We focus on a multidimensional field with uncorrelated spectrum and study the quality of the reconstructed signal when the field samples are irregularly spaced and affected by independent and identically distributed noise. More specifically, we apply linear reconstruction techniques and take the mean-square error (MSE) of the field estimate as a metric to evaluate the signal reconstruction quality. We find that the MSE analysis could be carried out by using the closed-form expression of the eigenvalue distribution of the matrix representing the sampling system. Unfortunately, such distribution is still unknown. Thus, we first derive a closed-form expression of the distribution moments, and we find that the eigenvalue distribution tends to the Marcenko-Pastur distribution as the field dimension goes to infinity. Finally, by using our approach, we derive a tight approximation to the MSE of the reconstructed field.
In the context of sensor networks, efficient techniques for spatial sampling are proposed in @cite_28 @cite_30 . In particular, in @cite_30 , an adaptive sampling is described, which allows the central data-collector to vary the number of active sensors, i.e., samples, according to the desired resolution level. Data acquisition is also studied in @cite_36 , where the authors consider a unidimensional field, uniformly sampled at the Nyquist frequency by low precision sensors. The authors show that the number of samples can be traded-off with the precision of sensors. The problem of the reconstruction of a bandlimited signal from an irregular set of samples at unknown locations is addressed in @cite_5 . There, different solution methods are proposed, and the conditions for which there exist multiple solutions or a unique solution are discussed. Differently from @cite_5 , we assume that the sink can either acquire or estimate the sensor locations and that sensors are randomly deployed.
@cite_28 @cite_5 @cite_36 @cite_30
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We consider wireless sensor networks whose nodes are randomly deployed and, thus, provide an irregular sampling of the sensed field. The field is assumed to be bandlimited; a sink node collects the data gathered by the sensors and reconstructs the field by using a technique based on linear filtering. By taking the mean square error (MSE) as performance metric, we evaluate the effect of quasi-equally spaced sensor layouts on the quality of the reconstructed signal. The MSE is derived through asymptotic analysis for different sensor spatial distributions, and for two of them we are able to obtain an approximate closed form expression. The case of uniformly distributed sensors is also considered for the sake of comparison. The validity of our asymptotic analysis is shown by comparison against numerical results and it is proven to hold even for a small number of nodes. Finally, with the help of a simple example, we show the key role that our results play in the deployment of sensor networks. We address the problem of deterministic oversampling of bandlimited sensor fields in a distributed communication-constrained processing environment, where it is desired for a central intelligent unit to reconstruct the sensor field to maximum pointwise accuracy.We show, using a dither-based sampling scheme, that is is possible to accomplish this using minimal inter-sensor communication with the aid of a multitude of low-precision sensors. Furthermore, we show the feasibility of having a flexible tradeoff between the average oversampling rate and the Analog to Digital (A D) quantization precision per sensor sample with respect to achieving exponential accuracy in the number of bits per Nyquist-period, thereby exposing a key underpinning "conservation of bits" principle. That is, we can distribute the bit budget per Nyquist-period along the amplitude-axis (precision of A D converter) and space (or time or space-time) using oversampling in an almost arbitrary discrete-valued manner, while retaining the same reconstruction error decay profile. Interestingly this oversampling is possible in a highly localized communication setting, with only nearest-neighbor communication, making it very attractive for dense sensor networks operating under stringent inter-node communication constraints. Finally we show how our scheme incorporates security as a by-product due to the presence of an underlying dither signal which can be used as a natural encryption device for security. The choice of the dither function enhances the security of the network. In a document network such as a citation network of scientific documents, web-logs, etc., the content produced by authors exhibits their interest in certain topics. In addition some authors influence other authors' interests. In this work, we propose to model the influence of cited authors along with the interests of citing authors. Moreover, we hypothesize that apart from the citations present in documents, the context surrounding the citation mention provides extra topical information about the cited authors. However, associating terms in the context to the cited authors remains an open problem. We propose novel document generation schemes that incorporate the context while simultaneously modeling the interests of citing authors and influence of the cited authors. Our experiments show significant improvements over baseline models for various evaluation criteria such as link prediction between document and cited