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Improved bounds for the rate loss of multiresolution source codes
 IEEE Transactions on Information Theory
, 2003
"... Abstract—In this paper, we present new bounds for the rate loss of multiresolution source codes (MRSCs). Considering anresolution code, the rate loss at the th resolution with distortion is defined as = (), where is the rate achievable by the MRSC at stage. This rate loss describes the performanc ..."
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Abstract—In this paper, we present new bounds for the rate loss of multiresolution source codes (MRSCs). Considering anresolution code, the rate loss at the th resolution with distortion is defined as = (), where is the rate achievable by the MRSC at stage. This rate loss describes the performance degradation of the MRSC compared to the best singleresolution code with the same distortion. For tworesolution source codes, there are three scenarios of particular interest: i) when both resolutions are equally important; ii) when the rate loss at the first resolution is 0 (
Algorithms for Optimal Multiresolution Quantization”,
 Journal of Algorithms,
, 2004
"... AbstractMultiresolution quantization is a way of constructing a progressively refinable description of a discrete random variable. The underlying discrete optimization problem is to minimize an expected distortion over all refinement levels weighted by the probability or importance of the descrip ..."
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AbstractMultiresolution quantization is a way of constructing a progressively refinable description of a discrete random variable. The underlying discrete optimization problem is to minimize an expected distortion over all refinement levels weighted by the probability or importance of the descriptions of different resolutions. This research is motivated by the application of multimedia communications via variablerate channels. We propose an O(rN 2 ) time and O(N 2 log N ) space algorithm to design a minimumdistortion quantizer of r levels for a random variable drawn from an alphabet of size N . It is shown that for a very large class of distortion measures the objective function of optimal multiresolution quantization satisfies the convex Monge property. The efficiency of the proposed algorithm hinges on the convex Monge property. But our algorithm is simpler (even though of the same asymptotic complexity) than the wellknown SMAWK fast matrix search technique, which is the best existing solution to the quantization problem. For exponential random variables our approach leads to a solution of even lower complexity: O(rN ) time and O(N log N ) space, which outperforms all the known algorithms for optimal quantization in both multiand singleresolution cases. We also generalize the multiresolution quantization problem to a graph problem, for which our algorithm offers an efficient solution.
Robustness and the Internet: Theoretical Foundations
, 2002
"... While control and communications theory have played a crucial role throughout in designing aspects of the Internet, a unified and integrated theory of the Internet as a whole has only recently become a practical and achievable research objective. Dramatic progress has been made recently in analytica ..."
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While control and communications theory have played a crucial role throughout in designing aspects of the Internet, a unified and integrated theory of the Internet as a whole has only recently become a practical and achievable research objective. Dramatic progress has been made recently in analytical results that provide for the first time a nascent but promising foundation for a rigorous and coherent mathematical theory underpinning Internet technology. This new theory addresses directly the performance and robustness of both the “horizontal ” decentralized and asynchronous nature of control in TCP/IP as well as the “vertical ” separation into the layers of the TCP/IP protocol stack from application down to the link layer. These results generalize notions of source and channel coding from information theory as well as decentralized versions of robust control. The new theoretical insights gained about the Internet also combine with our understanding of its origins and evolution to provide a rich source of ideas about complex systems in general. Most surprisingly, our deepening understanding from genomics and molecular biology has revealed that at the network and protocol level, cells and organisms are strikingly similar to technological networks, despite having completely different material substrates, evolution, and development/construction. 1
MULTIRESOLUTION VECTORS: A TREE STRUCTURED VECTOR QUANTIZER APPROACH
, 2002
"... ISR develops, applies and teaches advanced methodologies of design and analysis to solve complex, hierarchical, ..."
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ISR develops, applies and teaches advanced methodologies of design and analysis to solve complex, hierarchical,
3. DATES COVERED 4. TITLE AND SUBTITLE Classification and Compression of MultiResolution Vectors: A Tree Structured Vector Quantizer Approach
"... ISR develops, applies and teaches advanced methodologies of design and analysis to solve complex, hierarchical, ..."
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ISR develops, applies and teaches advanced methodologies of design and analysis to solve complex, hierarchical,
Theoretical Foundations for Ubiquitous, Networked Control, Communications and Computing
"... Our lives are increasingly dominated by our interactions with a wide variety of networks in the areas of transportation, energy,... ..."
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Our lives are increasingly dominated by our interactions with a wide variety of networks in the areas of transportation, energy,...
CLASSIFICATION AND COMPRESSION OF MULTIRESOLUTION VECTORS: A TREE STRUCTURED VECTOR QUANTIZER APPROACH
, 2002
"... Tree structured classifiers and quantizers have been used with good success for problems ranging from successive refinement coding of speech and images to classification of texture, faces and radar returns. Although these methods have worked well in practice there are few results on the theoretical ..."
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Tree structured classifiers and quantizers have been used with good success for problems ranging from successive refinement coding of speech and images to classification of texture, faces and radar returns. Although these methods have worked well in practice there are few results on the theoretical side. We present several existing algorithms for tree structured clustering using multiresolution data and develop some results on their convergence and asymptotic performance. We show that greedy growing algorithms will result in asymptotic distortion going to zero for the case of quantizers and prove termination in finite time for constraints on the rate. We derive an online algorithm for the minimization of distortion. We also show that a multiscale LVQ algorithm for the design of a tree structured classifier converges to an equilibrium point of a related ordinary differential equation. Simulation results and description of several applications are used to illustrate the advantages of this approach.
Network Source Coding
 IEEE Trans. Inform. Theory
, 2004
"... We present an algorithm for designing locally optimal vector quantizers for general networks. We discuss the algorithm’s implementation and compare the performance of the resulting “network vector quantizers” to traditional vector quantizers (VQs) and to ratedistortion (RD) bounds where available ..."
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We present an algorithm for designing locally optimal vector quantizers for general networks. We discuss the algorithm’s implementation and compare the performance of the resulting “network vector quantizers” to traditional vector quantizers (VQs) and to ratedistortion (RD) bounds where available. While some special cases of network codes (e.g., multiresolution (MR) and multiple description (MD) codes) have been studied in the literature, we here present a unifying approach that both includes these existing solutions as special cases and provides solutions to previously unsolved examples.
Classification Results(%) Human Motion Classification
"... •Recent rapid developments of mocap systems have resulted in a large datasets of mocap sequences •An automated annotation technique is needed to fully exploit these datasets ..."
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•Recent rapid developments of mocap systems have resulted in a large datasets of mocap sequences •An automated annotation technique is needed to fully exploit these datasets