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RateDistortion problem for Physicsbased distributed sensing
BeferullLozano, B.; Konsbruck, R. L.; Vetterli, M.
(2004). ArticleWe consider the ratedistortion problem for sensing the continuous spacetime physical temperature in a circular ring on which a heat source is applied over space and time, and which is also allowed to cool by radiation or convection to its surrounding medium. The heat source is modelled as a continuous spacetime stochastic process which is bandlimited over space and time. The temperature field is the result of a circular convolution over space and a continuoustime causal filtering over time of the heat source with the Green's function corresponding to the heat equation, which is space and time invariant. The temperature field is sampled at uniform spatial locations by a set of sensors...
We consider the ratedistortion problem for sensing the continuous spacetime physical temperature in a circular ring on which a heat source is applied over space and time, and which is also allowed to cool by radiation or convection to its surrounding medium. The heat source is modelled as a continuous spacetime stochastic process which is bandlimited over space and time. The temperature field is the result of a circular convolution over space and a continuoustime causal filtering over time of the heat source with the Green's function corresponding to the heat equation, which is space and time invariant. The temperature field is sampled at uniform spatial locations by a set of sensors and it has to be reconstructed at a base station. The goal is to minimize the meansquareerror per second, for a given number of nats per second, assuming ideal communication channels between sensors and base station. We find a) the centralized Rc (D) function of the temperature field, where all the spacetime samples can be observed and encoded jointly. Then, we obtain b) the Rsi (D) function, where each sensor, independently, encodes its samples optimally over time and c) the Rsti (D) function, where each sensor is constrained to encode also independently over time. We also study two distributed predictionbased approaches: a) with perfect feedback from the base station, where temporal prediction is performed at the base station and each sensor performs differential encoding, and b) without feedback, where each sensor locally performs temporal prediction.
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Networked SlepianWolf: Theory and Algorithms
Cristescu, R.; BeferullLozano, B.; Vetterli, M.
(2004). ArticleConsider a set of correlated sources located at the nodes of a network, and a set of sinks that are the destinations for some of the sources. The minimization of cost functions which are the product of a function of the rate and a function of the path weight is considered, for both the datagathering scenario, which is relevant in sensor networks, and general traffic matrices, relevant for general networks. The minimization is achieved by jointly optimizing a) the transmission structure, which is shown to consist in general of a superposition of trees, and b) the rate allocation across the source nodes, which is done by SlepianWolf coding. The overall minimization can be achieved in two...
Consider a set of correlated sources located at the nodes of a network, and a set of sinks that are the destinations for some of the sources. The minimization of cost functions which are the product of a function of the rate and a function of the path weight is considered, for both the datagathering scenario, which is relevant in sensor networks, and general traffic matrices, relevant for general networks. The minimization is achieved by jointly optimizing a) the transmission structure, which is shown to consist in general of a superposition of trees, and b) the rate allocation across the source nodes, which is done by SlepianWolf coding. The overall minimization can be achieved in two concatenated steps. First, the optimal transmission structure is found, which in general amounts to finding a Steiner tree, and second, the optimal rate allocation is obtained by solving an optimization problem with cost weights determined by the given optimal transmission structure, and with linear constraints given by the SlepianWolf rate region. For the case of data gathering, the optimal transmission structure is fully characterized and a closedform solution for the optimal rate allocation is provided. For the general case of an arbitrary traffic matrix, the problem of finding the optimal transmission structure is NPcomplete. For large networks, in some simplified scenarios, the total costs associated with SlepianWolf coding and explicit communication (conditional encoding based on explicitly communicated side information) are compared. Finally, the design of decentralized algorithms for the optimal rate allocation is analyzed.
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On Network Correlated Data Gathering
Cristescu, R.; BeferullLozano, B.; Vetterli, M.
(2004). ArticleWe consider the problem of correlated data gathering by a network with a sink node and a tree communication structure, where the goal is to minimize the total transmission cost of transporting the information collected by the nodes, to the sink node. Two coding strategies are analyzed: a SlepianWolf model where optimal coding is complex and transmission optimization is simple, and a joint entropy coding model with explicit communication where coding is simple and transmission optimization is difficult. This problem requires a joint optimization of the rate allocation at the nodes and of the transmission structure. For the SlepianWolf setting, we derive a closed form solution and an...
We consider the problem of correlated data gathering by a network with a sink node and a tree communication structure, where the goal is to minimize the total transmission cost of transporting the information collected by the nodes, to the sink node. Two coding strategies are analyzed: a SlepianWolf model where optimal coding is complex and transmission optimization is simple, and a joint entropy coding model with explicit communication where coding is simple and transmission optimization is difficult. This problem requires a joint optimization of the rate allocation at the nodes and of the transmission structure. For the SlepianWolf setting, we derive a closed form solution and an efficient distributed approximation algorithm with a good performance. For the explicit communication case, we prove that building an optimal data gathering tree is NPcomplete and we propose various distributed approximation algorithms.
