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ABSTRACT: We study the source coding problem in sensor networks deployed to monitor the evolution of spatio-temporal temperature distributions. The sensors sample the temperature field, quantize the samples and transmit the encoded samples through digital channels to some central unit, which computes an estimate of the original temperature field. Our analysis is based on the heat kernel's spectral properties, which are induced by the physics of heat diffusion. We determine rate distortion functions for various source coding schemes. In particular, we compare centralized coding, independent coding, Berger-Tung coding, and predictive quantization.
IEEE Transactions on Communications 05/2011; · 1.68 Impact Factor
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ABSTRACT: Directionlets are built as basis functions of critically sampled perfect-reconstruction transforms with directional vanishing moments imposed along different directions. We combine the directionlets with the space-frequency quantization (SFQ) image compression method, originally based on the standard two-dimensional wavelet transform. We show that our new compression method outperforms the standard SFQ as well as the state-of-the-art image compression methods, such as SPIHT and JPEG-2000, in terms of the quality of compressed images, especially in a low-rate compression regime. We also show that the order of computational complexity remains the same, as compared to the complexity of the standard SFQ algorithm.
Information, Communications & Signal Processing, 2007 6th International Conference on; 01/2008
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IEEE/ACM Transactions on Networking 11/2006; 14(5):1150- 1150. · 2.03 Impact Factor
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ABSTRACT: Sensor networks measuring correlated data are considered, where the task is to gather data from the network nodes to a sink. A specific scenario is addressed, where data at nodes are lossy coded with high-resolution, and the information measured by the nodes has to be reconstructed at the sink within both certain total and individual distortion bounds. The first problem considered is to find the optimal transmission structure and the rate-distortion allocations at the various spatially located nodes, such as to minimize the total power consumption cost of the network, by assuming fixed nodes positions. The optimal transmission structure is the shortest path tree and the problems of rate and distortion allocation separate in the high-resolution case, namely, first the distortion allocation is found as a function of the transmission structure, and second, for a given distortion allocation, the rate allocation is computed. The second problem addressed is the case when the node positions can be chosen, by finding the optimal node placement for two different targets of interest, namely total power minimization and network lifetime maximization. Finally, a node placement solution that provides a tradeoff between the two metrics is proposed.
IEEE Transactions on Information Theory 07/2006; · 3.01 Impact Factor
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ABSTRACT: We study the problem of A/D conversion and error-rate dependence of a class of nonbandlimited signals with finite rate of innovation. In particular, we analyze a continuous periodic stream of Diracs, characterized by a finite set of time positions and weights. Previous research has only considered sampling of this type of signals, ignoring the presence of quantization, necessary for any practical implementation. To this end, we first define the concept of consistent reconstruction and introduce corresponding oversampling in both time and frequency. High accuracy in a consistent reconstruction is achieved by enforcing the reconstructed signal to satisfy three sets of constraints, related to low-pass filtering, quantization and the space of continuous periodic streams of Diracs. We provide two schemes to reconstruct the signal. For the first one, we prove that the estimation mean squared error of the time positions is O(1/R<sub>t</sub><sup>2</sup>R<sub>f</sub><sup>3</sup>), where R<sub>t</sub> and R<sub>f</sub> are the oversampling ratios in time and frequency, respectively. For the second scheme, it is experimentally observed that, at the cost of higher complexity, the estimation accuracy lowers to O(1/R<sub>t</sub><sup>2</sup>R<sub>f</sub><sup>5</sup>). Our experimental results show a clear advantage of consistent over nonconsistent reconstruction. Regarding the rate, we consider a threshold crossing based scheme where, as opposed to previous research, both oversampling in time and in frequency influence the coding rate. We compare the error-rate behavior resulting, on the one hand, from increasing the oversampling in time and/or frequency, and, on the other hand, from decreasing the quantization stepsize.
IEEE Transactions on Signal Processing 07/2006; · 2.63 Impact Factor
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ABSTRACT: We consider the problem of correlated data gathering by a network with a sink node and a tree-based communication structure, where the goal is to minimize the total transmission cost of transporting the information collected by the nodes, to the sink node. For source coding of correlated data, we consider a joint entropy-based coding model with explicit communication where coding is simple and the transmission structure optimization is difficult. We first formulate the optimization problem definition in the general case and then we study further a network setting where the entropy conditioning at nodes does not depend on the amount of side information, but only on its availability. We prove that even in this simple case, the optimization problem is NP-hard. We propose some efficient, scalable, and distributed heuristic approximation algorithms for solving this problem and show by numerical simulations that the total transmission cost can be significantly improved over direct transmission or the shortest path tree. We also present an approximation algorithm that provides a tree transmission structure with total cost within a constant factor from the optimal.
