Near-Optimal Sensor Placement for Linear Inverse Problems

Ranieri, Juri; Chebira, Amina; Vetterli, Martin

doi:10.1109/tsp.2014.2299518

Cited by 200 publications

(218 citation statements)

References 35 publications

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“…Using the above notations, we can write the discrete-domain version of (1) as (2) We need to design how to choose the minimum number of sampling locations out of initial ones such that a desired estimation performance of the inverse problem (2) can be guaranteed. This problem is referred to as sensor selection.…”

Section: A Sensor Selectionmentioning

confidence: 99%

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Continuous Sensor Placement

Chepuri

Leus

2015

IEEE Signal Process. Lett.

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Abstract-Existing solutions to the sensor placement problem are based on sensor selection, in which the best subset of available sampling locations is chosen such that a desired estimation accuracy is achieved. However, the achievable estimation accuracy of sensor placement via sensor selection is limited to the initial set of sampling locations, which are typically obtained by gridding the continuous sampling domain. To circumvent this issue, we propose a framework of continuous sensor placement. A continuous variable is augmented to the grid-based model, which allows for off-the-grid sensor placement. The proposed offline design problem can be solved using readily available convex optimization solvers.Index Terms-Convex optimization, joint sparsity, sensor placement, sensor selection, sparse sensing, sparsity. I. PROBLEM STATEMENT SENSOR networks are widely used in a variety of applications like environmental monitoring, security and safety, to list a few. Sensors are devices capable of sensing a certain physical phenomenon, processing data, and communicating information to a central unit. Sensors are geographically deployed, and the data acquired by such distributed sensors are often used to solve statistical inference problems like field (e.g., heat, sound) estimation, target localization, and so on.The number of sensors available are often limited due to various factors like availability of physical or data storage space, economical constraints, or due to energy-efficiency reasons. Such a restriction on the number of sensors naturally limits the estimation accuracy. Moreover, selecting different sampling locations for the sensors generally leads to different values of the mean-squared-error. In this article, we are interested in finding the best placement of the sensors such that a desired estimation accuracy is ensured and the number of sensors are as low as possible. In other words, the focus will be on designing a sparse sensing technique to capture only informative data, thereby reducing the costs associated with sensing, data storage, and communication overheads.Let denote the observation signal with a continuousdomain argument, where without loss of generality (w.l.o.g.) denotes the sampling domain. We will restrict ourselves to the one-dimensional spatial domain, but the ideas presented can be applied directly to higher dimensions and even to temporal or spatio-temporal domains 1 . Assume that represents the measured physical field over a continuous one-dimensional space , and it satisfies the linear model (1) where collects the parameters to be estimated, is the known linear model representing the mapping between the parameters and the measurements, and is the noise. For example, in field estimation, might contain the source location and its field intensity. Furthermore, we assume for and . In other words, is completely described by its variation in the interval where we can place the sensors.The fundamental question of interest is-where to place the sensors such that the estimation error is as lo...

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Section: A Sensor Selectionmentioning

confidence: 99%

“…The problem of choosing the best subset of sampling locations (or sensors) out of given locations is combinatorial in nature. To simplify this problem, solutions based on greedy methods [1], [2] and convex optimization [4], [5], [7]- [9] are proposed. Sensor selection can be formulated as the design of a Boolean selection vector.…”

Section: A Sensor Selectionmentioning

confidence: 99%

Continuous Sensor Placement

Chepuri

Leus

2015

IEEE Signal Process. Lett.

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“…One such computationally less intensive implementation of the relaxed sensor selection problem is based on the projected subgradient algorithm [13]. Alternative approaches to convex optimization based sensor selection exploit the submodularity of the objective function using proxies for the MSE, like the mutual information [19] or the frame potential [7]. The submodularity of the objective function helps in developing low-complexity greedy algorithms, which sequentially adds sensors that maximize the increase in the cost.…”

Section: A Sensor Selection For Estimationmentioning

confidence: 99%

“…Sensor deployment can also be interpreted as a sensor selection problem in which the best subset of the available sensor locations are selected subject to a performance constraint. Sensor selection has been applied to a wide variety of problems: dynamical systems [1]- [5], network monitoring [6], field estimation [7], array optimization [8], sourceinformative sensor identification [9], anchor placement [10], and outlier detection [11].…”

Section: Introductionmentioning

confidence: 99%

Sensor selection for estimation, filtering, and detection

Chepuri

Leus

2014

2014 International Conference on Signal Processing and Communications (SPCOM)

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Abstract-Sensor selection is a crucial aspect in sensor network design. Due to the limitations on the hardware costs, availability of storage or physical space, and to minimize the processing and communication burden, the limited number of available sensors has to be smartly deployed. The node deployment should be such that a certain performance is ensured. Optimizing the sensors' spatial constellation or their temporal sampling patterns can be casted as a sensor selection problem. Sensor selection is essentially a combinatorial problem involving a performance evaluation over all possible choices, and it is intractable even for problems of modest scale. Nevertheless, using convex relaxation techniques, the sensor selection problem can be solved efficiently. In this paper, we present a brief overview and recent advances on the sensor selection problem from a statistical signal processing perspective. In particular, we focus on some of the important statistical inference problems like estimation, tracking, and detection.

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“…However, there are two aspects that are often neglected and may significantly impact the performance of the system: the optimization of the sensors' locations, to improve the reconstruction of the physical field from the measurements, and of the sources' locations, to improve the control of the physical field itself. While the first problem has recently received some attention [1][2][3][4], the second one is rarely discussed in the literature. …”

Section: Introductionmentioning

confidence: 99%

Near-optimal source placement for linear physical fields

Ranieri

Vetterli

2014

2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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In real-word applications, signal processing is often used to measure and control a physical field by means of sensors and sources, respectively. An aspect that has been often neglected is the optimization of the sources' locations. In this work, we discuss the source placement problem as the dual of the sensor placement problem and propose two polynomial-time algorithms, for scenarios with or without noise. Both algorithms are near-optimal and indicate the possibility to make the control of such physical fields easier, more efficient and more stable to noise.

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Near-Optimal Sensor Placement for Linear Inverse Problems

Cited by 200 publications

References 35 publications

Continuous Sensor Placement

Continuous Sensor Placement

Sensor selection for estimation, filtering, and detection

Near-optimal source placement for linear physical fields

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