author, and quantitatively explaining unseen text. Scholars are increasingly citing electronic “web references” which are not preserved in libraries or full text archives. WebCite is a new standard for citing web references. To “webcite” a document involves archiving the cited Web page through www.webcitation.org and citing the WebCite permalink instead of (or in addition to) the unstable live Web page. This journal has amended its “instructions for authors” accordingly, asking authors to archive cited Web pages before submitting a manuscript. Almost 200 other journals are already using the system. We discuss the rationale for WebCite, its technology, and how scholars, editors, and publishers can benefit from the service. Citing scholars initiate an archiving process of all cited Web references, ideally before they submit a manuscript. Authors of online documents and websites which are expected to be cited by others can ensure that their work is permanently available by creating an archived copy using WebCite and providing the citation information including the WebCite link on their Web document(s). Editors should ask their authors to cache all cited Web addresses (Uniform Resource Locators, or URLs) “prospectively” before submitting their manuscripts to their journal. Editors and publishers should also instruct their copyeditors to cache cited Web material if the author has not done so already. Finally, WebCite can process publisher submitted “citing articles” (submitted for example as eXtensible Markup Language [XML] documents) to automatically archive all cited Web pages shortly before or on publication. Finally, WebCite can act as a focussed crawler, caching retrospectively references of already published articles. Copyright issues are addressed by honouring respective Internet standards (robot exclusion files, no-cache and no-archive tags). Long-term preservation is ensured by agreements with libraries and digital preservation organizations. The resulting WebCite Index may also have applications for research assessment exercises, being able to measure the impact of Web services and published Web documents through access and Web citation metrics. @PARASPLIT [J Med Internet Res 2005;7(5):e60] Distributed sampling and reconstruction of a physical field using an array of sensors is a problem of considerable interest in environmental monitoring applications of sensor networks. Our recent work has focused on the sampling of bandlimited sensor fields. However, sensor fields are not perfectly bandlimited but typically have rapidly decaying spectra. In a classical sampling set-up it is possible to precede the A D sampling operation with an appropriate analog anti-aliasing filter. However, in the case of sensor networks, this is infeasible since sampling must precede filtering. We show that even though the effects of aliasing on the reconstruction cannot be prevented due to the "filter-less" sampling constraint, they can be suitably controlled by oversampling and carefully reconstructing the field from the samples. We show using a dither-based scheme that it is possible to estimate non-bandlimited fields with a precision that depends on how fast the spectral content of the field decays. We develop a framework for analyzing non-bandlimited fields that lead to upper bounds on the maximum pointwise error for a spatial bit rate of R bits meter. We present results for fields with exponentially decaying spectra as an illustration. In particular, we show that for fields f(t) with exponential tails; i.e., F( spl omega ) < spl pi spl alpha sup - spl alpha | spl omega | , the maximum pointwise error decays as c2e sup -a sub 1 spl radic R+ c3 1 spl radic R (e sup -2a sub 1 spl radic R) with spatial bit rate R bits meter. Finally, we show that for fields with spectra that have a finite second moment, the distortion decreases as O((1 N) sup 2 3 ) as the density of sensors, N, scales up to infinity . We show that if D is the targeted non-zero distortion, then the required (finite) rate R scales as O (1 spl radic D log 1 D). Abstract Irregular sampling and “stable sampling” of band-limited functions have been studied by H.J. Landau [H.J. Landau, Necessary density conditions for sampling and interpolation of certain entire functions, Acta Math. 117 (1967) 37–52]. We prove that quasicrystals are sets of stable sampling. To cite this article: B. Matei, Y. Meyer, C. R. Acad. Sci. Paris, Ser. I 346 (2008). In this paper, we study how to reduce energy consumption in large-scale sensor networks, which systematically sample a spatio-temporal field. We begin by formulating a distributed compression problem subject to aggregation (energy) costs to a single sink. We show that the optimal solution is greedy and based on ordering sensors according to their aggregation costs-typically related to proximity-and, perhaps surprisingly, it is independent of the distribution of data sources. Next, we consider a simplified hierarchical model for a sensor network including multiple sinks, compressors aggregation nodes, and sensors. Using a reasonable metric for energy cost, we show that the optimal organization of devices is associated with a Johnson-Mehl tessellation induced by their locations. Drawing on techniques from stochastic geometry, we analyze the energy savings that optimal hierarchies provide relative to previously proposed organizations based on proximity, i.e., associated Voronoi tessellations. Our analysis and simulations