IEEE/ACM Transactions on Networking 03/2006; · 2.03 Impact Factor
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ABSTRACT: 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 data-gathering 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 Slepian-Wolf 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 Slepian-Wolf rate region. For the case of data gathering, the optimal transmission structure is fully characterized and a closed-form 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 NP-complete. For large networks, in some simplified scenarios, the total costs associated with Slepian-Wolf 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.
IEEE Transactions on Information Theory 01/2006; 51(12):4057- 4073. · 3.01 Impact Factor
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ABSTRACT: In this work, we consider the problem of designing adaptive distributed processing algorithms in large sensor networks that are efficient in terms of minimizing the total power spent for gathering the spatially correlated data from the sensor nodes to a sink node. We take into account both the power spent for purposes of communication as well as the power spent for local computation. Our distributed algorithms are also matched to the nature of the correlated field, namely, for piecewise smooth signals, we provide two distributed multiresolution wavelet-based algorithms, while for correlated Gaussian fields, we use distributed prediction based processing. In both cases, we provide distributed algorithms that perform network division into groups of different sizes. The distribution of the group sizes within the network is the result of an optimal trade-off between the local communication inside each group needed to perform decorrelation, the communication needed to bring the processed data (coefficients) to the sink and the local computation cost, which grows as the network becomes larger. Our experimental results show clearly that important gains in power consumption can be obtained with respect to the case of not performing any distributed decorrelating processing.
Wireless Networks, Communications and Mobile Computing, 2005 International Conference on; 07/2005
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ABSTRACT: The analysis and design of routing algorithms for finite buffer networks requires solving the associated queue network problem which is known to be hard. We propose alternative and more accurate approximation models to the usual Jackson's theorem that give more insight into the effect of routing algorithms on the queue size distributions. Using the proposed approximation models, we analyze and design routing algorithms that minimize overflow losses in grid networks with finite buffers and different communication patterns, namely uniform communication and data gathering. We show that the buffer size required to achieve the maximum possible rate decreases as the network size increases. Motivated by the insight gained in grid networks, we apply the same principles to the design of routing algorithms for random networks with finite buffers that minimize overflow losses. We show that this requires adequately combining shortest path tree routing and traveling salesman routing. Our results show that such specially designed routing algorithms increase the transmitted rate for a given loss probability up to almost three times, on average, with respect to the usual shortest path tree routing.
Information Processing in Sensor Networks, 2005. IPSN 2005. Fourth International Symposium on; 05/2005
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ABSTRACT: We consider large sensor networks where the cost of collecting data from the network nodes to the data gathering sink is critical. We propose several algorithms that use limited local communication and distributed signal processing to make communication more efficient in terms of transmission cost. We consider a model that uses distributed wavelet-based signal processing. We first propose an algorithm that performs processing at nodes as data is forwarded to the sink. Then, we analyze algorithms that perform network division into groups of adaptive size and for which signal processing is applied separately to each group. We show by numerical simulations that such multiresolution approaches result in significant improvements for data gathering in terms of total communication costs.
Acoustics, Speech, and Signal Processing, 2005. Proceedings. (ICASSP '05). IEEE International Conference on; 04/2005 · 4.63 Impact Factor
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ABSTRACT: We consider 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. This problem requires a joint optimization of the data representation at the nodes and of the transmission structure. First, we study the case when the measured data are correlated random variables, both in the lossless scenario with Slepian-Wolf coding, and in the high-resolution lossy scenario with optimal rate-distortion allocation. We show that the optimal transmission structure is the shortest path tree, and we find, in closed-form, the rate and distortion allocation. Second, we study the case when the measured data are deterministic piecewise constant signals, and data is described with adaptive level wavelet-based multiresolution representation. We show experimentally that, when computation is decentralized, there is an optimal network division into node groups of adaptive size. Finally, we also analyze the node positioning problem where, given a correlation structure and an available number of sensors, the goal is to place the nodes optimally in terms of minimizing the transmission cost; our results show that important gains can be obtained compared to a uniformly distributed sensor positioning
Acoustics, Speech, and Signal Processing, 2005. Proceedings. (ICASSP '05). IEEE International Conference on; 02/2005 · 4.63 Impact Factor
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ABSTRACT: Recent 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 analog-to-digital (A/D) conversion of these signals, introducing two types of oversampling and consistent reconstruction.
Information Theory, 2004. ISIT 2004. Proceedings. International Symposium on; 08/2004
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ABSTRACT: We consider the problem of A/D conversion for non-bandlimited 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/R<sub>t</sub><sup>2</sup> R<sub>f</sub><sup>3</sup>), and O(1/R<sub>t</sub><sup>2</sup> R<sub>f</sub><sup>4</sup>), where R<sub>t</sub> and R<sub>f</sub> 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/R<sub>t</sub><sup>2</sup> R<sub>f</sub><sup>3</sup>).
