivation of revised boundary wavelets. In addition, a direct method of decomposition results in significant bandwidth reduction on solving an associated linear systems. Image distortion is reduced by employing natural spline projection. Finally, a hybrid projection scheme is proposed, which particularly for large systems further lowers operation count. Numerical experiments which try the algorithm are performed: The problems of edge detection, data compression, and data smoothing by thresholding in the wavelet transform domain are examined. The cubic B-spline wavelet yields compression ratios as high as 40 to 1 in the numerical experiments

Wavelets and Subband Coding

First published in 1995, Wavelets and Subband Coding offered a unified view of the exciting field of wavelets and their discrete-time cousins, filter banks, or subband coding. The book developed the theory in both continuous and discrete time, and presented important applications. During the past decade, it filled a useful need in explaining a new view of signal processing based on flexible time-frequency analysis and its applications. Since 2007, the authors now retain the copyright and allow open access to the book

リフティング構造を利用した非分離型ウェーブレット変換のノイズ低減に関する研究

国立大学法人長岡技術科学大

画像の輝度調整に伴うノイズの低減手法とそのデータ圧縮への応用に関する研究

国立大学法人長岡技術科学大

Straggler-Resilient Distributed Computing

In reference to IEEE copyrighted material which is used with permission in this thesis, the IEEE does not endorse any of University of Bergen's products or services. Internal or personal use of this material is permitted. If interested in reprinting/republishing IEEE copyrighted material for advertising or promotional purposes or for creating new collective works for resale or redistribution, please go to http://www.ieee.org/publications_standards/publications/rights/rights_link.html to learn how to obtain a License from RightsLink.Utbredelsen av distribuerte datasystemer har økt betydelig de siste årene. Dette skyldes først og fremst at behovet for beregningskraft øker raskere enn hastigheten til en enkelt datamaskin, slik at vi må bruke flere datamaskiner for å møte etterspørselen, og at det blir stadig mer vanlig at systemer er spredt over et stort geografisk område. Dette paradigmeskiftet medfører mange tekniske utfordringer. En av disse er knyttet til "straggler"-problemet, som er forårsaket av forsinkelsesvariasjoner i distribuerte systemer, der en beregning forsinkes av noen få langsomme noder slik at andre noder må vente før de kan fortsette. Straggler-problemet kan svekke effektiviteten til distribuerte systemer betydelig i situasjoner der en enkelt node som opplever en midlertidig overbelastning kan låse et helt system. I denne avhandlingen studerer vi metoder for å gjøre beregninger av forskjellige typer motstandsdyktige mot slike problemer, og dermed gjøre det mulig for et distribuert system å fortsette til tross for at noen noder ikke svarer i tide. Metodene vi foreslår er skreddersydde for spesielle typer beregninger. Vi foreslår metoder tilpasset distribuert matrise-vektor-multiplikasjon (som er en grunnleggende operasjon i mange typer beregninger), distribuert maskinlæring og distribuert sporing av en tilfeldig prosess (for eksempel det å spore plasseringen til kjøretøy for å unngå kollisjon). De foreslåtte metodene utnytter redundans som enten blir introdusert som en del av metoden, eller som naturlig eksisterer i det underliggende problemet, til å kompensere for manglende delberegninger. For en av de foreslåtte metodene utnytter vi redundans for også å øke effektiviteten til kommunikasjonen mellom noder, og dermed redusere mengden data som må kommuniseres over nettverket. I likhet med straggler-problemet kan slik kommunikasjon begrense effektiviteten i distribuerte systemer betydelig. De foreslåtte metodene gir signifikante forbedringer i ventetid og pålitelighet sammenlignet med tidligere metoder.The number and scale of distributed computing systems being built have increased significantly in recent years. Primarily, that is because: i) our computing needs are increasing at a much higher rate than computers are becoming faster, so we need to use more of them to meet demand, and ii) systems that are fundamentally distributed, e.g., because the components that make them up are geographically distributed, are becoming increasingly prevalent. This paradigm shift is the source of many engineering challenges. Among them is the straggler problem, which is a problem caused by latency variations in distributed systems, where faster nodes are held up by slower ones. The straggler problem can significantly impair the effectiveness of distributed systems—a single node experiencing a transient outage (e.g., due to being overloaded) can lock up an entire system. In this thesis, we consider schemes for making a range of computations resilient against such stragglers, thus allowing a distributed system to proceed in spite of some nodes failing to respond on time. The schemes we propose are tailored for particular computations. We propose schemes designed for distributed matrix-vector multiplication, which is a fundamental operation in many computing applications, distributed machine learning—in the form of a straggler-resilient first-order optimization method—and distributed tracking of a time-varying process (e.g., tracking the location of a set of vehicles for a collision avoidance system). The proposed schemes rely on exploiting redundancy that is either introduced as part of the scheme, or exists naturally in the underlying problem, to compensate for missing results, i.e., they are a form of forward error correction for computations. Further, for one of the proposed schemes we exploit redundancy to also improve the effectiveness of multicasting, thus reducing the amount of data that needs to be communicated over the network. Such inter-node communication, like the straggler problem, can significantly limit the effectiveness of distributed systems. For the schemes we propose, we are able to show significant improvements in latency and reliability compared to previous schemes.Doktorgradsavhandlin