show that an optimal organization of aggregation compression can yield 8 -28 energy savings depending on the compression ratio. While high resolution, regularly gridded observations are generally preferred in remote sensing, actual observations are often not evenly sampled and have lower-than-desired resolution. Hence, there is an interest in resolution enhancement and image reconstruction. This paper discusses a general theory and techniques for image reconstruction and creating enhanced resolution images from irregularly sampled data. Using irregular sampling theory, we consider how the frequency content in aperture function-attenuated sidelobes can be recovered from oversampled data using reconstruction techniques, thus taking advantage of the high frequency content of measurements made with nonideal aperture filters. We show that with minor modification, the algebraic reconstruction technique (ART) is functionally equivalent to Grochenig's (1992) irregular sampling reconstruction algorithm. Using simple Monte Carlo simulations, we compare and contrast the performance of additive ART, multiplicative ART, and the scatterometer image reconstruction (SIR) (a derivative of multiplicative ART) algorithms with and without noise. The reconstruction theory and techniques have applications with a variety of sensors and can enable enhanced resolution image production from many nonimaging sensors. The technique is illustrated with ERS-2 and SeaWinds scatterometer data. We discuss the design of an acquisitional query processor for data collection in sensor networks. Acquisitional issues are those that pertain to where, when, and how often data is physically acquired (sampled) and delivered to query processing operators. By focusing on the locations and costs of acquiring data, we are able to significantly reduce power consumption over traditional passive systems that assume the a priori existence of data. We discuss simple extensions to SQL for controlling data acquisition, and show how acquisitional issues influence query optimization, dissemination, and execution. We evaluate these issues in the context of TinyDB, a distributed query processor for smart sensor devices, and show how acquisitional techniques can provide significant reductions in power consumption on our sensor devices. The design of conventional sensors is based primarily on the Shannon?Nyquist sampling theorem, which states that a signal of bandwidth W Hz is fully determined by its discrete time samples provided the sampling rate exceeds 2 W samples per second. For discrete time signals, the Shannon?Nyquist theorem has a very simple interpretation: the number of data samples must be at least as large as the dimensionality of the signal being sampled and recovered. This important result enables signal processing in the discrete time domain without any loss of information. However, in an increasing number of applications, the Shannon-Nyquist sampling theorem dictates an unnecessary and often prohibitively high sampling rate (see lWhat Is the Nyquist Rate of a Video Signal?r). As a motivating example, the high resolution of the image sensor hardware in modern cameras reflects the large amount of data sensed to capture an image. A 10-megapixel camera, in effect, takes 10 million measurements of the scene. Yet, almost immediately after acquisition, redundancies in the image are exploited to compress the acquired data significantly, often at compression ratios of 100:1 for visualization and even higher for detection and classification tasks. This example suggests immense wastage in the overall design of conventional cameras. In this paper we study the global localization problem in SLAM: the determination of the vehicle location in a previously mapped environment with no other prior information. We show that, using a grid sampling representation of the configuration space, it is possible to evaluate all vehicle location hypotheses in the environment (up to a certain resolution) with a computational cost that is bilinear: linear both in the number of map features and in the number of sensor measurements. We propose a pairing-driven algorithm that considers only individual measurement-feature pairings and thus, in contrast with current correspondence space algorithms, it avoids searching in the exponential correspondence space. It uses a voting strategy that accumulates evidence for each vehicle location hypothesis, assuring robustness to noise in the sensor measurements and environment models. The general nature of the proposed strategy allows the consideration of different types of features and sensor measurements. Using the popular Victoria Park dataset, we compare its performance with location-driven algorithms where the solution space is usually randomly sampled. We show that the proposed pairing-driven technique is computationally more efficient in proportion to the density of features in the environment. This paper addresses the problem of driving robotic sensors for an energy-constrained mobile wireless network in efficiently monitoring and predicting spatial phenomena, under data locational errors. The paper first discusses how errors of mobile sensor locations affect estimating and predicting the spatial physical processes, given that spatial field to be monitored is modeled by a Gaussian process. It then proposes an optimality criterion for designing optimal sampling paths for the mobile robotic sensors given the localization