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Scaling Laws for Correlated Data Gathering
Cristescu, R.; BeferullLozano, B.; Vetterli, M.
(2004). ArticleConsider a set of correlated sources located at the nodes of a network, and a sink to which the data from all the sources have to arrive. We address the minimization of a separable joint communication cost function given by the product [rate] o [edge weight]. We present two possible approaches for rate allocation, namely SlepianWolf coding, and coding by explicit communication, and compare asymptotically (large networks) the associated total costs by finding their corresponding scaling laws and analyzing the ratio between them. We also provide the specific conditions on the correlation structure which determine the different cases of asymptotic behaviors.

Oversampled A/D Conversion of NonBandlimited Signals with Finite Rate of Innovation
Jovanovic, I.; BefferullLozano, B.
(2004). ArticleWe consider the problem of A/D conversion for nonbandlimited signals that have a finite rate of innovation, in particular, the class of a continuous periodic stream of Diracs, characterized by a set of time positions and weights. Previous research has only considered the sampling of these signals, ignoring quantization which is necessary for any practical application (e.g. UWB, CDMA). In order to achieve accuracy under quantization, we introduce two types of oversampling, namely, oversampling in frequency and oversampling in time. High accuracy is achieved by enforcing the reconstruction to satisfy either three convex sets of constraints related to (1) sampling kernel, (2) quantization and...
We consider the problem of A/D conversion for nonbandlimited signals that have a finite rate of innovation, in particular, the class of a continuous periodic stream of Diracs, characterized by a set of time positions and weights. Previous research has only considered the sampling of these signals, ignoring quantization which is necessary for any practical application (e.g. UWB, CDMA). In order to achieve accuracy under quantization, we introduce two types of oversampling, namely, oversampling in frequency and oversampling in time. High accuracy is achieved by enforcing the reconstruction to satisfy either three convex sets of constraints related to (1) sampling kernel, (2) quantization and (3) periodic streams of Diracs, which is then said to provide strong consistency, or only the first two, providing weak consistency. We propose three reconstruction algorithms, the first two achieving weak consistency and the third one achieving strong consistency. For these three algorithms, respectively, the experimental MSE performance for time positions decreases as O(1/Rt2 Rf3), and O(1/Rt2 Rf4), where Rt and Rf are the oversampling ratios in time and in frequency, respectively. It is also proved theoretically that our reconstruction algorithms satisfying weak consistency achieve an MSE performance of at least O(1/Rt2 Rf3).
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ErrorRate Dependence of NonBandlimited Signals with Finite Rate of Innovation
Jovanovic, I.; BeferullLozano, B.
(2004). ArticleRecent results in sampling theory [M. Vetterli et al., (2002)] showed that perfect reconstruction of nonbandlimited signals with finite rate of innovation can be achieved performing uniform sampling at or above the rate of innovation. We study analogtodigital (A/D) conversion of these signals, introducing two types of oversampling and consistent reconstruction.

PowerEfficient Sensor Placement and Transmission Structure for Data Gathering under Distortion Constraints
Ganesan, D.; Cristescu, R.; BeferullLozano, B.
(2004). ArticleWe consider the joint optimization of sensor placement and transmission structure for data gathering, where a given number of nodes need to be placed in a field such that the sensed data can be reconstructed at a sink within specified distortion bounds while minimizing the energy consumed for communication. We assume that the nodes use joint entropy coding based on explicit communication between sensor nodes, and consider both maximum and average distortion bounds. The optimization is complex since it involves an interplay between the spaces of possible transmission structures given radio reachability limitations, and feasible placements satisfying distortion bounds. We address this problem...
We consider the joint optimization of sensor placement and transmission structure for data gathering, where a given number of nodes need to be placed in a field such that the sensed data can be reconstructed at a sink within specified distortion bounds while minimizing the energy consumed for communication. We assume that the nodes use joint entropy coding based on explicit communication between sensor nodes, and consider both maximum and average distortion bounds. The optimization is complex since it involves an interplay between the spaces of possible transmission structures given radio reachability limitations, and feasible placements satisfying distortion bounds. We address this problem by first looking at the simplified problem of optimal placement in the onedimensional case. An analytical solution is derived for the case when there is a simple aggregation scheme, and numerical results are provided for the cases when joint entropy encoding is used. We use the insight from our 1D analysis to extend our results to the 2D case, and show that our algorithm for twodimensional placement and transmission structure provides significant power benefit over a commonly used combination of uniformly random placement and shortest path trees.