Object-based 3-d motion and structure analysis for video coding applications

Ankara : Department of Electrical and Electronics Engineering and the Institute of Engineering and Sciences of Bilkent University, 1997.Thesis (Ph.D.) -- -Bilkent University, 1997.Includes bibliographical references leaves 102-115Novel 3-D motion analysis tools, which can be used in object-based video codecs, are proposed. In these tools, the movements of the objects, which are observed through 2-D video frames, are modeled in 3-D space. Segmentation of 2-D frames into objects and 2-D dense motion vectors for each object are necessary as inputs for the proposed 3-D analysis. 2-D motion-based object segmentation is obtained by Gibbs formulation; the initialization is achieved by using a fast graph-theory based region segmentation algorithm which is further improved to utilize the motion information. Moreover, the same Gibbs formulation gives the needed dense 2-D motion vector field. The formulations for the 3-D motion models are given for both rigid and non- rigid moving objects. Deformable motion is modeled by a Markov random field which permits elastic relations between neighbors, whereas, rigid 3-D motion parameters are estimated using the E-matrix method. Some improvements on the E-matrix method are proposed to make this algorithm more robust to gross errors like the consequence of incorrect segmentation of 2-D correspondences between frames. Two algorithms are proposed to obtain dense depth estimates, which are robust to input errors and suitable for encoding, respectively. While the former of these two algorithms gives simply a MAP estimate, the latter uses rate-distortion theory. Finally, 3-D motion models are further utilized for occlusion detection and motion compensated temporal interpolation, and it is observed that for both applications 3-D motion models have superiority over their 2-D counterparts. Simulation results on artificial and real data show the advantages of the 3-D motion models in object-based video coding algorithms.Alatan, A AydinPh.D

Greedy routing and virtual coordinates for future networks

At the core of the Internet, routers are continuously struggling with ever-growing routing and forwarding tables. Although hardware advances do accommodate such a growth, we anticipate new requirements e.g. in data-oriented networking where each content piece has to be referenced instead of hosts, such that current approaches relying on global information will not be viable anymore, no matter the hardware progress. In this thesis, we investigate greedy routing methods that can achieve similar routing performance as today but use much less resources and which rely on local information only. To this end, we add specially crafted name spaces to the network in which virtual coordinates represent the addressable entities. Our scheme enables participating routers to make forwarding decisions using only neighbourhood information, as the overarching pseudo-geometric name space structure already organizes and incorporates "vicinity" at a global level. A first challenge to the application of greedy routing on virtual coordinates to future networks is that of "routing dead-ends" that are local minima due to the difficulty of consistent coordinates attribution. In this context, we propose a routing recovery scheme based on a multi-resolution embedding of the network in low-dimensional Euclidean spaces. The recovery is performed by routing greedily on a blurrier view of the network. The different network detail-levels are obtained though the embedding of clustering-levels of the graph. When compared with higher-dimensional embeddings of a given network, our method shows a significant diminution of routing failures for similar header and control-state sizes. A second challenge to the application of virtual coordinates and greedy routing to future networks is the support of "customer-provider" as well as "peering" relationships between participants, resulting in a differentiated services environment. Although an application of greedy routing within such a setting would combine two very common fields of today's networking literature, such a scenario has, surprisingly, not been studied so far. In this context we propose two approaches to address this scenario. In a first approach we implement a path-vector protocol similar to that of BGP on top of a greedy embedding of the network. This allows each node to build a spatial map associated with each of its neighbours indicating the accessible regions. Routing is then performed through the use of a decision-tree classifier taking the destination coordinates as input. When applied on a real-world dataset (the CAIDA 2004 AS graph) we demonstrate an up to 40% compression ratio of the routing control information at the network's core as well as a computationally efficient decision process comparable to methods such as binary trees and tries. In a second approach, we take inspiration from consensus-finding in social sciences and transform the three-dimensional distance data structure (where the third dimension encodes the service differentiation) into a two-dimensional matrix on which classical embedding tools can be used. This transformation is achieved by agreeing on a set of constraints on the inter-node distances guaranteeing an administratively-correct greedy routing. The computed distances are also enhanced to encode multipath support. We demonstrate a good greedy routing performance as well as an above 90% satisfaction of multipath constraints when relying on the non-embedded obtained distances on synthetic datasets. As various embeddings of the consensus distances do not fully exploit their multipath potential, the use of compression techniques such as transform coding to approximate the obtained distance allows for better routing performances