uncertainties. Although the optimization problem is optimally intractable, it can be resolved by a polynomial approximation algorithm, which is proved to be practically feasible in an energy-constrained mobile sensor network. More importantly, near-optimal solutions of this navigation problem are guaranteed by a lower bound within @math of the optimum. The performance of the proposed approach is evaluated on simulated and real-world data sets, where impact of sensor location errors on the results is demonstrated by comparing the results with those obtained by using noise-less data locations. Wireless sensor networks provide an attractive approach to spatially monitoring environments. Wireless technology makes these systems relatively flexible, but also places heavy demands on energy consumption for communications. This raises a fundamental trade-off: using higher densities of sensors provides more measurements, higher resolution and better accuracy, but requires more communications and processing. This paper proposes a new approach, called "back-casting," which can significantly reduce communications and energy consumption while maintaining high accuracy. Back-casting operates by first having a small subset of the wireless sensors communicate their information to a fusion center. This provides an initial estimate of the environment being sensed, and guides the allocation of additional network resources. Specifically, the fusion center backcasts information based on the initial estimate to the network at large, selectively activating additional sensor nodes in order to achieve a target error level. The key idea is that the initial estimate can detect correlations in the environment, indicating that many sensors may not need to be activated by the fusion center. Thus, adaptive sampling can save energy compared to dense, non-adaptive sampling. This method is theoretically analyzed in the context of field estimation and it is shown that the energy savings can be quite significant compared to conventional approaches. For example, when sensing a piecewise smooth field with an array of 100 spl times 100 sensors, adaptive sampling can reduce the energy consumption by roughly a factor of 10 while providing the same accuracy achievable if all sensors were activated. In this work, we present a method for the selection of a subset of nodes in a wireless sensor network whose application is to reconstruct the image of a (spatially) bandlimited physical value (e.g., temperature). The selection method creates a sampling pattern based on blue noise masking and guarantees a near minimal number of activated sensors for a given signal-to-noise ratio. The selection method is further enhanced to guarantee that the sensor nodes with the least residual energy are the primary candidates for deselection, while enabling a tradeoff between sensor selection optimality and balanced load distribution. Simulation results show the effectiveness of these selection methods in improving signal-to-noise ratio and reducing the necessary number of active sensors compared with simpler selection approaches. A critical aspect of applications with wireless sensor networks is network lifetime. Power-constrained wireless sensor networks are usable as long as they can communicate sensed data to a processing node. Sensing and communications consume energy, therefore judicious power management and sensor scheduling can effectively extend network lifetime. To cover a set of targets with known locations when ground access in the remote area is prohibited, one solution is to deploy the sensors remotely, from an aircraft. The lack of precise sensor placement is compensated by a large sensor population deployed in the drop zone, that would improve the probability of target coverage. The data collected from the sensors is sent to a central node (e.g. cluster head) for processing. In this paper we propose un efficient method to extend the sensor network life time by organizing the sensors into a maximal number of set covers that are activated successively. Only the sensors from the current active set are responsible for monitoring all targets and for transmitting the collected data, while all other nodes are in a low-energy sleep mode. By allowing sensors to participate in multiple sets, our problem formulation increases the network lifetime compared with related work [M. ], that has the additional requirements of sensor sets being disjoint and operating equal time intervals. In this paper we model the solution as the maximum set covers problem and design two heuristics that efficiently compute the sets, using linear programming and a greedy approach. Simulation results are presented to verify our approaches. Abstract It is now well-known that one can reconstruct sparse or compressible signals accurately from a very limited number of measurements, possibly contaminated with noise. This technique known as “compressed sensing” or “compressive sampling” relies on properties of the sensing matrix such as the restricted isometry property . In this Note, we establish new results about the accuracy of the reconstruction from undersampled measurements which improve on earlier estimates, and have the advantage of being more elegant. To cite this article: E.J. Candes, C. R. Acad. Sci. Paris, Ser. I 346 (2008). Wireless sensor networks have attracted attention from a diverse set of researchers, due to the unique combination of distributed, resource and data processing