Acoustics, Speech, and Signal Processing, 2004. Proceedings. (ICASSP '04). IEEE International Conference on; 06/2004 · 4.63 Impact Factor
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ABSTRACT: 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.
Information Processing in Sensor Networks, 2004. IPSN 2004. Third International Symposium on; 05/2004
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ABSTRACT: 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 one-dimensional 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 1-D analysis to extend our results to the 2-D case, and show that our algorithm for two-dimensional placement and transmission structure provides significant power benefit over a commonly used combination of uniformly random placement and shortest path trees.
Information Processing in Sensor Networks, 2004. IPSN 2004. Third International Symposium on; 05/2004
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ABSTRACT: 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 Slepian-Wolf 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 Slepian-Wolf 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 NP-complete and we propose various distributed approximation algorithms.
INFOCOM 2004. Twenty-third AnnualJoint Conference of the IEEE Computer and Communications Societies; 04/2004
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ABSTRACT: In this paper, we propose a new rotation-invariant image retrieval system based on steerable pyramids and the concept of angular alignment across scales. First, we define energy-based texture features which are steerable under rotation, i.e., such that features corresponding to the rotated version of an image can be easily obtained from the features of the original (non-rotated) image. We also propose an approach to measure similarity between images that is robust to rotation; images are compared after being aligned in angle. The retrieval process is performed by means of a decision tree classifier where the angular alignment is performed at each node in the tree. To demonstrate the effectiveness of our system we consider a distributed image classification system, where the feature encoder and the classifier are physically apart and thus features are compressed before being transmitted. Our results of retrieval performance versus rate show a clear gain with respect to a wavelet transform (as an example, for the same rate, the retrieval precision is increased from 40% to 65%).
Image Processing, 2003. ICIP 2003. Proceedings. 2003 International Conference on; 10/2003
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ABSTRACT: We study construction of structured regular quantizers for overcomplete expansions in R<sup>N</sup>. Our goal is to design structured quantizers which allow simple reconstruction algorithms with low complexity and which have good performance in terms of accuracy. Most related work to date in quantized redundant expansions has assumed that the same uniform scalar quantizer was used on all the expansion coefficients. Several approaches have been proposed to improve the reconstruction accuracy, with some of these methods having significant complexity. Instead, we consider the joint design of the overcomplete expansion and the scalar quantizers (allowing different step sizes) in such a way as to produce an equivalent vector quantizer (EVQ) with periodic structure. The construction of a periodic quantizer is based on lattices in R<sup>N</sup> and the concept of geometrically scaled- similar sublattices. The periodicity makes it possible to achieve good accuracy using simple reconstruction algorithms (e.g., linear reconstruction or a small lookup table).
IEEE Transactions on Information Theory 02/2003; · 3.01 Impact Factor
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ABSTRACT: We study the construction of structured regular quantizers for
overcomplete expansions in R<sup>N</sup>. Our goal is to design
structured quantizers allowing simple reconstruction algorithms with low
(memory and computational) complexity and having good performance in
terms of accuracy. Most related work to date in quantized redundant
expansions has assumed that uniform scalar quantization with the same
stepsize was used on the redundant expansion and then has dealt with
more complex methods to improve the reconstruction. Instead, we consider
the design of scalar quantizers with different stepsizes for each
coefficient of an overcomplete expansion in such a way as to produce an
equivalent vector quantizer with periodic structure. The periodicity
makes it possible to achieve good accuracy using simple reconstruction
algorithms from the quantized coefficients of the overcomplete expansion
Data Compression Conference, 2001. Proceedings. DCC 2001.; 02/2001
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ABSTRACT: In this paper we study signal representation using oversampled steerable transforms. While in general it may not be efficient to use an oversampled representation for applications like compression, our work investigates efficient techniques for representing the oversampled data, given that after oversampling there exists substantial redundancy. We discuss different strategies which take advantage of this oversampling by establishing some consistency constraints on the representation that reduce uncertainty in the quantization. This results in a coding gain as we increase the oversampling in the steerable transform (number of orientations). Thus, while in general it will not be possible to achieve as good compression performance as with a critically sampled transform, having a compressed steerable representation will be useful for applications where a feature is needed (many significant image features can be extracted from an orientation analysis), and where for performance reasons it is preferable not to have to decompress and analyze each image (as may be necessary if standard non-steerable transforms are used for compression).
Signals, Systems, and Computers, 1999. Conference Record of the Thirty-Third Asilomar Conference on; 02/1999