Multiplexing, scheduling, and multicasting strategies for antenna arrays in wireless networks

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2002.Includes bibliographical references (p. 167-174).This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.A transmitter antenna array has the ability to direct data simultaneously to multiple receivers within a wireless network, creating potential for a more integrated view of algorithmic system components. In this thesis, such a perspective informs the design of two system tasks: the scheduling of packets from a number of data streams into groups; and the subsequent spatial multiplexing and encoding of these groups using array processing. We demonstrate how good system designs can help these two tasks reinforce one another, or alternatively enable tradeoffs in complexity between the two. Moreover, scheduling and array processing each benefit from a further awareness of both the fading channel state and certain properties of the data, providing information about key flexibilities, constraints and goals. Our development focuses on techniques that lead to high performance even with very low-complexity receivers. We first consider spatial precoding under simple scheduling and propose several extensions for implementation, such as a unified time-domain precoder that compensates for both cross-channel and intersymbol interfer- ence. We then show how more sophisticated, channel-aware scheduling can reduce the complexity requirements of the array processing. The scheduling algorithms presented are based on the receivers' fading channel realizations and the delay tolerances of the data streams. Finally, we address the multicasting of common data streams in terms of opportunities for reduced redundancy as well as the conflicting objectives inherent in sending to multiple receivers. Our channel-aware extensions of space-time codes for multicasting gain several dB over traditional versions that do not incorporate channel knowledge.by Michael J. Lopez.Ph.D

Multiplexing, Scheduling, and Multicasting Strategies for Antenna Arrays in Wireless Networks

Grant number: CCR-9979363A transmitter antenna array has the ability to direct data simultaneously to multiple receivers within a wireless network, creating potential for a more integrated view of algorithmic system components. In this thesis, such a perspective informs the design of two system tasks: the scheduling of packets from a number of data streams into groups; and the subsequent spatial multiplexing and encoding of these groups using array processing. We demonstrate how good system designs can help these two tasks reinforce one another, or alternatively enable tradeoffs in complexity between the two. Moreover, scheduling and array processing each benefit from a further awareness of both the fading channel state and certain properties of the data, providing information about key flexibilities, constraints and goals. Our development focuses on techniques that lead to high performance even with very low-complexity receivers. We first consider spatial precoding under simple scheduling and propose several extensions for implementation, such as a unified timedomain precoder that compensates for both cross-channel and intersymbol interference. We then show how more sophisticated, channel-aware scheduling can reduce the complexity requirements of the array processing. The scheduling algorithms presented are based on the receivers’ fading channel realizations and the delay tolerances of the data streams. Finally, we address the multicasting of common data streams in terms of opportunities for reduced redundancy as well as the conflicting objectives inherent in sending to multiple receivers. Our channel-aware extensions of space-time codes for multicasting gain several dB over traditional versions that do not incorporate channel knowledge.NSF, HP/MIT Alliance