constraints. However, until now, the lack of real sensor network deployments have resulted in ad-hoc assumptions on a wide range of issues including topology characteristics and data distribution. As deployments of sensor networks become more widespread [1, 2], many of these assumptions need to be revisited.This paper deals with the fundamental issue of spatio-temporal irregularity in sensor networks We make the case for the existence of such irregular spatio-temporal sampling, and show that it impacts many performance issues in sensor networks. For instance, data aggregation schemes provide inaccurate results, compression efficiency is dramatically reduced, data storage skews storage load among nodes and incurs significantly greater routing overhead. To mitigate the impact of irregularity, we outline a spectrum of solutions. For data aggregation and compression, we propose the use of spatial interpolation of data (first suggested by in [3] and temporal signal segmentation followed by alignment. To reduce the cost of data-centric storage and routing, we propose the use of virtualization, and boundary detection. A critical aspect of applications with wireless sensor networks is network lifetime. Battery-powered sensors are usable as long as they can communicate captured data to a processing node. Sensing and communications consume energy, therefore judicious power management and scheduling can effectively extend operational time. To monitor a set of targets with known locations when ground access in the monitored area is prohibited, one solution is to deploy the sensors remotely, from an aircraft. The loss of precise sensor placement would then be compensated by a large sensor population density in the drop zone, that would improve the probability of target coverage. The data collected from the sensors is sent to a central node for processing. In this paper we propose an efficient method to extend the sensor network operational time by organizing the sensors into a maximal number of disjoint set covers that are activated successively. Only the sensors from the current active set are responsible for monitoring all targets and for transmitting the collected data, while nodes from all other sets are in a low-energy sleep mode. In this paper we address the maximum disjoint set covers problem and we design a heuristic that computes the sets. Theoretical analysis and performance evaluation results are presented to verify our approach. In passive monitoring using sensor networks, low energy supplies drastically constrain sensors in terms of calculation and communication abilities. Designing processing algorithms at the sensor level that take into account these constraints is an important problem in this context. Here we study the estimation of correlation functions between sensors using compressed acquisition and one-bit-quantization. The estimation is achieved directly using compressed samples, without considering any reconstruction of the signals. We show that if the signals of interest are far from white noise, estimation of the correlation using @math compressed samples out of @math can be more advantageous than estimation of the correlation using @math consecutive samples. The analysis consists of studying the asymptotic performance of the estimators at a fixed compression rate. We provide the analysis when the compression is realized by a random projection matrix composed of independent and identically distributed entries. The framework includes widely used random projection matrices, such as Gaussian and Bernoulli matrices, and it also includes very sparse matrices. However, it does not include subsampling without replacement, for which a separate analysis is provided. When considering one-bit-quantization as well, the theoretical analysis is not tractable. However, empirical evidence allows the conclusion that in practical situations, compressed and quantized estimators behave sufficiently correctly to be useful in, for example, time-delay estimation and model estimation. With the advent of the Internet of Things (IoT), an increasing number of energy harvesting methods are being used to supplement or supplant battery based sensors. Energy harvesting sensors need to be configured according to the application, hardware, and environmental conditions to maximize their usefulness. As of today, the configuration of sensors is either manual or heuristics based, requiring valuable domain expertise. Reinforcement learning (RL) is a promising approach to automate configuration and efficiently scale IoT deployments, but it is not yet adopted in practice. We propose solutions to bridge this gap: reduce the training phase of RL so that nodes are operational within a short time after deployment and reduce the computational requirements to scale to large deployments. We focus on configuration of the sampling rate of indoor solar panel based energy harvesting sensors. We created a simulator based on 3 months of data collected from 5 sensor nodes subject to different lighting conditions. Our simulation results show that RL can effectively learn energy availability patterns and configure the sampling rate of the sensor nodes to maximize the sensing data while ensuring that energy storage is not depleted. The nodes can be operational within the first day by using our methods. We show that it is possible to reduce the number of RL policies by using a single policy for nodes that share similar lighting conditions.