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Subgaussian rotationinvariant features for steerable waveletbased image retrieval
Tzagkarakis, G.; BeferullLozano, B.; Tsakalides, P.
(2004). ArticleThis paper presents a new rotationinvariant image retrieval method, which extends a recently introduced classification technique based on steerable wavelet transforms. In the proposed procedure, the feature extraction step consists of estimating the covariations (lowerorder crosscorrelations) between the wavelet subband coefficients, which are modeled as subGaussian random vectors. The similarity measurement is carried out first by employing norms calculating the distance between the covariation matrices representing two distinct images and second by evaluating the KullbackLeibler Distance (KLD) between their corresponding subGaussian distributions. We provide analytical expressions...
This paper presents a new rotationinvariant image retrieval method, which extends a recently introduced classification technique based on steerable wavelet transforms. In the proposed procedure, the feature extraction step consists of estimating the covariations (lowerorder crosscorrelations) between the wavelet subband coefficients, which are modeled as subGaussian random vectors. The similarity measurement is carried out first by employing norms calculating the distance between the covariation matrices representing two distinct images and second by evaluating the KullbackLeibler Distance (KLD) between their corresponding subGaussian distributions. We provide analytical expressions relating the subGaussian features corresponding to a rotated image from the features of the original image. Finally, we relate the employed optimal lowerorder correlation (p≤2) to the degree of nonGaussianity of the wavelet coefficients, and we demonstrate the effectiveness of our method using real texture images.
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Lattice Sensor Networks: Capacity Limits, Optimal Routing and Robustness to Failures
Barreneche, G.; BeferullLozano, B.; Vetterli, M.
(2004). ArticleWe study network capacity limits and optimal routing algorithms for regular sensor networks, namely, square and torus grid sensor networks, in both, the static case (no node failures) and the dynamic case (node failures). For static networks, we derive upper bounds on the network capacity and then we characterize and provide optimal routing algorithms whose rate per node is equal to this upper bound, thus, obtaining the exact analytical expression for the network capacity. For dynamic networks, the unreliability of the network is modeled in two ways: a Markovian node failure and an energy based node failure. Depending on the probability of node failure that is present in the network, we...
We study network capacity limits and optimal routing algorithms for regular sensor networks, namely, square and torus grid sensor networks, in both, the static case (no node failures) and the dynamic case (node failures). For static networks, we derive upper bounds on the network capacity and then we characterize and provide optimal routing algorithms whose rate per node is equal to this upper bound, thus, obtaining the exact analytical expression for the network capacity. For dynamic networks, the unreliability of the network is modeled in two ways: a Markovian node failure and an energy based node failure. Depending on the probability of node failure that is present in the network, we propose to use a particular combination of two routing algorithms, the first one being optimal when there are no node failures at all and the second one being appropriate when the probability of node failure is high. The combination of these two routing algorithms defines a family of randomized routing algorithms, each of them being suitable for a given probability of node failure.
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RateDistortion Problem for Physics Based Distributed Sensing
BeferullLozano, B.; Konsbruck, Robert L.; Vetterli, M.
(2004). ArticleWe consider the ratedistortion problem for sensing the continuous spacetime physical temperature in a circular ring on which a heat source is applied over space and time, and which is also allowed to cool by radiation or convection to its surrounding medium. The heat source is modelled as a continuous spacetime stochastic process which is bandlimited over space and time. The temperature field is the result of a circular convolution over space and a continuoustime causal filtering over time of the heat source with the Green's function corresponding to the heat equation, which is space and time invariant. The temperature field is sampled at uniform spatial locations by a set of sensors...
We consider the ratedistortion problem for sensing the continuous spacetime physical temperature in a circular ring on which a heat source is applied over space and time, and which is also allowed to cool by radiation or convection to its surrounding medium. The heat source is modelled as a continuous spacetime stochastic process which is bandlimited over space and time. The temperature field is the result of a circular convolution over space and a continuoustime causal filtering over time of the heat source with the Green's function corresponding to the heat equation, which is space and time invariant. The temperature field is sampled at uniform spatial locations by a set of sensors and it has to be reconstructed at a base station. The goal is to minimize the meansquareerror per second, for a given number of nats per second, assuming ideal communication channels between sensors and base station. We find a) the centralized Rc (D) function of the temperature field, where all the spacetime samples can be observed and encoded jointly. Then, we obtain b) the Rsi (D) function, where each sensor, independently, encodes its samples optimally over time and c) the Rsti (D) function, where each sensor is constrained to encode also independently over time. We also study two distributed predictionbased approaches: a) with perfect feedback from the base station, where temporal prediction is performed at the base station and each sensor performs differential encoding, and b) without feedback, where each sensor locally performs temporal prediction.
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